binary.com Interview Question I - Comparison of Univariate GARCH Models

1 Introduction

There are quite some papers study on the GARCH models.

• EGARCH, GKR-GARCH, TGARCH, AVGARCH, NGARCH, IGARCH and APARCH Models for Pathogens at Marine Recreational Sites
• Predictive Accuracy of GARCH, GJR and EGARCH Models Select Exchange Rates Application

From previous papers, I tried to apply couple models for FOREX price forecasting and eventually got to know Fractional Intergrated GJR-GARCH is the best fit model as we can refer to GARCH模型中的ARMA(p,d,q)参数最优化¹. Due to I simulate whole dataset to get the result in menmtioned paper is time consuming, I tried to apply dccroll() to know the mse by resampling but not only based on single AIC². I parse my mv_fx() function³ and tested the Binary-Q1 - Multivariate GARCH Models and some additive parameters might probably need to be adjusted in the arguments of the function. Arma Part Overfitting in Arma Garch Model fitting via fGarch Package is a similar study for models comparison in GARCH.

I try to use 3 methods to compare the GARCH models.

• The default setting is forecast.length = 500, refit.every = 25, refit.window = 'recursive': refit couple times in order to make sure the stability of the prediction model.
• Set n.start = ns, forecast.length = nrow(x) - ns, refit.every = 1, refit.window = 'moving': refit once only with moving to know the prediction accuracy of the Markov model.
• Similar with Markov model above, but just seperates to ugarchfit() and ugarchforecast() and save every single observation. It will be easy to find the origin of error and rerun that particular data prediction.

Besides using the ugarchroll(), all models in this paper are Fractional Intergrated model which optimised the arfima q and also adjusted arma order p and q. AMATH546 - ECON589 HW3 also teach the use of ugarchroll().

## --- eval=FALSE, not run but display chunk ---
mv_fx <- function(...) {
  ...
  mod = dccroll(dccSpec, data = mbase, solver = .solver, 
                    forecast.length = 50, cluster = cl)
  cat('step 1/1 dccroll done!\n')
  ...
}

cl = makePSOCKcluster(ncol(mbase))

## Workable
test_roll <- dccroll(dccspec(
            multispec(c(ugarchspec(), ugarchspec(), ugarchspec(), 
                        ugarchspec(), ugarchspec(), ugarchspec(), 
                        ugarchspec())), distribution = 'mvt'), 
            data = mbase, cluster = cl)

## Not workable
test_roll2 <- dccroll(dccspec(
            multispec(c(
              uspec1 = ugarchspec(variance.model = list(model = 'gjrGARCH')), 
                uspec2 = ugarchspec(variance.model = list(model = 'gjrGARCH')), 
                uspec3 = ugarchspec(variance.model = list(model = 'gjrGARCH')), 
                uspec4 = ugarchspec(variance.model = list(model = 'gjrGARCH')), 
                uspec5 = ugarchspec(variance.model = list(model = 'gjrGARCH')), 
                uspec6 = ugarchspec(variance.model = list(model = 'gjrGARCH')), 
                uspec7 = ugarchspec(variance.model = list(model = 'gjrGARCH'))
                ))), data = mbase, cluster = cl)
#Error in checkForRemoteErrors(val) : 
#  one node produced an error: infinite or missing values in 'x'

## Workable
test_roll3 <- dccroll(dccspec(
            multispec(c(
              uspec1 = ugarchspec(
                variance.model = list(model = 'eGARCH'), 
                distribution.model = 'snorm'), 
                uspec2 = ugarchspec(
                  variance.model = list(model = 'eGARCH'), 
                  distribution.model = 'snorm'), 
                uspec3 = ugarchspec(
                  variance.model = list(model = 'eGARCH'), 
                  distribution.model = 'snorm'), 
                uspec4 = ugarchspec(
                  variance.model = list(model = 'eGARCH'), 
                  distribution.model = 'snorm'), 
                uspec5 = ugarchspec(
                  variance.model = list(model = 'eGARCH'), 
                  distribution.model = 'snorm'), 
                uspec6 = ugarchspec(
                  variance.model = list(model = 'eGARCH'), 
                  distribution.model = 'snorm'), 
                uspec7 = ugarchspec(
                  variance.model = list(model = 'eGARCH'), 
                  distribution.model = 'snorm')
                )), distribution = 'mvt'), data = mbase, cluster = cl)

## Not workable
test_roll4 <- dccroll(dccspec(
            multispec(c(
              uspec1 = ugarchspec(
                variance.model = list(model = 'gjrGARCH'), 
                distribution.model = 'snorm'), 
              uspec2 = ugarchspec(
                variance.model = list(model = 'gjrGARCH'), 
                distribution.model = 'snorm'), 
                uspec3 = ugarchspec(
                  variance.model = list(model = 'gjrGARCH'), 
                  distribution.model = 'snorm'), 
                uspec4 = ugarchspec(
                  variance.model = list(model = 'gjrGARCH'), 
                  distribution.model = 'snorm'), 
                uspec5 = ugarchspec(
                  variance.model = list(model = 'gjrGARCH'), 
                  distribution.model = 'snorm'), 
                uspec6 = ugarchspec(
                  variance.model = list(model = 'gjrGARCH'), 
                  distribution.model = 'snorm'), 
                uspec7 = ugarchspec(
                  variance.model = list(model = 'gjrGARCH'), 
                  distribution.model = 'snorm')
                )), distribution = 'mvt'), data = mbase, cluster = cl)
#Error in checkForRemoteErrors(val) : 
#  one node produced an error: infinite or missing values in 'x'

Binary-Q1⁴ compares all possible GARCH models in rugarch package while the result is in ROI (Return on Investment), due to the paper Binary-Q1 - Tick-Data-HiLo For Daily Trading (Blooper) found that the betting strategy is not workable in real-life. Therefore I try to compare again the GARCH models as well as suite for multivariate GARCH models.

Due to the multivartiate models will not coped with every univariate models. Here I tried to compare the accuracy of forecasting by univariate GARCH models and later will compare with the multivariate models.

2 Data

2.1 Read Data

Similar with GARCH模型中的ARMA(p,d,q)参数最优化, I use the dataset from Binary-Q1 (Extention)⁵ to ease the study.

cr_code <- c('AUDUSD=X', 'EURUSD=X', 'GBPUSD=X', 'CHF=X', 'CAD=X', 
             'CNY=X', 'JPY=X')

#'@ names(cr_code) <- c('AUDUSD', 'EURUSD', 'GBPUSD', 'USDCHF', 'USDCAD', 
#'@                     'USDCNY', 'USDJPY')

names(cr_code) <- c('USDAUD', 'USDEUR', 'USDGBP', 'USDCHF', 'USDCAD', 'USDCNY', 'USDJPY')

## Read presaved Yahoo data.
mbase <- sapply(names(cr_code), function(x) readRDS(paste0('./data/', x, '.rds')) %>% na.omit)

price_type <- c('Op', 'Hi', 'Lo', 'Cl')

gmds <- c('sGARCH', 'fGARCH.GARCH', 'fGARCH.TGARCH', 'fGARCH.AVGARCH', 'fGARCH.NGARCH', 'fGARCH.NAGARCH', 'fGARCH.APARCH', 'fGARCH.GJRGARCH', 'fGARCH.ALLGARCH', 'eGARCH', 'gjrGARCH', 'apARCH', 'iGARCH', 'csGARCH')

timeID <- llply(mbase, function(x) as.character(index(x))) %>% 
  unlist %>% unique %>% as.Date %>% sort
timeID <- c(timeID, xts::last(timeID) + days(1)) #the last date + 1 in order to predict the next day of last date to make whole dataset completed.
timeID0 <- ymd('2013-01-01')
timeID <- timeID[timeID >= timeID0]

.cl = FALSE

3 Testing Prediction Result

All my previous papers applied Markov theory which is \(p(x_{n}|x_{n-1}...x_{1})\), here I try to test if the model provides same result. Here I iteration 100 times.

## ================ eval=FALSE ====================
## sample data.
x <- mbase[['USDJPY']] %>% Cl

armaOrder = opt_arma(x)
spec = ugarchspec(
    variance.model = list(
        model = 'sGARCH', garchOrder = c(1, 1), 
        submodel = NULL, external.regressors = NULL, 
        variance.targeting = FALSE), 
    mean.model = list(
        armaOrder = armaOrder[c(1, 3)], 
        include.mean = TRUE, archm = FALSE, 
        archpow = 1, arfima = TRUE, 
        external.regressors = NULL, 
        archex = FALSE), 
    fixed.pars = list(arfima = armaOrder[2]), 
    distribution.model = 'snorm')

fit <- ugarchfit(spec, x, solver = 'hybrid')

## Execute 1 times.
fc1 = ugarchforecast(fit, n.ahead = 1)

## Execute 100 times to know if the coffecient value is applied ML method.
fc2 = replicate(100, ugarchforecast(fit, n.ahead = 1))

## retrieve the series and sigma values.
fc1 <- cbind(attributes(fc1)$`forecast`$seriesFor, attributes(fc1)$`forecast`$sigmaFor)

fc2 <- llply(fc2, function(x) cbind(attributes(x)$`forecast`$seriesFor, attributes(x)$`forecast`$sigmaFor)) %>% do.call('rbind', .)
fc2 %<>% unique

#> rbind(fc1, fc2)
#    2017-08-30 2017-08-30
#T+1   110.4566  0.6523954
#T+1   110.4566  0.6523954

#> fc1 == fc2
#    2017-08-30 2017-08-30
#T+1       TRUE       TRUE

rm(x)

From above test, we know that the prediction price is exactly same upon testing 100 times.

4 GARCH Models

4.1 sGARCH

4.1.1 Method 1 : Resampling

Below is the backtest simulation. The default setting is forecast.length = 500, refit.every = 25, refit.window = 'recursive' which only apply Monte Carlo method to resampling the model.

if (!file.exists('data/fx/mse.sGARCH.rds')) {
  mse.sGARCH <- ldply(mbase, function(x) {
    x <- Cl(x)
    if (.cl == TRUE) {
      .cl <- makePSOCKcluster(ncol(x))
    } else {
      .cl <- NULL
    }
    armaOrder = opt_arma(x)
    
    spec = ugarchspec(
      variance.model = list(
        model = 'sGARCH', garchOrder = c(1, 1), 
        submodel = NULL, external.regressors = NULL, 
        variance.targeting = FALSE), 
    mean.model = list(
        armaOrder = armaOrder[c(1, 3)], 
        include.mean = TRUE, archm = FALSE, 
        archpow = 1, arfima = TRUE, 
        external.regressors = NULL, 
        archex = FALSE), 
    fixed.pars = list(arfima = armaOrder[2]), 
    distribution.model = 'snorm')
    
    roll <- ugarchroll(spec, data = x, refit.window = 'recursive', 
                       cluster = .cl)
    res <- attributes(roll)$forecast$density
    
    if (!is.null(res)) {
      res %>% tbl_df %>% mutate(MSE = mean((Mu - Realized)^2)) %>% 
      .$MSE %>% unique
    } else {
      res <- NULL
    }
    return(res)
  }) %>% tbl_df
  #'@ names(mse.sGARCH)[2] <- 'MSE'
  mse.sGARCH %<>% ddply(.(.id), summarise, MSE = mean((Mu - Realized)^2))
  saveRDS(mse.sGARCH, 'data/fx/mse.sGARCH.rds')
  
} else {
  mse.sGARCH <- readRDS('data/fx/mse.sGARCH.rds')
}

mse.sGARCH %>% 
  rbind(., data.frame(.id = 'Mean', MSE = colMeans(.[2]))) %>% 
  kable(caption = 'MSE for Univariate sGARCH') %>% 
  kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive'))

MSE for Univariate sGARCH

	.id	MSE
1	USDAUD	0.0000717
2	USDEUR	0.0000232
3	USDGBP	0.0000277
4	USDCHF	0.0000267
5	USDCAD	0.0000466
6	USDCNY	0.0002822
7	USDJPY	0.5196658
MSE	Mean	0.0743063

Table 3.1.1A : MSE of basket currencies.

4.1.2 Method 2 : Markov Chain

By refer to below article, I use ugarchroll() which is a wrapper for ugarchfit() and ugarchforecast() which will made the thing use :

• estimation difference between ugarchroll and ugarchfit
• Window size in ugarchroll of rugarch package?

There has a concern to use it which is once there has an error during the course of simulation will cause whole data gone.⁶ All my previous preditive result based on the Markov Chain theory⁷ with statistical modelling and prediction model and saved every single predictive result.

Below is the simulation . n.start = ns is the start point of simulation which is ymd('2013-01-01'), forecast.length = nrow(x) - ns is the length of forecast equal to the length from the n.start until the end of the dataset, refit.every = 1 means re-estimate the fit value once only where refit.window = 'moving' where today’s dataset only can predict 1 trading day in advance.

## --- eval=FALSE ---- Due to errors.
if (!file.exists('data/fx/mse.sGARCH2.rds')) {
  mse.sGARCH2 <- ldply(mbase, function(x) {
    x <- Cl(x)
    if (.cl == TRUE) {
      .cl <- makePSOCKcluster(ncol(x))
    } else {
      .cl <- NULL
    }
    armaOrder = opt_arma(x)
    
    spec = ugarchspec(
      variance.model = list(
        model = 'sGARCH', garchOrder = c(1, 1), 
        submodel = NULL, external.regressors = NULL, 
        variance.targeting = FALSE), 
    mean.model = list(
        armaOrder = armaOrder[c(1, 3)], 
        include.mean = TRUE, archm = FALSE, 
        archpow = 1, arfima = TRUE, 
        external.regressors = NULL, 
        archex = FALSE), 
    fixed.pars = list(arfima = armaOrder[2]), 
    distribution.model = 'snorm')
    
    ns <- which(index(x) == timeID0)
    n <- nrow(x) - ns

    roll <- ugarchroll(spec, data = x, n.start = ns, forecast.length = n, 
                       refit.every = 1, refit.window = 'moving', 
                       cluster = .cl)
    res <- attributes(roll)$forecast$density
    
    if (!is.null(res)) {
      res %>% tbl_df %>% mutate(MSE = mean((Mu - Realized)^2)) %>% 
      .$MSE %>% unique
    } else {
      res <- NULL
    }
    return(res)
  }) %>% tbl_df
  mse.sGARCH2 %<>% ddply(.(.id), summarise, MSE = mean((Mu - Realized)^2))
  saveRDS(mse.sGARCH2, 'data/fx/mse.sGARCH2.rds')
  
} else {
  mse.sGARCH2 <- readRDS('data/fx/mse.sGARCH2.rds')
}

if (!is.null(mse.sGARCH2)) {
  mse.sGARCH2 %>% 
    rbind(., data.frame(.id = 'Mean', MSE = colMeans(.[2]))) %>% 
    kable(caption = 'MSE for Univariate sGARCH') %>% 
    kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive'))
}

MSE for Univariate sGARCH

	.id	MSE
1	USDAUD	6.250000e-05
2	USDCAD	4.524806e+131
3	USDCHF	5.310000e-05
4	USDCNY	1.839000e-04
5	USDEUR	2.330000e-05
6	USDGBP	1.660000e-05
7	USDJPY	4.885790e-01
MSE	Mean	6.464009e+130

Table 3.1.1B : MSE of basket currencies.

4.1.3 Method 3 : Markov Chain 2

Due to I am not statisfy and doubted onto the AIC result based on model comparison by using basic model above. Below I compared the Fractional Intergrated model which optimised the arfima q and also adjusted arma order p and q to proof if my previous study⁸ in Binary.com Interview Q1 is correct.

Binary.com Interview Q1 - Tick-Data-HiLo For Daily Trading (Blooper) directly use the mentioned gjrGARCH model but add another criteria which is the timing of daily High-Low price based on highest bid and lowest ask price within a day.

## ------------- Simulate uv_fx() ----------------------
## uv_fx just made the model and some argument flexible.
sGARCH <- list()

for (dt in timeID) {
  
  for (i in seq(cr_code)) {
    
    smp <- mbase[[names(cr_code)[i]]]
    timeID2 <- c(index(smp), xts::last(index(smp)) + days(1))
    
    if (dt %in% timeID2) {
      dtr <- xts::last(index(smp[index(smp) < dt]), 1) #tail(..., 1)
      smp <- smp[paste0(dtr %m-% years(1), '/', dtr)]
      
      sGARCH[[i]] <- tryCatch({ldply(price_type, function(y) {
        df = uv_fx(smp, .model = 'sGARCH', currency = cr_code[i], 
                   price = y, .cluster = .cl)
        df = data.frame(Date = index(df$latestPrice[1]), 
                        Type = paste0(names(df$latestPrice), '.', y), 
                        df$latestPrice, df$forecastPrice, t(df$AIC))
        names(df)[4] %<>% str_replace_all('1', 'T+1')
        df
      })}, error = function(e) NULL)
      
      if (!dir.exists(paste0('data/fx/', names(sGARCH[[i]])[3]))) 
        dir.create(paste0('data/fx/', names(sGARCH[[i]])[3]))
      
      saveRDS(sGARCH[[i]], paste0(
        'data/fx/', names(sGARCH[[i]])[3], '/sGARCH.', 
        unique(sGARCH[[i]]$Date), '.rds'))
    
      cat(paste0(
        'data/fx/', names(sGARCH[[i]])[3], '/sGARCH.', 
        unique(sGARCH[[i]]$Date), '.rds saved!\n'))
    }
    }; rm(i)
  }

4.2 fGARCH

4.2.1 GARCH

4.2.1.1 Method 1 : Resampling

The default setting is forecast.length = 500, refit.every = 25, refit.window = 'recursive'.

MSE for Univariate fGARCH-GARCH

	.id	MSE
1	USDAUD	0.0000717
2	USDEUR	0.0000232
3	USDGBP	0.0000277
4	USDCHF	0.0000267
5	USDCAD	0.0000469
6	USDCNY	0.0002822
7	USDJPY	NA
MSE	Mean	0.0000797

Table 3.2.1.1A : MSE of basket currencies.

4.2.1.2 Method 2 : Markov Chain

Set n.start = ns, forecast.length = nrow(x) - ns, refit.every = 1, refit.window = 'moving'.

MSE for Univariate fGARCH-GARCH

	.id	MSE
1	USDAUD	6.250000e-05
2	USDCAD	6.449515e+178
3	USDCHF	5.300000e-05
4	USDCNY	1.839000e-04
5	USDEUR	2.330000e-05
6	USDGBP	1.660000e-05
7	USDJPY	4.895937e-01
MSE	Mean	9.213592e+177

Table 3.2.1.1B : MSE of basket currencies.

4.2.1.3 Method 3 : Markov Chain 2

Below I compared the Fractional Intergrated model which optimised the arfima q and also adjusted arma order p and q.

4.2.2 TGARCH

4.2.2.1 Method 1 : Resampling

The default setting is forecast.length = 500, refit.every = 25, refit.window = 'recursive'.

MSE for Univariate fGARCH-TGARCH

	.id	MSE
1	USDAUD	0.0000719
2	USDCAD	0.0000470
3	USDCHF	0.0000249
4	USDEUR	0.0000232
5	USDGBP	0.0000277
6	USDJPY	0.5291517
MSE	Mean	0.0882244

Table 3.2.2.1A : MSE of basket currencies.

4.2.2.2 Method 2 : Markov Chain

Set n.start = ns, forecast.length = nrow(x) - ns, refit.every = 1, refit.window = 'moving'.

MSE for Univariate fGARCH-TGARCH

	.id	MSE
1	USDJPY	0.4901144
MSE	Mean	0.4901144

Table 3.2.2.1B : MSE of basket currencies.

4.2.2.3 Method 3 : Markov Chain 2

Below I compared the Fractional Intergrated model which optimised the arfima q and also adjusted arma order p and q.

4.2.3 AVGARCH

4.2.3.1 Method 1 : Resampling

The default setting is forecast.length = 500, refit.every = 25, refit.window = 'recursive'.

MSE for Univariate fGARCH-AVGARCH

	.id	MSE
1	USDAUD	0.0000718
2	USDCAD	0.0000473
3	USDCHF	0.0000259
4	USDEUR	0.0000233
5	USDGBP	0.0000277
6	USDJPY	0.5321997
MSE	Mean	0.0887326

Table 3.2.3.1A : MSE of basket currencies.

4.2.3.2 Method 2 : Markov Chain

Set n.start = ns, forecast.length = nrow(x) - ns, refit.every = 1, refit.window = 'moving'.

Table 3.2.3.1B : MSE of basket currencies.

4.2.3.3 Method 3 : Markov Chain 2

Below I compared the Fractional Intergrated model which optimised the arfima q and also adjusted arma order p and q.

4.2.4 NGARCH

4.2.4.1 Method 1 : Resampling

The default setting is forecast.length = 500, refit.every = 25, refit.window = 'recursive'.

MSE for Univariate fGARCH-NGARCH

	.id	MSE
1	USDAUD	0.0000719
2	USDCAD	0.0000469
3	USDCHF	0.0000250
4	USDCNY	0.0002831
5	USDEUR	0.0000232
6	USDGBP	0.0000277
7	USDJPY	0.5222741
MSE	Mean	0.0746788

Table 3.2.4.1A : MSE of basket currencies.

4.2.4.2 Method 2 : Markov Chain

Set n.start = ns, forecast.length = nrow(x) - ns, refit.every = 1, refit.window = 'moving'.

MSE for Univariate fGARCH-NGARCH

	.id	MSE
1	USDCHF	0.0000682
2	USDCNY	0.0001853
3	USDEUR	0.0000235
MSE	Mean	0.0000924

Table 3.2.4.1B : MSE of basket currencies.

4.2.4.3 Method 3 : Markov Chain 2

Below I compared the Fractional Intergrated model which optimised the arfima q and also adjusted arma order p and q.

4.2.5 NAGARCH

4.2.5.1 Method 1 : Resampling

The default setting is forecast.length = 500, refit.every = 25, refit.window = 'recursive'.

MSE for Univariate fGARCH-NAGARCH

	.id	MSE
1	USDAUD	0.0000717
2	USDCAD	0.0000469
3	USDCHF	0.0000237
4	USDCNY	0.0002824
5	USDEUR	0.0000232
6	USDGBP	0.0000277
MSE	Mean	0.0000792

Table 3.2.5.1A : MSE of basket currencies.

4.2.5.2 Method 2 : Markov Chain

Set n.start = ns, forecast.length = nrow(x) - ns, refit.every = 1, refit.window = 'moving'.

MSE for Univariate fGARCH-NAGARCH

	.id	MSE
1	USDCNY	0.0001836
MSE	Mean	0.0001836

Table 3.2.5.1B : MSE of basket currencies.

4.2.5.3 Method 3 : Markov Chain 2

Below I compared the Fractional Intergrated model which optimised the arfima q and also adjusted arma order p and q.

4.2.6 APARCH

4.2.6.1 Method 1 : Resampling

The default setting is forecast.length = 500, refit.every = 25, refit.window = 'recursive'.

MSE for Univariate fGARCH-APARCH

	.id	MSE
1	USDAUD	0.0000717
2	USDCHF	0.0000259
3	USDEUR	0.0000232
4	USDJPY	0.5236997
MSE	Mean	0.1309551

Table 3.2.6.1A : MSE of basket currencies.

4.2.6.2 Method 2 : Markov Chain

Set n.start = ns, forecast.length = nrow(x) - ns, refit.every = 1, refit.window = 'moving'.

Table 3.2.6.1B : MSE of basket currencies.

4.2.6.3 Method 3 : Markov Chain 2

Below I compared the Fractional Intergrated model which optimised the arfima q and also adjusted arma order p and q.

4.2.7 GJRGARCH

4.2.7.1 Method 1 : Resampling

The default setting is forecast.length = 500, refit.every = 25, refit.window = 'recursive'.

MSE for Univariate fGARCH-GJRGARCH

	.id	MSE
1	USDAUD	7.17e-05
2	USDCAD	4.68e-05
3	USDCHF	2.41e-05
4	USDCNY	2.82e-04
5	USDEUR	2.32e-05
6	USDGBP	2.77e-05
MSE	Mean	7.93e-05

Table 3.2.7.1A : MSE of basket currencies.

4.2.7.2 Method 2 : Markov Chain

Set n.start = ns, forecast.length = nrow(x) - ns, refit.every = 1, refit.window = 'moving'.

MSE for Univariate fGARCH-GJRGARCH

	.id	MSE
1	USDGBP	0.0000166
2	USDJPY	0.4880047
MSE	Mean	0.2440106

Table 3.2.7.1B : MSE of basket currencies.

4.2.7.3 Method 3 : Markov Chain 2

Below I compared the Fractional Intergrated model which optimised the arfima q and also adjusted arma order p and q.

4.2.8 ALLGARCH

4.2.8.1 Method 1 : Resampling

The default setting is forecast.length = 500, refit.every = 25, refit.window = 'recursive'.

MSE for Univariate fGARCH-ALLGARCH

	.id	MSE
1	USDAUD	0.0000717
2	USDEUR	0.0000232
3	USDGBP	0.0000277
4	USDCHF	0.0000236
5	USDCAD	0.0000470
6	USDCNY	0.0002821
7	USDJPY	0.5237676
MSE	Mean	0.0748918

Table 3.2.8.1A : MSE of basket currencies.

4.2.8.2 Method 2 : Markov Chain

Set n.start = ns, forecast.length = nrow(x) - ns, refit.every = 1, refit.window = 'moving'.

Table 3.2.8.1B : MSE of basket currencies.

4.2.8.3 Method 3 : Markov Chain 2

Below I compared the Fractional Intergrated model which optimised the arfima q and also adjusted arma order p and q.

4.3 eGARCH

4.3.1 Method 1 : Resampling

The default setting is forecast.length = 500, refit.every = 25, refit.window = 'recursive'.

MSE for Univariate eGARCH

	.id	MSE
1	USDAUD	0.0000717
2	USDCAD	0.0000469
3	USDCHF	0.0000236
4	USDCNY	0.0002793
5	USDEUR	0.0000232
6	USDGBP	0.0000277
7	USDJPY	0.5199591
MSE	Mean	0.0743473

Table 3.3.1A : MSE of basket currencies.

4.3.2 Method 2 : Markov Chain

Set n.start = ns, forecast.length = nrow(x) - ns, refit.every = 1, refit.window = 'moving'.

Table 3.3.1B : MSE of basket currencies.

4.3.3 Method 3 : Markov Chain 2

Below I compared the Fractional Intergrated model which optimised the arfima q and also adjusted arma order p and q.

4.4 gjrGARCH

4.4.1 Method 1 : Resampling

The default setting is forecast.length = 500, refit.every = 25, refit.window = 'recursive'.

MSE for Univariate gjrGARCH

	.id	MSE
1	USDAUD	0.0000717
2	USDCAD	0.0000470
3	USDCHF	0.0000242
4	USDCNY	0.0002820
5	USDEUR	0.0000232
6	USDGBP	0.0000277
7	USDJPY	0.5288255
MSE	Mean	0.0756145

Table 3.4.1A : MSE of basket currencies.

4.4.2 Method 2 : Markov Chain

Set n.start = ns, forecast.length = nrow(x) - ns, refit.every = 1, refit.window = 'moving'.

MSE for Univariate gjrGARCH

	.id	MSE
1	USDAUD	6.280000e-05
2	USDCAD	3.590000e-05
3	USDCHF	4.990000e-05
4	USDCNY	2.277193e+142
5	USDEUR	2.340000e-05
6	USDGBP	1.660000e-05
7	USDJPY	4.881093e-01
MSE	Mean	3.253132e+141

Table 3.4.1B : MSE of basket currencies.

4.4.3 Method 3 : Markov Chain 2

Below I compared the Fractional Intergrated model which optimised the arfima q and also adjusted arma order p and q.

Here I do not execute this model but directly read the previous dataset due to it is the model pred2 in GARCH模型中的ARMA(p,d,q)参数最优化.

4.5 apARCH

4.5.1 Method 1 : Resampling

The default setting is forecast.length = 500, refit.every = 25, refit.window = 'recursive'.

MSE for Univariate apARCH

	.id	MSE
1	USDAUD	0.0000718
2	USDCAD	0.0000472
3	USDCNY	0.0002826
4	USDEUR	0.0000294
5	USDGBP	0.0000277
6	USDJPY	0.5229902
MSE	Mean	0.0872415

Table 3.5.1A : MSE of basket currencies.

4.5.2 Method 2 : Markov Chain

Set n.start = ns, forecast.length = nrow(x) - ns, refit.every = 1, refit.window = 'moving'.

Table 3.5.1B : MSE of basket currencies.

4.5.3 Method 3 : Markov Chain 2

Below I compared the Fractional Intergrated model which optimised the arfima q and also adjusted arma order p and q.

4.6 iGARCH

4.6.1 Method 1 : Resampling

The default setting is forecast.length = 500, refit.every = 25, refit.window = 'recursive'.

MSE for Univariate iGARCH

	.id	MSE
1	USDAUD	0.0000717
2	USDCHF	0.0000259
3	USDCNY	0.0002845
4	USDEUR	0.0000232
5	USDGBP	0.0000277
6	USDJPY	0.5238451
MSE	Mean	0.0873797

Table 3.6.1A : MSE of basket currencies.

4.6.2 Method 2 : Markov Chain

Set n.start = ns, forecast.length = nrow(x) - ns, refit.every = 1, refit.window = 'moving'.

Table 3.6.1B : MSE of basket currencies.

4.6.3 Method 3 : Markov Chain 2

Below I compared the Fractional Intergrated model which optimised the arfima q and also adjusted arma order p and q.

4.7 csGARCH

4.7.1 Method 1 : Resampling

The default setting is forecast.length = 500, refit.every = 25, refit.window = 'recursive'.

MSE for Univariate csGARCH

	.id	MSE
1	USDAUD	0.0000717
2	USDCHF	0.0000259
3	USDCNY	0.0002817
4	USDEUR	0.0000232
5	USDGBP	0.0000277
6	USDJPY	0.5227716
MSE	Mean	0.0872003

Table 3.7.1A : MSE of basket currencies.

4.7.2 Method 2 : Markov Chain

Set n.start = ns, forecast.length = nrow(x) - ns, refit.every = 1, refit.window = 'moving'.

Table 3.7.1B : MSE of basket currencies.

4.7.3 Method 3 : Markov Chain 2

Below I compared the Fractional Intergrated model which optimised the arfima q and also adjusted arma order p and q.

5 1st Stage Model Comparison

5.1 MSE, AIC and BIC

Due to some unknown reasons, the NGARCH and NAGARCH always bias to confuse the model selection. Here I try to look for some supportive methods.

5.1.1 Calculate AIC for MSE

By refer to How to Choose a Forecast for Your Time Series, here I calculated the AIC of MSE to choose the best fitted model.

\[AIC = 2k - 2log(L)\]

where \(k\) is the number of parameter, log is the logarithm and L is the likelihood function.

\[MSE = \sum_{i=1}^{n}(x_{i}-\mu_{i})^2\]

\[AIC = 2k+nlog(MSE)\]

5.1.2 Using Bayes instead of AIC

Below picture shows the use of BIC for Markov model (as well as few parameters used in the model) while AIC for static model. For section Resampling Method, we can refer to AIC while section Markov Method and section Markov Method 2 we refer to BIC.

5.1.3 Calculate the MSE for AIC

In order to know the stability of AIC value, here I try to measure the mean squared error of AIC as well.

5.1.4 Filter the Bias Data

As states, due to some unknown reasons, there has some data bias more than 100 times which is totally wrong. Some prediction price became AIC value and somemore the currency became NULL values after calculation.

Here I also filter and count the number of bias to pick the best fit model.

5.2 Resampling Method

The default setting is forecast.length = 500, refit.every = 25, refit.window = 'recursive'. Below is the MSE summary for the models.

## remove all mse.*objects to save memory.
eval(parse(text = paste0('rm(\'', ls()[str_detect(ls(), 'mse.')],'\')')))

models <- llply(gmds, function(txt) {
    readRDS(paste0('data/fx/mse.', txt, '.rds')) %>% 
    data.frame(Cat = txt, .)
  })
names(models) <- gmds

models <- suppressAll(bind_rows(models)) %>% tbl_df %>% 
    mutate(Cat = factor(Cat), .id = factor(.id))

models %>% ddply(.(.id, Cat), summarise, MSE = mean(MSE, na.rm=TRUE)) %>% 
  kable(caption = 'Summary') %>% 
  kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive')) %>% 
  group_rows('USD/AUD', 1, 14, label_row_css = 'background-color: #003399; color: #fff;') %>%
  group_rows('USD/CAD', 15, 25, label_row_css = 'background-color: #003399; color: #fff;') %>%
  group_rows('USD/CHF', 26, 38, label_row_css = 'background-color: #003399; color: #fff;') %>%
  group_rows('USD/CNY', 39, 49, label_row_css = 'background-color: #003399; color: #fff;') %>%
  group_rows('USD/EUR', 50, 63, label_row_css = 'background-color: #003399; color: #fff;') %>%
  group_rows('USD/GBP', 64, 76, label_row_css = 'background-color: #003399; color: #fff;') %>%
  group_rows('USD/JPY', 77, 88, label_row_css = 'background-color: #003399; color: #fff;') %>% 
  scroll_box(width = '100%', height = '400px')

Summary

.id	Cat	MSE
USD/AUD
USDAUD	apARCH	0.0000718
USDAUD	csGARCH	0.0000717
USDAUD	eGARCH	0.0000717
USDAUD	fGARCH.ALLGARCH	0.0000717
USDAUD	fGARCH.APARCH	0.0000717
USDAUD	fGARCH.AVGARCH	0.0000718
USDAUD	fGARCH.GARCH	0.0000717
USDAUD	fGARCH.GJRGARCH	0.0000717
USDAUD	fGARCH.NAGARCH	0.0000717
USDAUD	fGARCH.NGARCH	0.0000719
USDAUD	fGARCH.TGARCH	0.0000719
USDAUD	gjrGARCH	0.0000717
USDAUD	iGARCH	0.0000717
USDAUD	sGARCH	0.0000717
USD/CAD
USDCAD	apARCH	0.0000472
USDCAD	eGARCH	0.0000469
USDCAD	fGARCH.ALLGARCH	0.0000470
USDCAD	fGARCH.AVGARCH	0.0000473
USDCAD	fGARCH.GARCH	0.0000469
USDCAD	fGARCH.GJRGARCH	0.0000468
USDCAD	fGARCH.NAGARCH	0.0000469
USDCAD	fGARCH.NGARCH	0.0000469
USDCAD	fGARCH.TGARCH	0.0000470
USDCAD	gjrGARCH	0.0000470
USDCAD	sGARCH	0.0000466
USD/CHF
USDCHF	csGARCH	0.0000259
USDCHF	eGARCH	0.0000236
USDCHF	fGARCH.ALLGARCH	0.0000236
USDCHF	fGARCH.APARCH	0.0000259
USDCHF	fGARCH.AVGARCH	0.0000259
USDCHF	fGARCH.GARCH	0.0000267
USDCHF	fGARCH.GJRGARCH	0.0000241
USDCHF	fGARCH.NAGARCH	0.0000237
USDCHF	fGARCH.NGARCH	0.0000250
USDCHF	fGARCH.TGARCH	0.0000249
USDCHF	gjrGARCH	0.0000242
USDCHF	iGARCH	0.0000259
USDCHF	sGARCH	0.0000267
USD/CNY
USDCNY	apARCH	0.0002826
USDCNY	csGARCH	0.0002817
USDCNY	eGARCH	0.0002793
USDCNY	fGARCH.ALLGARCH	0.0002821
USDCNY	fGARCH.GARCH	0.0002822
USDCNY	fGARCH.GJRGARCH	0.0002820
USDCNY	fGARCH.NAGARCH	0.0002824
USDCNY	fGARCH.NGARCH	0.0002831
USDCNY	gjrGARCH	0.0002820
USDCNY	iGARCH	0.0002845
USDCNY	sGARCH	0.0002822
USD/EUR
USDEUR	apARCH	0.0000294
USDEUR	csGARCH	0.0000232
USDEUR	eGARCH	0.0000232
USDEUR	fGARCH.ALLGARCH	0.0000232
USDEUR	fGARCH.APARCH	0.0000232
USDEUR	fGARCH.AVGARCH	0.0000233
USDEUR	fGARCH.GARCH	0.0000232
USDEUR	fGARCH.GJRGARCH	0.0000232
USDEUR	fGARCH.NAGARCH	0.0000232
USDEUR	fGARCH.NGARCH	0.0000232
USDEUR	fGARCH.TGARCH	0.0000232
USDEUR	gjrGARCH	0.0000232
USDEUR	iGARCH	0.0000232
USDEUR	sGARCH	0.0000232
USD/GBP
USDGBP	apARCH	0.0000277
USDGBP	csGARCH	0.0000277
USDGBP	eGARCH	0.0000277
USDGBP	fGARCH.ALLGARCH	0.0000277
USDGBP	fGARCH.AVGARCH	0.0000277
USDGBP	fGARCH.GARCH	0.0000277
USDGBP	fGARCH.GJRGARCH	0.0000277
USDGBP	fGARCH.NAGARCH	0.0000277
USDGBP	fGARCH.NGARCH	0.0000277
USDGBP	fGARCH.TGARCH	0.0000277
USDGBP	gjrGARCH	0.0000277
USDGBP	iGARCH	0.0000277
USDGBP	sGARCH	0.0000277
USD/JPY
USDJPY	apARCH	0.5229902
USDJPY	csGARCH	0.5227716
USDJPY	eGARCH	0.5199591
USDJPY	fGARCH.ALLGARCH	0.5237676
USDJPY	fGARCH.APARCH	0.5236997
USDJPY	fGARCH.AVGARCH	0.5321997
USDJPY	fGARCH.GARCH	NaN
USDJPY	fGARCH.NGARCH	0.5222741
USDJPY	fGARCH.TGARCH	0.5291517
USDJPY	gjrGARCH	0.5288255
USDJPY	iGARCH	0.5238451
USDJPY	sGARCH	0.5196658

Due to some models unable produced a result, here I only filter and display the models with 7 currencies as below.

#'@ dplyr::count(models, Cat) %>% dplyr::filter(n == 7)
cats <- dplyr::count(models, Cat) %>% dplyr::filter(n == 7) %>% .[1] %>% unlist %>% factor

models %>% ddply(.(Cat), summarise, MSE = mean(MSE, na.rm=TRUE)) %>% 
    dplyr::filter(Cat %in% cats) %>% 
  kable(caption = 'Summary') %>% 
  kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive'))

Summary

Cat	MSE
eGARCH	0.0743473
fGARCH.ALLGARCH	0.0748918
fGARCH.GARCH	0.0000797
fGARCH.NGARCH	0.0746788
gjrGARCH	0.0756145
sGARCH	0.0743063

Now I plot a table with rank where shows all possible models.

MSE Comparison

GARCH models

5.3 Markov Method

Set n.start = ns, forecast.length = nrow(x) - ns, refit.every = 1, refit.window = 'moving'.

Summary

.id	Cat	MSE
USDAUD	fGARCH.GARCH	6.250000e-05
USDAUD	gjrGARCH	6.280000e-05
USDAUD	sGARCH	6.250000e-05
USDCAD	fGARCH.GARCH	6.449515e+178
USDCAD	gjrGARCH	3.590000e-05
USDCAD	sGARCH	4.524806e+131
USDCHF	fGARCH.GARCH	5.300000e-05
USDCHF	fGARCH.NGARCH	6.820000e-05
USDCHF	gjrGARCH	4.990000e-05
USDCHF	sGARCH	5.310000e-05
USDCNY	fGARCH.GARCH	1.839000e-04
USDCNY	fGARCH.NAGARCH	1.836000e-04
USDCNY	fGARCH.NGARCH	1.853000e-04
USDCNY	gjrGARCH	2.277193e+142
USDCNY	sGARCH	1.839000e-04
USDEUR	fGARCH.GARCH	2.330000e-05
USDEUR	fGARCH.NGARCH	2.350000e-05
USDEUR	gjrGARCH	2.340000e-05
USDEUR	sGARCH	2.330000e-05
USDGBP	fGARCH.GARCH	1.660000e-05
USDGBP	fGARCH.GJRGARCH	1.660000e-05
USDGBP	gjrGARCH	1.660000e-05
USDGBP	sGARCH	1.660000e-05
USDJPY	fGARCH.GARCH	4.895937e-01
USDJPY	fGARCH.GJRGARCH	4.880047e-01
USDJPY	fGARCH.TGARCH	4.901144e-01
USDJPY	gjrGARCH	4.881093e-01
USDJPY	sGARCH	4.885790e-01

Due to some models unable produced a result, here I only filter and display the models with 7 currencies as below.

Summary

Cat	MSE
fGARCH.GARCH	9.213592e+177
gjrGARCH	3.253132e+141
sGARCH	6.464009e+130

Now I plot a table with rank where shows all possible models.

MSE Comparison

GARCH models

5.4 Markov Method 2

Now, we look at the mse where I use ugarchfit() and ugarchforecast, actually it is same with above Markov Method but just seperate all prediction result as single file where we able to filter the error to find the most accurate model (as well as know he frequence of bias and precise among the models.).

5.4.1 Data Progress

Below check the progress of the saved files. From below tables we can know how many day from date to date - calculated. x indicate the number of days and n indicates the total number of trading days for that particular currency. One x contain OHLC 4 prices.

## check how many data saved in progress.
l_ply(gmds, function(x) {
  x2 <- ifelse(x == 'gjrGARCH', 'pred2', x)
  task_progress(.pattern = paste0('^', x2, '.'), .loops = FALSE)
  })

## Current Tokyo Time : 2018-08-27 16:52:39 
## ^sGARCH. 
## 
##      .id    x    n progress
## 1 USDAUD 1215 1215  100.00%
## 2 USDEUR 1215 1215  100.00%
## 3 USDGBP 1216 1216  100.00%
## 4 USDCHF 1214 1215   99.92%
## 5 USDCAD 1214 1214  100.00%
## 6 USDCNY 1214 1215   99.92%
## 7 USDJPY 1215 1215  100.00%
## 
## ================ 99.98% ================
## 
## Current Tokyo Time : 2018-08-27 16:52:41 
## ^fGARCH.GARCH. 
## 
##      .id    x    n progress
## 1 USDAUD 1214 1215   99.92%
## 2 USDEUR 1214 1215   99.92%
## 3 USDGBP 1215 1216   99.92%
## 4 USDCHF 1215 1215  100.00%
## 5 USDCAD 1214 1214  100.00%
## 6 USDCNY 1214 1215   99.92%
## 7 USDJPY 1215 1215  100.00%
## 
## ================ 99.95% ================
## 
## Current Tokyo Time : 2018-08-27 16:52:42 
## ^fGARCH.TGARCH. 
## 
##      .id    x    n progress
## 1 USDAUD 1203 1215   99.01%
## 2 USDEUR 1137 1215   93.58%
## 3 USDGBP 1200 1216   98.68%
## 4 USDCHF 1176 1215   96.79%
## 5 USDCAD 1181 1214   97.28%
## 6 USDCNY 1195 1215   98.35%
## 7 USDJPY 1213 1215   99.84%
## 
## ================ 97.65% ================
## 
## Current Tokyo Time : 2018-08-27 16:52:43 
## ^fGARCH.AVGARCH. 
## 
##      .id  x    n progress
## 1 USDAUD 78 1215    6.42%
## 2 USDEUR 45 1215    3.70%
## 3 USDGBP 56 1216    4.61%
## 4 USDCHF 19 1215    1.56%
## 5 USDCAD 62 1214    5.11%
## 6 USDCNY 13 1215    1.07%
## 7 USDJPY 61 1215    5.02%
## 
## ================ 3.93% ================
## 
## Current Tokyo Time : 2018-08-27 16:52:45 
## ^fGARCH.NGARCH. 
## 
##      .id    x    n progress
## 1 USDAUD 1210 1215   99.59%
## 2 USDEUR 1214 1215   99.92%
## 3 USDGBP 1213 1216   99.75%
## 4 USDCHF 1215 1215  100.00%
## 5 USDCAD 1207 1214   99.42%
## 6 USDCNY 1215 1215  100.00%
## 7 USDJPY 1210 1215   99.59%
## 
## ================ 99.75% ================
## 
## Current Tokyo Time : 2018-08-27 16:52:46 
## ^fGARCH.NAGARCH. 
## 
##      .id    x    n progress
## 1 USDAUD 1048 1215   86.26%
## 2 USDEUR 1025 1215   84.36%
## 3 USDGBP 1147 1216   94.33%
## 4 USDCHF  862 1215   70.95%
## 5 USDCAD 1134 1214   93.41%
## 6 USDCNY 1184 1215   97.45%
## 7 USDJPY 1191 1215   98.02%
## 
## ================ 89.25% ================
## 
## Current Tokyo Time : 2018-08-27 16:52:47 
## ^fGARCH.APARCH. 
## 
##      .id   x    n progress
## 1 USDAUD 512 1215   42.14%
## 2 USDEUR 179 1215   14.73%
## 3 USDGBP 512 1216   42.11%
## 4 USDCHF 512 1215   42.14%
## 5 USDCAD 510 1214   42.01%
## 6 USDCNY 509 1215   41.89%
## 7 USDJPY 183 1215   15.06%
## 
## ================ 34.30% ================
## 
## Current Tokyo Time : 2018-08-27 16:52:48 
## ^fGARCH.GJRGARCH. 
## 
##      .id    x    n progress
## 1 USDAUD  855 1215   70.37%
## 2 USDEUR 1167 1215   96.05%
## 3 USDGBP 1209 1216   99.42%
## 4 USDCHF 1176 1215   96.79%
## 5 USDCAD 1193 1214   98.27%
## 6 USDCNY  918 1215   75.56%
## 7 USDJPY 1203 1215   99.01%
## 
## ================ 90.78% ================
## 
## Current Tokyo Time : 2018-08-27 16:52:49 
## ^fGARCH.ALLGARCH. 
## 
##      .id   x    n progress
## 1 USDAUD 387 1215   31.85%
## 2 USDEUR 547 1215   45.02%
## 3 USDGBP 547 1216   44.98%
## 4 USDCHF 545 1215   44.86%
## 5 USDCAD 546 1214   44.98%
## 6 USDCNY 548 1215   45.10%
## 7 USDJPY 295 1215   24.28%
## 
## ================ 40.15% ================
## 
## Current Tokyo Time : 2018-08-27 16:52:50 
## ^eGARCH. 
## 
##      .id   x    n progress
## 1 USDAUD 921 1215   75.80%
## 2 USDEUR 918 1215   75.56%
## 3 USDGBP 920 1216   75.66%
## 4 USDCHF 922 1215   75.88%
## 5 USDCAD 916 1214   75.45%
## 6 USDCNY 921 1215   75.80%
## 7 USDJPY 922 1215   75.88%
## 
## ================ 75.72% ================
## 
## Current Tokyo Time : 2018-08-27 16:52:51 
## ^pred2. 
## 
##      .id    x    n progress
## 1 USDAUD 1215 1215  100.00%
## 2 USDEUR 1215 1215  100.00%
## 3 USDGBP 1216 1216  100.00%
## 4 USDCHF 1215 1215  100.00%
## 5 USDCAD 1214 1214  100.00%
## 6 USDCNY 1212 1215   99.75%
## 7 USDJPY 1215 1215  100.00%
## 
## ================ 99.96% ================
## 
## Current Tokyo Time : 2018-08-27 16:52:52 
## ^apARCH. 
## 
##      .id   x    n progress
## 1 USDAUD 125 1215   10.29%
## 2 USDEUR 125 1215   10.29%
## 3 USDGBP 125 1216   10.28%
## 4 USDCHF 124 1215   10.21%
## 5 USDCAD 124 1214   10.21%
## 6 USDCNY 125 1215   10.29%
## 7 USDJPY 122 1215   10.04%
## 
## ================ 10.23% ================
## 
## Current Tokyo Time : 2018-08-27 16:52:53 
## ^iGARCH. 
## 
##      .id    x    n progress
## 1 USDAUD 1215 1215  100.00%
## 2 USDEUR 1215 1215  100.00%
## 3 USDGBP 1216 1216  100.00%
## 4 USDCHF 1215 1215  100.00%
## 5 USDCAD 1214 1214  100.00%
## 6 USDCNY 1215 1215  100.00%
## 7 USDJPY 1215 1215  100.00%
## 
## ================ 100.00% ================
## 
## Current Tokyo Time : 2018-08-27 16:52:54 
## ^csGARCH. 
## 
##      .id    x    n progress
## 1 USDAUD 1210 1215   99.59%
## 2 USDEUR 1215 1215  100.00%
## 3 USDGBP 1216 1216  100.00%
## 4 USDCHF 1214 1215   99.92%
## 5 USDCAD 1210 1214   99.67%
## 6 USDCNY 1215 1215  100.00%
## 7 USDJPY 1215 1215  100.00%
## 
## ================ 99.88% ================

## check latest date saved in progress.
#' @ l_ply(gmds, function(x) {
#' @   x2 <- ifelse(x == 'gjrGARCH', 'pred2', x)
#' @   task_progress(.date = TRUE, .pattern = paste0('^', x2, '.'), .loops = FALSE)
#' @   })

if (!exists('fx')) {
  fx <- read_umodels(cr_code, gmds, mbase, .print = FALSE)
}

5.4.2 MSE and AIC

acc <- ddply(fx, .(.id, Model), summarise, 
             MSE = mean((Price.T1 - Price)^2), 
             n = length(Price), 
             AIC.MSE = (-2*MSE)/n+2*4/n, 
             MSE.AIC = mean((Akaike - mean(Akaike))^2), 
             Akaike = mean(Akaike), 
             Bayes = mean(Bayes), 
             Shibata = mean(Shibata), 
             Hannan.Quinn = mean(Hannan.Quinn)) %>% 
  tbl_df %>% mutate(MSE = round(MSE, 7))

acc %>% arrange(.id) %>% 
  kable(caption = 'Group Table Summary') %>% 
  kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive')) %>%
  group_rows('USD/AUD', 1, 14, label_row_css = 'background-color: #003399; color: #fff;') %>%
  group_rows('USD/CAD', 15, 28, label_row_css = 'background-color: #003399; color: #fff;') %>%
  group_rows('USD/CHF', 29, 42, label_row_css = 'background-color: #003399; color: #fff;') %>%
  group_rows('USD/CNY', 43, 56, label_row_css = 'background-color: #003399; color: #fff;') %>%
  group_rows('USD/EUR', 57, 70, label_row_css = 'background-color: #003399; color: #fff;') %>%
  group_rows('USD/GBP', 71, 84, label_row_css = 'background-color: #003399; color: #fff;') %>%
  group_rows('USD/JPY', 85, 98, label_row_css = 'background-color: #003399; color: #fff;') %>% 
  scroll_box(width = '100%', height = '400px')

Group Table Summary

.id	Model	MSE	n	AIC.MSE	MSE.AIC	Akaike	Bayes	Shibata	Hannan.Quinn
USD/AUD
USDAUD	sGARCH	5.000000e-07	4857	1.647100e-03	2.694948e-01	-7.102248	-7.022686	-7.103259	-7.070268
USDAUD	fGARCH.GARCH	5.000000e-07	4856	1.647400e-03	2.690199e-01	-7.101370	-7.021819	-7.102379	-7.069394
USDAUD	fGARCH.TGARCH	1.159071e+00	4812	1.180800e-03	7.703073e-01	-6.905361	-6.812168	-6.906724	-6.867902
USDAUD	fGARCH.AVGARCH	7.432400e+91	312	-4.764359e+89	2.671358e+02	-6.449270	-6.340982	-6.451100	-6.405742
USDAUD	fGARCH.NGARCH	3.284775e+74	4840	-1.357345e+71	4.595300e+03	-15.278746	-15.185573	-15.280108	-15.241294
USDAUD	fGARCH.NAGARCH	2.209303e+60	4192	-1.054057e+57	2.606909e+01	-7.062614	-6.968379	-7.064007	-7.024736
USDAUD	fGARCH.APARCH	2.700000e-06	2048	3.906200e-03	3.305634e+03	-13.139417	-13.032675	-13.141188	-13.096509
USDAUD	fGARCH.GJRGARCH	6.000000e-07	3420	2.339200e-03	2.489345e-01	-7.278103	-7.185104	-7.279462	-7.240721
USDAUD	fGARCH.ALLGARCH	6.111942e+19	1548	-7.896566e+16	3.462435e+03	-13.872358	-13.747152	-13.874776	-13.822030
USDAUD	eGARCH	6.000000e-07	3672	2.178600e-03	2.165283e+00	-7.154850	-7.061813	-7.156211	-7.117453
USDAUD	gjrGARCH	9.000000e-07	4860	1.646100e-03	2.806975e-01	-7.105727	-7.012506	-7.107091	-7.068257
USDAUD	apARCH	5.441374e+146	500	-2.176550e+144	3.860640e+03	-9.767500	-9.653693	-9.769528	-9.721753
USDAUD	iGARCH	1.098765e+287	4860	-4.521666e+283	1.146959e+02	-6.951070	-6.885141	-6.951781	-6.924570
USDAUD	csGARCH	7.000000e-07	4840	1.652900e-03	2.711930e-01	-7.087811	-6.980909	-7.089582	-7.044841
USD/CAD
USDEUR	sGARCH	4.000000e-07	4860	1.646100e-03	3.379221e-01	-8.119430	-8.037839	-8.120496	-8.086634
USDEUR	fGARCH.GARCH	1.483144e+181	4856	-6.108501e+177	6.410805e+01	-7.956977	-7.875412	-7.958043	-7.924192
USDEUR	fGARCH.TGARCH	8.000000e-07	4548	1.759000e-03	5.054985e-01	-7.979369	-7.883811	-7.980805	-7.940959
USDEUR	fGARCH.AVGARCH	1.000000e-07	180	4.444440e-02	9.730104e+00	-7.722639	-7.616830	-7.724373	-7.680108
USDEUR	fGARCH.NGARCH	8.391581e+98	4856	-3.456170e+95	5.524109e+03	-17.259838	-17.164598	-17.261265	-17.221556
USDEUR	fGARCH.NAGARCH	4.000000e-07	4100	1.951200e-03	1.695563e+01	-8.118368	-8.022222	-8.119824	-8.079722
USDEUR	fGARCH.APARCH	4.048772e+158	716	-1.130942e+156	2.905338e+03	-14.176505	-14.064878	-14.178455	-14.131636
USDEUR	fGARCH.GJRGARCH	3.000000e-07	4668	1.713800e-03	3.432437e-01	-8.136069	-8.040670	-8.137500	-8.097723
USDEUR	fGARCH.ALLGARCH	2.200000e-06	2188	3.656300e-03	4.719765e+03	-16.788217	-16.663667	-16.790602	-16.738151
USDEUR	eGARCH	7.000000e-07	3672	2.178600e-03	1.864406e+00	-8.200094	-8.103768	-8.201553	-8.161375
USDEUR	gjrGARCH	3.000000e-07	4860	1.646100e-03	3.459734e-01	-8.136542	-8.041304	-8.137969	-8.098261
USDEUR	apARCH	1.000000e-07	500	1.600000e-02	3.842920e-02	-8.174484	-8.068989	-8.176210	-8.132078
USDEUR	iGARCH	5.000000e-07	4860	1.646100e-03	3.405014e-01	-8.112925	-8.044980	-8.113684	-8.085614
USDEUR	csGARCH	2.300000e-06	4860	1.646100e-03	3.318425e-01	-8.103875	-7.994992	-8.105716	-8.060109
USD/CHF
USDGBP	sGARCH	7.000000e-07	4864	1.644700e-03	4.306269e-01	-8.645250	-8.561637	-8.646384	-8.611643
USDGBP	fGARCH.GARCH	7.000000e-07	4860	1.646100e-03	4.304506e-01	-8.644493	-8.560908	-8.645626	-8.610897
USDGBP	fGARCH.TGARCH	2.502052e+143	4800	-1.042521e+140	2.969831e+01	-8.339996	-8.242703	-8.341499	-8.300891
USDGBP	fGARCH.AVGARCH	0.000000e+00	224	3.571430e-02	4.781526e+01	-8.126520	-8.024918	-8.128121	-8.085684
USDGBP	fGARCH.NGARCH	1.118436e+146	4852	-4.610207e+142	3.962445e+03	-14.926321	-14.829084	-14.927822	-14.887238
USDGBP	fGARCH.NAGARCH	5.000000e-07	4588	1.743700e-03	6.311911e+01	-8.336187	-8.239475	-8.337673	-8.297315
USDGBP	fGARCH.APARCH	3.000000e-07	2048	3.906200e-03	1.612287e+03	-12.526748	-12.418871	-12.528579	-12.483386
USDGBP	fGARCH.GJRGARCH	6.000000e-07	4836	1.654300e-03	4.283653e-01	-8.660125	-8.562876	-8.661626	-8.621037
USDGBP	fGARCH.ALLGARCH	3.295167e+148	2188	-3.012036e+145	1.637920e+03	-11.888681	-11.766055	-11.891015	-11.839391
USDGBP	eGARCH	8.000000e-07	3668	2.181000e-03	1.840693e+01	-8.736630	-8.638653	-8.738157	-8.697249
USDGBP	gjrGARCH	8.000000e-07	4864	1.644700e-03	4.290970e-01	-8.670272	-8.573029	-8.671773	-8.631187
USDGBP	apARCH	1.000000e-07	500	1.600000e-02	5.524340e-02	-9.099763	-8.997746	-9.101379	-9.058760
USDGBP	iGARCH	9.000000e-07	4864	1.644700e-03	4.297069e-01	-8.645209	-8.575227	-8.646028	-8.617081
USDGBP	csGARCH	1.772474e+296	4864	-7.288131e+292	1.215273e+02	-8.473194	-8.362320	-8.475116	-8.428630
USD/CNY
USDCHF	sGARCH	2.630000e-05	4856	1.647400e-03	3.242167e-01	-7.629761	-7.549492	-7.630794	-7.597497
USDCHF	fGARCH.GARCH	2.497679e+121	4860	-1.027851e+118	2.905288e+01	-7.552617	-7.472346	-7.553649	-7.520351
USDCHF	fGARCH.TGARCH	2.500000e-05	4704	1.700700e-03	4.234093e-01	-7.552770	-7.458658	-7.554164	-7.514941
USDCHF	fGARCH.AVGARCH	3.000000e-07	76	1.052631e-01	7.608750e-02	-7.769682	-7.656999	-7.771688	-7.724381
USDCHF	fGARCH.NGARCH	1.723339e+00	4860	9.369000e-04	3.764700e+03	-14.529679	-14.435761	-14.531067	-14.491928
USDCHF	fGARCH.NAGARCH	6.908758e+287	3448	-4.007400e+284	4.414594e+02	-6.528485	-6.434230	-6.529883	-6.490598
USDCHF	fGARCH.APARCH	4.087595e+72	2048	-3.991792e+69	3.805622e+03	-15.224741	-15.114544	-15.226636	-15.180444
USDCHF	fGARCH.GJRGARCH	2.610000e-05	4704	1.700700e-03	3.043563e-01	-7.650429	-7.556385	-7.651821	-7.612627
USDCHF	fGARCH.ALLGARCH	9.028781e+12	2180	-8.283285e+09	5.084668e+03	-16.468168	-16.344250	-16.470536	-16.418356
USDCHF	eGARCH	1.236519e+197	3676	-6.727522e+193	8.439458e+00	-7.589893	-7.494704	-7.591322	-7.551631
USDCHF	gjrGARCH	4.460000e-05	4860	1.646100e-03	3.123489e-01	-7.669332	-7.575414	-7.670720	-7.631581
USDCHF	apARCH	1.000000e-07	496	1.612900e-02	1.370770e-02	-7.901480	-7.798088	-7.903137	-7.859918
USDCHF	iGARCH	1.620000e-04	4860	1.646000e-03	4.215382e-01	-7.576818	-7.510194	-7.577548	-7.550038
USDCHF	csGARCH	6.450000e-05	4856	1.647400e-03	3.372855e-01	-7.604900	-7.497336	-7.606697	-7.561664
USD/EUR
USDCAD	sGARCH	9.000000e-07	4856	1.647400e-03	3.553528e-01	-7.708202	-7.626037	-7.709294	-7.675175
USDCAD	fGARCH.GARCH	9.000000e-07	4856	1.647400e-03	3.554005e-01	-7.708185	-7.626020	-7.709277	-7.675158
USDCAD	fGARCH.TGARCH	1.900000e-06	4724	1.693500e-03	7.176105e-01	-7.492619	-7.396743	-7.494076	-7.454081
USDCAD	fGARCH.AVGARCH	1.000000e-07	248	3.225810e-02	3.687486e+01	-7.860242	-7.752867	-7.862029	-7.817081
USDCAD	fGARCH.NGARCH	3.549701e+119	4828	-1.470464e+116	5.548612e+03	-17.997704	-17.901883	-17.999160	-17.959188
USDCAD	fGARCH.NAGARCH	4.000000e-07	4536	1.763700e-03	2.932958e+00	-7.726134	-7.630444	-7.727585	-7.687671
USDCAD	fGARCH.APARCH	4.000000e-07	2040	3.921600e-03	2.741533e+03	-13.472457	-13.366488	-13.474196	-13.429860
USDCAD	fGARCH.GJRGARCH	1.000000e-06	4772	1.676400e-03	3.604163e-01	-7.716214	-7.620373	-7.717670	-7.677690
USDCAD	fGARCH.ALLGARCH	1.152578e+31	2184	-1.055474e+28	4.024178e+03	-15.747334	-15.626874	-15.749560	-15.698913
USDCAD	eGARCH	1.612176e+247	3648	-8.838683e+243	5.834309e+00	-7.770530	-7.675118	-7.771968	-7.732179
USDCAD	gjrGARCH	1.400000e-06	4856	1.647400e-03	3.623402e-01	-7.712466	-7.616652	-7.713921	-7.673953
USDCAD	apARCH	0.000000e+00	496	1.612900e-02	9.127900e-03	-8.381424	-8.274472	-8.383199	-8.338432
USDCAD	iGARCH	7.000000e-07	4856	1.647400e-03	3.569074e-01	-7.707116	-7.638600	-7.707898	-7.679575
USDCAD	csGARCH	5.000000e-07	4840	1.652900e-03	3.543181e-01	-7.693255	-7.583768	-7.695127	-7.649246
USD/GBP
USDCNY	sGARCH	5.273000e-04	4856	1.647200e-03	1.197338e+00	-6.151748	-6.063258	-6.152983	-6.116180
USDCNY	fGARCH.GARCH	4.171000e-04	4856	1.647300e-03	1.197976e+00	-6.151725	-6.063230	-6.152961	-6.116155
USDCNY	fGARCH.TGARCH	6.276028e+03	4780	-2.624280e+00	6.332603e+00	-5.853054	-5.750984	-5.854675	-5.812028
USDCNY	fGARCH.AVGARCH	1.100000e-06	52	1.538461e-01	2.449294e-01	-6.841904	-6.724169	-6.844013	-6.794586
USDCNY	fGARCH.NGARCH	5.596976e+84	4860	-2.303282e+81	5.898227e+03	-17.578427	-17.476307	-17.580049	-17.537380
USDCNY	fGARCH.NAGARCH	1.821397e+02	4736	-7.522790e-02	2.567161e+01	-5.932229	-5.830031	-5.933854	-5.891151
USDCNY	fGARCH.APARCH	3.672713e+134	2036	-3.607773e+131	1.316949e+04	-28.947330	-28.826609	-28.949565	-28.898806
USDCNY	fGARCH.GJRGARCH	4.742892e-01	3672	1.920300e-03	6.907089e+00	-6.377420	-6.274790	-6.379057	-6.336168
USDCNY	fGARCH.ALLGARCH	1.564667e+57	2192	-1.427616e+54	1.020284e+04	-24.776176	-24.642736	-24.778888	-24.722540
USDCNY	eGARCH	6.786000e-04	3668	2.180700e-03	1.630299e+00	-6.270236	-6.168453	-6.271849	-6.229324
USDCNY	gjrGARCH	4.138000e-04	4848	1.650000e-03	1.246110e+00	-6.191716	-6.089568	-6.193339	-6.150658
USDCNY	apARCH	1.730000e-05	500	1.599990e-02	3.601446e+03	-9.471731	-9.353260	-9.473876	-9.424115
USDCNY	iGARCH	6.520000e-04	4860	1.645800e-03	1.329561e+00	-6.084940	-6.010098	-6.085841	-6.054858
USDCNY	csGARCH	4.628831e+295	4860	-1.904869e+292	1.225855e+02	-5.967233	-5.851474	-5.969295	-5.920704
USD/JPY
USDJPY	sGARCH	9.224400e-03	4860	1.642300e-03	2.221979e-01	1.813514	1.898669	1.812339	1.847742
USDJPY	fGARCH.GARCH	9.306400e-03	4860	1.642300e-03	2.216443e-01	1.813549	1.898705	1.812375	1.847777
USDJPY	fGARCH.TGARCH	5.605500e+175	4852	-2.310594e+172	3.867787e+01	1.910811	2.009578	1.909263	1.950510
USDJPY	fGARCH.AVGARCH	7.955620e-02	244	3.213480e-02	3.566636e-01	1.116023	1.253730	1.113095	1.171370
USDJPY	fGARCH.NGARCH	3.433530e+245	4840	-1.418814e+242	5.098377e+03	-7.571801	-7.473060	-7.573348	-7.532113
USDJPY	fGARCH.NAGARCH	6.985600e-03	4764	1.676300e-03	2.288033e-01	1.793739	1.892446	1.792193	1.833414
USDJPY	fGARCH.APARCH	4.805514e+123	732	-1.312982e+121	1.291003e+04	-22.172463	-22.044965	-22.174999	-22.121219
USDJPY	fGARCH.GJRGARCH	7.894200e-03	4812	1.659200e-03	2.252854e-01	1.805879	1.904749	1.804328	1.845620
USDJPY	fGARCH.ALLGARCH	1.132928e+274	1180	-1.920218e+271	7.380809e+03	-11.181572	-11.049798	-11.184263	-11.128607
USDJPY	eGARCH	4.251282e+156	3672	-2.315513e+153	5.203122e+01	2.070914	2.171756	2.069303	2.111447
USDJPY	gjrGARCH	7.529600e-03	4860	1.643000e-03	2.303997e-01	1.802256	1.901051	1.800708	1.841966
USDJPY	apARCH	3.214289e+242	488	-1.317332e+240	1.282936e+05	-94.891516	-94.759889	-94.894215	-94.838612
USDJPY	iGARCH	9.308000e-03	4860	1.642300e-03	2.265083e-01	1.815783	1.887300	1.814929	1.844529
USDJPY	csGARCH	6.170350e-02	4860	1.620700e-03	2.221000e-01	1.823600	1.936033	1.821624	1.868792

Above table is the raw prediction dataset without any filter. You can compare the best model based on more n and lowest MSE and AIC/BIC. However there has bias and also not yet filter some date without prediction result. For example :

• sGARCH does not has prediction result on AUDUSD on 2013-01-02.
• The open price of fGARCH.ALLGARCH on USDGBP on 2014-06-08 bias.
• The AIC and BIC value of eGARCH for currency USDJPY bias, hundred times than normal price.
• The data source close price gather from Yahoo for USDCNY is 2.856 but open, highest, lowest is normal. We cannot judge if the lowest price on that particular date is true or wrong, but need to filter as well.

acc <- ddply(fx, .(Model), summarise, 
             MSE = mean((Price.T1 - Price)^2), 
             n = length(Price), 
             AIC.MSE = (-2*MSE)/n+2*4/n, 
             MSE.AIC = mean((Akaike - mean(Akaike))^2), 
             Akaike = mean(Akaike), 
             Bayes = mean(Bayes), 
             Shibata = mean(Shibata), 
             Hannan.Quinn = mean(Hannan.Quinn)) %>% 
  tbl_df %>% mutate(MSE = round(MSE, 7))

acc %>% 
  kable(caption = 'Model Summary') %>% 
  kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive')) %>% 
  scroll_box(width = '100%', height = '400px')

Model Summary

Model	MSE	n	AIC.MSE	MSE.AIC	Akaike	Bayes	Shibata	Hannan.Quinn
sGARCH	1.397600e-03	34009	2.351000e-04	11.73935	-6.220321	-6.137343	-6.221427	-6.186968
fGARCH.GARCH	2.118029e+180	34004	-1.245753e+176	24.83641	-6.185483	-6.102513	-6.186589	-6.152133
fGARCH.TGARCH	8.187202e+174	33220	-4.929080e+170	22.44225	-5.995799	-5.899087	-5.997274	-5.956926
fGARCH.AVGARCH	1.735710e+91	1336	-2.598368e+88	89.92217	-5.872674	-5.760020	-5.874667	-5.827393
fGARCH.NGARCH	4.896949e+244	33936	-2.885991e+240	4923.61504	-15.021548	-14.924939	-15.023020	-14.982716
fGARCH.NAGARCH	7.845276e+286	30364	-5.167485e+282	81.61159	-5.870236	-5.773205	-5.871720	-5.831234
fGARCH.APARCH	2.484505e+157	11668	-4.258665e+153	5332.61496	-16.844855	-16.733402	-16.846793	-16.800055
fGARCH.GJRGARCH	5.762570e-02	30884	2.553000e-04	13.41298	-6.226137	-6.129452	-6.227613	-6.187275
fGARCH.ALLGARCH	9.786644e+272	13660	-1.432891e+269	5158.06349	-16.252993	-16.127381	-16.255424	-16.202501
eGARCH	2.290551e+246	25676	-1.784196e+242	24.94858	-6.234284	-6.137060	-6.235776	-6.195205
gjrGARCH	1.141900e-03	34008	2.352000e-04	11.76857	-6.240673	-6.144049	-6.242145	-6.201835
apARCH	4.507394e+241	3480	-2.590456e+238	19956.74226	-20.873597	-20.761971	-20.875545	-20.828729
iGARCH	1.569664e+286	34020	-9.227889e+281	28.06237	-6.180438	-6.111102	-6.181232	-6.152568
csGARCH	3.199212e+295	33980	-1.882997e+291	46.32877	-6.156747	-6.046472	-6.158638	-6.112422

Above models compare all prediction result includes all bias and all possible result from calculation.

5.4.3 Filtered MSE

Here I put this section as next topic as Markov Method 2 : Filtered MSE due to I need to filter OHLC, Close and HiLo three sub-sections.

6 Markov Method 2 : Filtered MSE

6.1 OHLC

6.1.1 All Models

Due to some errors, the MSE values is not accurate. I can either filter AIC and BIC values or MSE values. Since the standard deviation based on price, even though the AIC value does not bias, but finally we take price figure but not the AIC figure.

• Normally we need to follow AIC and BIC figure, but some unknown errors cause the forecast price became AIC or BIC values etc
• Some unknown error made the AIC values bias 100 times than mean AIC value in their currency accordingly.

There is the solution for filter unknown error. Here I filtered all dataset which \(\sigma^2_{i} >= 0.2\) and the AIC, BIC values just for reference in order to know there has .

## filter all predictive error.
#'@ fx %>% mutate(diff = Price.T1 - Price, se = ifelse(abs(diff) > Price, 1, 0)) %>% .[,-c(8:10)] %>% dplyr::filter(se == 1) %>% data.frame

fx %<>% mutate(diff = abs(Price.T1/Price), 
               se = ifelse(diff <= 0.8 | diff >= 1.25, 1, 0))

## filter all predictive error where sd >= 20%.
notID <- fx %>% dplyr::filter(se == 1)
ntimeID <- notID %>% .$Date %>% unique %>% sort

## filter all date which contain OHLC of 7 currencies.
ntimeID2 <- fx %>% dplyr::count(Date) %>% 
    dplyr::filter(n == 392) %>% .$Date %>% sort #14 models x 7 currencies x OHLC 4 types = 392 observations per day.

acc <- fx %>% 
  dplyr::filter(!Date %in% ntimeID) %>% 
  ddply(.(.id, Model), summarise, 
        MSE = mean((Price.T1 - Price)^2), 
        n = length(Price), 
        AIC.MSE = (-2*MSE)/n+2*4/n, 
        MSE.AIC = mean((Akaike - mean(Akaike))^2),
        Akaike = mean(Akaike), 
        Bayes = mean(Bayes), 
        Shibata = mean(Shibata), 
        Hannan.Quinn = mean(Hannan.Quinn)) %>% 
      tbl_df %>% mutate(MSE = round(MSE, 7))

Group Table Summary of MSE

.id	Model	MSE	n	AIC.MSE	MSE.AIC	Akaike	Bayes	Shibata	Hannan.Quinn
USD/AUD
USDAUD	sGARCH	0.0000005	4237	0.0018881	2.625621e-01	-7.041480	-6.962601	-7.042469	-7.009774
USDAUD	fGARCH.GARCH	0.0000005	4236	0.0018886	2.619517e-01	-7.040507	-6.961642	-7.041496	-7.008807
USDAUD	fGARCH.TGARCH	0.0000027	4200	0.0019048	5.427742e-01	-6.851330	-6.758793	-6.852670	-6.814134
USDAUD	fGARCH.AVGARCH	0.0000001	264	0.0303030	3.855170e+01	-7.236056	-7.128579	-7.237854	-7.192854
USDAUD	fGARCH.NGARCH	0.0000038	4220	0.0018957	4.363591e+03	-14.944784	-14.852304	-14.946122	-14.907612
USDAUD	fGARCH.NAGARCH	0.0000011	3592	0.0022272	2.344820e-01	-7.152012	-7.058432	-7.153382	-7.114398
USDAUD	fGARCH.APARCH	0.0000015	1560	0.0051282	3.239403e+03	-12.961663	-12.855961	-12.963393	-12.919174
USDAUD	fGARCH.GJRGARCH	0.0000007	2820	0.0028369	2.616901e-01	-7.220796	-7.128821	-7.222121	-7.183826
USDAUD	fGARCH.ALLGARCH	0.0000012	1056	0.0075758	2.766247e+03	-12.611466	-12.487341	-12.613836	-12.561572
USDAUD	eGARCH	0.0000006	3072	0.0026042	2.531229e+00	-7.083762	-6.991649	-7.085091	-7.046736
USDAUD	gjrGARCH	0.0000010	4240	0.0018868	2.734547e-01	-7.043891	-6.951352	-7.045231	-7.006695
USDAUD	apARCH	0.0000004	400	0.0200000	1.138510e-02	-7.822066	-7.709866	-7.824033	-7.776965
USDAUD	iGARCH	0.0000006	4240	0.0018868	2.635497e-01	-7.043833	-6.978585	-7.044526	-7.017606
USDAUD	csGARCH	0.0000007	4220	0.0018957	2.645474e-01	-7.027054	-6.920833	-7.028798	-6.984358
USD/CAD
USDEUR	sGARCH	0.0000004	4240	0.0018868	2.824928e-01	-8.031937	-7.950900	-8.032987	-7.999364
USDEUR	fGARCH.GARCH	0.0000004	4240	0.0018868	2.824588e-01	-8.031911	-7.950873	-8.032961	-7.999338
USDEUR	fGARCH.TGARCH	0.0000007	3964	0.0020182	4.471741e-01	-7.887775	-7.792756	-7.889194	-7.849582
USDEUR	fGARCH.AVGARCH	0.0000001	156	0.0512820	1.115540e+01	-7.694693	-7.588904	-7.696424	-7.652170
USDEUR	fGARCH.NGARCH	0.0000017	4236	0.0018886	5.155437e+03	-16.511584	-16.416899	-16.512993	-16.473525
USDEUR	fGARCH.NAGARCH	0.0000004	3500	0.0022857	1.973535e+01	-8.012523	-7.916836	-8.013963	-7.974061
USDEUR	fGARCH.APARCH	0.0000011	552	0.0144927	1.802796e+03	-11.511134	-11.400133	-11.513061	-11.466516
USDEUR	fGARCH.GJRGARCH	0.0000003	4064	0.0019685	2.900221e-01	-8.048991	-7.954148	-8.050404	-8.010869
USDEUR	fGARCH.ALLGARCH	0.0000004	1652	0.0048426	2.385536e+03	-12.649663	-12.525738	-12.652022	-12.599849
USDEUR	eGARCH	0.0000006	3084	0.0025940	2.101583e+00	-8.099908	-8.003971	-8.101354	-8.061346
USDEUR	gjrGARCH	0.0000003	4240	0.0018868	2.929391e-01	-8.049614	-7.954931	-8.051023	-8.011556
USDEUR	apARCH	0.0000001	400	0.0200000	4.372810e-02	-8.166151	-8.060413	-8.167885	-8.123648
USDEUR	iGARCH	0.0000004	4240	0.0018868	2.844981e-01	-8.024650	-7.957257	-8.025395	-7.997561
USDEUR	csGARCH	0.0000024	4240	0.0018868	2.776284e-01	-8.018013	-7.909685	-8.019833	-7.974470
USD/CHF
USDGBP	sGARCH	0.0000008	4244	0.0018850	4.074706e-01	-8.557508	-8.474264	-8.558628	-8.524049
USDGBP	fGARCH.GARCH	0.0000008	4240	0.0018868	4.071691e-01	-8.556825	-8.473612	-8.557945	-8.523379
USDGBP	fGARCH.TGARCH	0.0000009	4200	0.0019048	6.483761e-01	-8.335256	-8.238371	-8.336743	-8.296314
USDGBP	fGARCH.AVGARCH	0.0000000	180	0.0444444	5.930195e+01	-7.949880	-7.847750	-7.951499	-7.908832
USDGBP	fGARCH.NGARCH	0.0000017	4232	0.0018904	3.945180e+03	-14.779766	-14.682902	-14.781253	-14.740834
USDGBP	fGARCH.NAGARCH	0.0000005	3984	0.0020080	5.686508e+01	-8.260802	-8.164545	-8.262270	-8.222113
USDGBP	fGARCH.APARCH	0.0000003	1564	0.0051151	1.958838e+03	-13.240809	-13.134172	-13.242595	-13.197946
USDGBP	fGARCH.GJRGARCH	0.0000007	4216	0.0018975	4.047155e-01	-8.571812	-8.474936	-8.573299	-8.532874
USDGBP	fGARCH.ALLGARCH	0.0000002	1652	0.0048426	1.217201e+03	-11.438499	-11.317369	-11.440773	-11.389811
USDGBP	eGARCH	0.0000009	3068	0.0026076	3.935341e+00	-8.720159	-8.622603	-8.721670	-8.680948
USDGBP	gjrGARCH	0.0000009	4244	0.0018850	4.051936e-01	-8.582778	-8.485905	-8.584264	-8.543841
USDGBP	apARCH	0.0000001	400	0.0200000	6.679700e-02	-9.094661	-8.991973	-9.096302	-9.053389
USDGBP	iGARCH	0.0000010	4244	0.0018850	4.069242e-01	-8.557934	-8.488319	-8.558742	-8.529953
USDGBP	csGARCH	0.0000009	4244	0.0018850	3.967495e-01	-8.544580	-8.434078	-8.546485	-8.500166
USD/CNY
USDCHF	sGARCH	0.0000028	4236	0.0018886	2.952817e-01	-7.576211	-7.496335	-7.577229	-7.544104
USDCHF	fGARCH.GARCH	0.0000028	4240	0.0018868	2.954395e-01	-7.576116	-7.496238	-7.577134	-7.544008
USDCHF	fGARCH.TGARCH	0.0000017	4120	0.0019417	4.013689e-01	-7.500039	-7.406354	-7.501417	-7.462382
USDCHF	fGARCH.AVGARCH	0.0000004	72	0.1111111	6.717750e-02	-7.785479	-7.671861	-7.787518	-7.739802
USDCHF	fGARCH.NGARCH	0.0000022	4240	0.0018868	3.601465e+03	-13.962682	-13.869158	-13.964055	-13.925090
USDCHF	fGARCH.NAGARCH	0.0000023	2884	0.0027739	1.094073e+02	-6.947367	-6.853501	-6.948748	-6.909637
USDCHF	fGARCH.APARCH	0.0000036	1560	0.0051282	3.579324e+03	-14.765248	-14.655371	-14.767127	-14.721079
USDCHF	fGARCH.GJRGARCH	0.0000018	4088	0.0019569	2.776090e-01	-7.595209	-7.501531	-7.596587	-7.557555
USDCHF	fGARCH.ALLGARCH	0.0000014	1652	0.0048426	5.190600e+03	-16.419914	-16.296191	-16.422270	-16.370180
USDCHF	eGARCH	0.0000045	3080	0.0025974	2.957916e+00	-7.579385	-7.484499	-7.580802	-7.541245
USDCHF	gjrGARCH	0.0000019	4240	0.0018868	2.787113e-01	-7.615097	-7.521573	-7.616470	-7.577505
USDCHF	apARCH	0.0000001	396	0.0202020	1.418610e-02	-7.900710	-7.796674	-7.902390	-7.858889
USDCHF	iGARCH	0.0000383	4240	0.0018868	3.945255e-01	-7.520421	-7.454191	-7.521139	-7.493799
USDCHF	csGARCH	0.0000118	4236	0.0018886	3.051741e-01	-7.553248	-7.446079	-7.555028	-7.510171
USD/EUR
USDCAD	sGARCH	0.0000009	4236	0.0018886	3.457555e-01	-7.635505	-7.553377	-7.636596	-7.602493
USDCAD	fGARCH.GARCH	0.0000010	4236	0.0018886	3.458516e-01	-7.635527	-7.553398	-7.636617	-7.602514
USDCAD	fGARCH.TGARCH	0.0000020	4116	0.0019436	7.260493e-01	-7.409235	-7.313325	-7.410692	-7.370683
USDCAD	fGARCH.AVGARCH	0.0000001	208	0.0384615	4.391638e+01	-7.780511	-7.674241	-7.782256	-7.737794
USDCAD	fGARCH.NGARCH	0.0000063	4208	0.0019011	5.691368e+03	-18.181319	-18.085534	-18.182773	-18.142817
USDCAD	fGARCH.NAGARCH	0.0000004	3928	0.0020367	3.320489e+00	-7.650075	-7.554392	-7.651525	-7.611615
USDCAD	fGARCH.APARCH	0.0000004	1560	0.0051282	3.013111e+03	-14.130830	-14.024944	-14.132564	-14.088267
USDCAD	fGARCH.GJRGARCH	0.0000011	4152	0.0019268	3.524198e-01	-7.643116	-7.547309	-7.644571	-7.604606
USDCAD	fGARCH.ALLGARCH	0.0000004	1648	0.0048544	4.079308e+03	-16.114722	-15.994731	-16.116928	-16.066489
USDCAD	eGARCH	0.0000022	3048	0.0026247	7.547218e-01	-7.754953	-7.659588	-7.756388	-7.716620
USDCAD	gjrGARCH	0.0000015	4236	0.0018886	3.515886e-01	-7.640152	-7.544375	-7.641605	-7.601654
USDCAD	apARCH	0.0000000	396	0.0202020	9.142000e-03	-8.372531	-8.266175	-8.374283	-8.329780
USDCAD	iGARCH	0.0000008	4236	0.0018886	3.475985e-01	-7.634421	-7.565940	-7.635202	-7.606895
USDCAD	csGARCH	0.0000005	4220	0.0018957	3.449715e-01	-7.620769	-7.511317	-7.622639	-7.576774
USD/GBP
USDCNY	sGARCH	0.0003844	4236	0.0018884	1.025825e+00	-6.143679	-6.054758	-6.144926	-6.107938
USDCNY	fGARCH.GARCH	0.0002631	4236	0.0018884	1.023986e+00	-6.143958	-6.055029	-6.145205	-6.108213
USDCNY	fGARCH.TGARCH	0.0011038	4164	0.0019207	5.891562e+00	-5.841889	-5.739395	-5.843523	-5.800692
USDCNY	fGARCH.AVGARCH	0.0000011	52	0.1538461	2.449294e-01	-6.841904	-6.724169	-6.844013	-6.794586
USDCNY	fGARCH.NGARCH	0.0660925	4240	0.0018556	3.623761e+03	-13.619580	-13.517031	-13.621216	-13.578361
USDCNY	fGARCH.NAGARCH	0.0001809	4120	0.0019417	1.526861e+01	-6.009059	-5.906422	-6.010697	-5.967805
USDCNY	fGARCH.APARCH	0.0007004	1548	0.0051671	1.291332e+04	-28.184116	-28.061422	-28.186421	-28.134799
USDCNY	fGARCH.GJRGARCH	0.0003035	3064	0.0026108	8.905794e-01	-6.475073	-6.371679	-6.476734	-6.433514
USDCNY	fGARCH.ALLGARCH	0.0005428	1656	0.0048303	2.654545e+03	-11.260582	-11.125038	-11.263376	-11.206100
USDCNY	eGARCH	0.0004397	3072	0.0026039	1.388956e+00	-6.297661	-6.195309	-6.299292	-6.256521
USDCNY	gjrGARCH	0.0002736	4232	0.0018902	1.089222e+00	-6.186365	-6.083799	-6.188001	-6.145139
USDCNY	apARCH	0.0000167	400	0.0199999	4.499346e+03	-10.171161	-10.051991	-10.173331	-10.123264
USDCNY	iGARCH	0.0004230	4240	0.0018866	1.172098e+00	-6.069652	-5.994378	-6.070562	-6.039396
USDCNY	csGARCH	0.0005736	4240	0.0018865	1.164230e+00	-6.114273	-5.998085	-6.116350	-6.067572
USD/JPY
USDJPY	sGARCH	0.0087084	4240	0.0018827	1.953176e-01	1.879246	1.963626	1.878093	1.913162
USDJPY	fGARCH.GARCH	0.0087105	4240	0.0018827	1.947522e-01	1.879214	1.963594	1.878060	1.913130
USDJPY	fGARCH.TGARCH	0.0077724	4236	0.0018849	2.092384e-01	1.886530	1.984525	1.885007	1.925919
USDJPY	fGARCH.AVGARCH	0.0623884	204	0.0386040	3.971346e-01	1.096750	1.233458	1.093865	1.151696
USDJPY	fGARCH.NGARCH	0.0387301	4224	0.0018756	4.702883e+03	-7.223234	-7.125245	-7.224757	-7.183848
USDJPY	fGARCH.NAGARCH	0.0063934	4144	0.0019274	2.010840e-01	1.860903	1.958803	1.859383	1.900253
USDJPY	fGARCH.APARCH	72.1888124	560	-0.2435315	1.153160e+04	-19.851534	-19.723830	-19.854080	-19.800207
USDJPY	fGARCH.GJRGARCH	0.0073333	4192	0.0019049	1.978985e-01	1.872267	1.970363	1.870740	1.911696
USDJPY	fGARCH.ALLGARCH	0.5988183	1028	0.0066171	5.643592e+03	-8.686667	-8.555768	-8.689322	-8.634053
USDJPY	eGARCH	0.0171090	3072	0.0025930	1.477447e+00	1.858907	1.959056	1.857319	1.899162
USDJPY	gjrGARCH	0.0070359	4240	0.0018835	2.012316e-01	1.869662	1.967680	1.868138	1.909060
USDJPY	apARCH	0.0993631	388	0.0201064	1.164008e+05	-89.214526	-89.083392	-89.217206	-89.161821
USDJPY	iGARCH	0.0086665	4240	0.0018827	1.990533e-01	1.882447	1.953189	1.881612	1.910881
USDJPY	csGARCH	0.0102435	4240	0.0018820	1.948294e-01	1.888441	2.000097	1.886494	1.933320

6.1.1.1A : Table summary

From above table 6.1.1.1A, we can compare the MSE of models which n > 4000. More number of observations, the testing of the prediction will be more accurate. For example, we try to look at the AIC and BIC values of the models, the -6 < AIC < -8 and -6 < BIC < -8 will be normal but AIC < -10 and BIC < -10 will be abnormal due to the MSE value is higher but AIC or BIC is lower.

Table Summary of the Models

Model	MSE	n	AIC.MSE	MSE.AIC	Akaike	Bayes	Shibata	Hannan.Quinn
sGARCH	0.0013002	29669	0.0002696	11.66946	-6.157999	-6.075361	-6.159095	-6.124783
fGARCH.GARCH	0.0012832	29668	0.0002696	11.66802	-6.157631	-6.074998	-6.158726	-6.124417
fGARCH.TGARCH	0.0012949	29000	0.0002758	12.34057	-5.957988	-5.861613	-5.959451	-5.919251
fGARCH.AVGARCH	0.0112037	1136	0.0070225	39.22538	-6.032229	-5.919944	-6.034204	-5.987096
fGARCH.NGARCH	0.0149964	29600	0.0002693	4449.26850	-14.173134	-14.076863	-14.174594	-14.134438
fGARCH.NAGARCH	0.0010422	26152	0.0003058	38.12585	-5.880098	-5.783370	-5.881572	-5.841219
fGARCH.APARCH	4.5402998	8904	-0.0001214	5180.24425	-16.521420	-16.410123	-16.523350	-16.476682
fGARCH.GJRGARCH	0.0011915	26596	0.0003007	12.79483	-6.165853	-6.069522	-6.167316	-6.127133
fGARCH.ALLGARCH	0.0595987	10344	0.0007619	3328.67618	-12.990287	-12.864894	-12.992707	-12.939884
eGARCH	0.0025092	21496	0.0003719	13.59811	-6.238944	-6.142035	-6.240424	-6.199991
gjrGARCH	0.0010452	29672	0.0002695	11.70280	-6.178444	-6.082163	-6.179904	-6.139744
apARCH	0.0138705	2780	0.0028677	17674.48813	-19.842106	-19.730555	-19.844050	-19.797268
iGARCH	0.0013044	29680	0.0002695	11.68434	-6.138476	-6.069479	-6.139261	-6.110743
csGARCH	0.0015497	29640	0.0002698	11.68391	-6.139894	-6.029960	-6.141772	-6.095707

6.1.1.1B : Table summary

Similar with table 6.1.1.1A but table 6.1.1.1B shows model breakdown without differentiate currency.

Table Summary of Bias

Model	n
sGARCH	2
fGARCH.GARCH	5
fGARCH.TGARCH	5
fGARCH.AVGARCH	1
fGARCH.NGARCH	69
fGARCH.NAGARCH	14
fGARCH.APARCH	17
fGARCH.GJRGARCH	4
fGARCH.ALLGARCH	63
eGARCH	13
gjrGARCH	3
apARCH	10
iGARCH	10
csGARCH	5

6.1.1.1C : Table summary number of errors.

Table above compare the numnber of bias among the models. Less number of bias will be more accurate.

Table Contains Bias

.id	Model	Date	Type	Price	Price.T1	Akaike	Bayes	Shibata	Hannan.Quinn	diff	se
USDAUD	fGARCH.TGARCH	2013-06-03	USDAUD.Op	1.02600	-7.365624e+01	24.941247	25.064162	24.938973	24.990655	7.178971e+01	1
USDAUD	fGARCH.AVGARCH	2013-04-11	USDAUD.Op	0.94800	-1.522796e+47	263.587327	263.764870	263.582672	263.658694	1.606325e+47	1
USDAUD	fGARCH.NGARCH	2013-06-27	USDAUD.Lo	1.07700	2.542027e+00	-590.320340	-590.197426	-590.322615	-590.270933	2.360285e+00	1
USDAUD	fGARCH.NGARCH	2013-08-04	USDAUD.Op	1.12300	1.260885e+39	-299.194470	-299.084911	-299.196290	-299.150426	1.122783e+39	1
USDAUD	fGARCH.NGARCH	2013-08-04	USDAUD.Cl	1.12290	9.147871e+10	192.689015	192.798574	192.687195	192.733059	8.146648e+10	1
USDAUD	fGARCH.NGARCH	2014-04-14	USDAUD.Op	1.06200	1.419924e+09	-416.149142	-416.012570	-416.151936	-416.094244	1.337028e+09	1
USDAUD	fGARCH.NGARCH	2017-03-26	USDAUD.Lo	1.30700	1.111220e-02	-586.980288	-586.857373	-586.982562	-586.930880	8.502100e-03	1
USDAUD	fGARCH.NAGARCH	2015-02-09	USDAUD.Op	1.28800	9.042209e+09	101.921621	102.058192	101.918826	101.976518	7.020349e+09	1
USDAUD	fGARCH.NAGARCH	2015-02-10	USDAUD.Op	1.28300	-9.623617e+31	153.814604	153.950801	153.811831	153.869344	7.500870e+31	1
USDAUD	fGARCH.ALLGARCH	2014-07-08	USDAUD.Op	1.06200	-3.075920e+11	-560.319314	-560.155428	-560.323299	-560.253437	2.896347e+11	1
USDAUD	apARCH	2013-05-16	USDAUD.Hi	1.03000	5.216021e+74	363.188288	363.379488	363.182914	363.265144	5.064098e+74	1
USDAUD	iGARCH	2014-10-15	USDAUD.Cl	1.13730	2.310843e+145	738.699064	738.808021	738.697272	738.742856	2.031868e+145	1
USDEUR	fGARCH.GARCH	2015-02-05	USDEUR.Hi	0.88400	2.683682e+92	412.262447	412.385024	412.260190	412.311713	3.035839e+92	1
USDEUR	fGARCH.GARCH	2017-06-18	USDEUR.Cl	0.89220	6.667688e+68	356.680437	356.817009	356.677643	356.735335	7.473311e+68	1
USDEUR	fGARCH.NGARCH	2014-10-14	USDEUR.Lo	0.77900	-2.018651e+51	-468.909622	-468.759806	-468.912961	-468.849407	2.591336e+51	1
USDEUR	fGARCH.NGARCH	2015-03-02	USDEUR.Lo	0.89000	-4.015994e+07	83.346290	83.510176	83.342305	83.412167	4.512353e+07	1
USDEUR	fGARCH.NGARCH	2015-06-04	USDEUR.Lo	0.88700	-1.394863e+18	-545.380537	-545.244340	-545.383310	-545.325796	1.572562e+18	1
USDEUR	fGARCH.NGARCH	2015-06-24	USDEUR.Lo	0.89100	1.892803e+10	77.586765	77.722962	77.583992	77.641506	2.124358e+10	1
USDEUR	fGARCH.NGARCH	2016-04-28	USDEUR.Hi	0.88000	4.510825e-01	-594.671515	-594.535319	-594.674288	-594.616775	5.125938e-01	1
USDEUR	fGARCH.APARCH	2014-10-14	USDEUR.Cl	0.79120	5.384163e+80	-406.951735	-406.815539	-406.954508	-406.896995	6.805059e+80	1
USDGBP	fGARCH.TGARCH	2014-06-19	USDGBP.Lo	0.58600	-3.465523e+73	364.832355	365.037213	364.826216	364.914701	5.913861e+73	1
USDGBP	fGARCH.NGARCH	2014-03-31	USDGBP.Cl	0.60001	-1.642110e+04	-444.661563	-444.524991	-444.664357	-444.606666	2.736805e+04	1
USDGBP	fGARCH.NGARCH	2014-05-01	USDGBP.Cl	0.59188	9.637298e-01	-516.051131	-515.914560	-516.053925	-515.996234	1.628252e+00	1
USDGBP	fGARCH.NGARCH	2014-06-19	USDGBP.Lo	0.58600	4.316118e-01	-160.018385	-159.813528	-160.024525	-159.936039	7.365389e-01	1
USDGBP	fGARCH.NGARCH	2015-04-16	USDGBP.Cl	0.67016	1.865748e+15	-556.647438	-556.511242	-556.650211	-556.592698	2.784033e+15	1
USDGBP	fGARCH.NGARCH	2015-04-21	USDGBP.Op	0.67000	-1.002521e+06	-574.983967	-574.847770	-574.986740	-574.929227	1.496300e+06	1
USDGBP	fGARCH.NGARCH	2015-06-08	USDGBP.Op	0.65200	5.022905e+36	-490.210255	-490.087678	-490.212512	-490.160989	7.703841e+36	1
USDGBP	fGARCH.NGARCH	2015-06-16	USDGBP.Op	0.63900	1.392346e+72	349.939882	350.048839	349.938090	349.983675	2.178945e+72	1
USDGBP	fGARCH.NGARCH	2016-07-19	USDGBP.Cl	0.76287	-6.365327e+09	114.898499	115.034323	114.895747	114.953084	8.343921e+09	1
USDGBP	fGARCH.NGARCH	2016-07-20	USDGBP.Hi	0.75900	7.366569e+74	-405.810489	-405.701830	-405.812268	-405.766822	9.705624e+74	1
USDGBP	fGARCH.ALLGARCH	2014-03-17	USDGBP.Op	0.60100	1.849141e+38	-496.809119	-496.644780	-496.813134	-496.743052	3.076773e+38	1
USDGBP	fGARCH.ALLGARCH	2014-04-06	USDGBP.Op	0.60300	-8.491069e+75	422.062223	422.240257	422.057533	422.133795	1.408138e+76	1
USDGBP	csGARCH	2014-12-05	USDGBP.Lo	0.63700	9.285102e+149	758.957433	759.107249	758.954093	759.017647	1.457630e+150	1
USDCHF	sGARCH	2015-01-16	USDCHF.Lo	0.85000	1.189676e+00	-6.687989	-6.606271	-6.689007	-6.655145	1.399619e+00	1
USDCHF	fGARCH.GARCH	2014-05-25	USDCHF.Hi	0.89700	-3.484066e+62	366.067877	366.273301	366.061692	366.150461	3.884132e+62	1
USDCHF	fGARCH.GARCH	2015-01-16	USDCHF.Lo	0.85000	1.189676e+00	-6.687989	-6.606271	-6.689007	-6.655145	1.399619e+00	1
USDCHF	fGARCH.TGARCH	2015-01-16	USDCHF.Lo	0.85000	1.182560e+00	-6.882116	-6.786779	-6.883495	-6.843798	1.391247e+00	1
USDCHF	fGARCH.NGARCH	2013-12-12	USDCHF.Op	0.88700	-3.879205e+00	-432.539483	-432.402912	-432.542277	-432.484586	4.373400e+00	1
USDCHF	fGARCH.NGARCH	2015-01-16	USDCHF.Lo	0.85000	1.182556e+00	-6.811955	-6.716617	-6.813334	-6.773637	1.391243e+00	1
USDCHF	fGARCH.NGARCH	2015-09-07	USDCHF.Lo	0.97000	-8.823318e+01	-587.029347	-586.920390	-587.031140	-586.985555	9.096204e+01	1
USDCHF	fGARCH.NGARCH	2015-10-30	USDCHF.Hi	0.99100	-1.889325e+01	-584.267632	-584.158374	-584.269437	-584.223714	1.906483e+01	1
USDCHF	fGARCH.NAGARCH	2013-12-05	USDCHF.Op	0.90200	4.359195e+145	731.450007	731.586578	731.447212	731.504904	4.832810e+145	1
USDCHF	fGARCH.NAGARCH	2013-12-16	USDCHF.Op	0.89000	2.195181e+145	732.215372	732.352321	732.212557	732.270427	2.466495e+145	1
USDCHF	fGARCH.NAGARCH	2015-01-09	USDCHF.Op	1.01800	-1.228938e+24	226.375920	226.539355	226.371964	226.441608	1.207208e+24	1
USDCHF	fGARCH.NAGARCH	2015-01-16	USDCHF.Lo	0.85000	1.188451e+00	-6.758750	-6.663413	-6.760129	-6.720432	1.398178e+00	1
USDCHF	fGARCH.APARCH	2014-07-28	USDCHF.Op	0.90400	-9.149533e+37	-500.116161	-499.924961	-500.121535	-500.039305	1.012116e+38	1
USDCHF	fGARCH.GJRGARCH	2015-01-16	USDCHF.Lo	0.85000	1.189203e+00	-6.775060	-6.679723	-6.776439	-6.736742	1.399062e+00	1
USDCHF	fGARCH.ALLGARCH	2014-03-13	USDCHF.Op	0.87400	1.402952e+08	-564.395228	-564.231341	-564.399213	-564.329351	1.605208e+08	1
USDCHF	fGARCH.ALLGARCH	2015-01-16	USDCHF.Lo	0.85000	1.184971e+00	-6.882670	-6.760093	-6.884927	-6.833404	1.394083e+00	1
USDCHF	eGARCH	2014-01-13	USDCHF.Op	0.90200	2.132004e+100	108.984490	109.121440	108.981675	109.039546	2.363641e+100	1
USDCHF	eGARCH	2014-08-28	USDCHF.Cl	0.91504	-3.241158e+02	62.349543	62.472457	62.347269	62.398951	3.542094e+02	1
USDCHF	eGARCH	2015-01-16	USDCHF.Lo	0.85000	1.179679e+00	-6.756294	-6.660957	-6.757673	-6.717976	1.387858e+00	1
USDCHF	eGARCH	2015-01-21	USDCHF.Lo	0.85100	5.746862e-01	-6.615293	-6.519955	-6.616671	-6.576975	6.753070e-01	1
USDCHF	gjrGARCH	2015-01-16	USDCHF.Lo	0.85000	1.187461e+00	-6.834457	-6.739119	-6.835835	-6.796138	1.397013e+00	1
USDCHF	gjrGARCH	2015-01-19	USDCHF.Lo	0.85700	5.503465e-01	-6.799206	-6.703606	-6.800595	-6.760778	6.421780e-01	1
USDCHF	iGARCH	2015-01-16	USDCHF.Lo	0.85000	1.189656e+00	-6.696311	-6.628212	-6.697021	-6.668940	1.399595e+00	1
USDCHF	iGARCH	2015-01-19	USDCHF.Lo	0.85700	5.467194e-01	-6.659730	-6.591444	-6.660445	-6.632281	6.379457e-01	1
USDCHF	iGARCH	2015-01-20	USDCHF.Lo	0.86900	1.169574e+00	-6.632037	-6.563939	-6.632748	-6.604667	1.345885e+00	1
USDCHF	iGARCH	2015-01-21	USDCHF.Lo	0.85100	5.536845e-01	-6.599117	-6.531019	-6.599827	-6.571747	6.506281e-01	1
USDCHF	iGARCH	2015-01-22	USDCHF.Lo	0.85300	1.132264e+00	-6.569994	-6.501896	-6.570705	-6.542624	1.327390e+00	1
USDCHF	iGARCH	2015-01-26	USDCHF.Lo	0.87600	1.153558e+00	-6.519110	-6.450824	-6.519825	-6.491661	1.316847e+00	1
USDCHF	iGARCH	2015-01-27	USDCHF.Lo	0.89400	6.896106e-01	-6.470927	-6.402829	-6.471637	-6.443557	7.713765e-01	1
USDCHF	iGARCH	2015-02-02	USDCHF.Lo	0.92000	7.319616e-01	-6.350835	-6.255235	-6.352225	-6.312407	7.956105e-01	1
USDCHF	csGARCH	2015-01-16	USDCHF.Lo	0.85000	1.193636e+00	-6.688153	-6.579196	-6.689945	-6.644361	1.404278e+00	1
USDCHF	csGARCH	2015-01-22	USDCHF.Lo	0.85300	1.141360e+00	-6.534724	-6.425767	-6.536516	-6.490932	1.338054e+00	1
USDCHF	csGARCH	2015-01-23	USDCHF.Lo	0.86800	6.200740e-01	-6.493151	-6.384194	-6.494943	-6.449359	7.143710e-01	1
USDCAD	fGARCH.NGARCH	2015-02-05	USDCAD.Hi	1.25800	-2.752758e+42	-487.602382	-487.425326	-487.607002	-487.531219	2.188202e+42	1
USDCAD	fGARCH.NGARCH	2015-02-09	USDCAD.Cl	1.25170	-7.979335e+22	142.673774	142.783031	142.671968	142.717692	6.374798e+22	1
USDCAD	fGARCH.NGARCH	2015-03-29	USDCAD.Hi	1.27000	-6.542943e+22	-529.240306	-529.131049	-529.242112	-529.196389	5.151924e+22	1
USDCAD	fGARCH.NGARCH	2015-07-21	USDCAD.Hi	1.30500	4.139802e+61	-435.142670	-435.006474	-435.145443	-435.087930	3.172262e+61	1
USDCAD	fGARCH.NGARCH	2016-05-02	USDCAD.Hi	1.27000	2.847428e+37	-493.891329	-493.741100	-493.894693	-493.830942	2.242069e+37	1
USDCAD	fGARCH.ALLGARCH	2015-02-09	USDCAD.Op	1.25200	1.586578e+17	110.076307	110.212879	110.073513	110.131204	1.267235e+17	1
USDCAD	eGARCH	2015-08-26	USDCAD.Hi	1.33000	-3.733849e+102	106.421678	106.557874	106.418905	106.476418	2.807405e+102	1
USDCAD	eGARCH	2016-02-11	USDCAD.Cl	1.39230	-2.425122e+125	65.726271	65.862843	65.723477	65.781169	1.741810e+125	1
USDCNY	sGARCH	2014-07-10	USDCNY.Lo	2.20100	2.987751e+00	-4.665480	-4.583537	-4.666505	-4.632541	1.357452e+00	1
USDCNY	fGARCH.GARCH	2014-07-10	USDCNY.Lo	2.20100	2.987874e+00	-4.665479	-4.583536	-4.666505	-4.632541	1.357508e+00	1
USDCNY	fGARCH.TGARCH	2013-10-09	USDCNY.Op	6.11100	5.483283e+03	60.013013	60.135928	60.010739	60.062421	8.972808e+02	1
USDCNY	fGARCH.NGARCH	2014-07-17	USDCNY.Lo	6.19200	-5.016306e+02	-585.712986	-585.631043	-585.714011	-585.680047	8.101269e+01	1
USDCNY	fGARCH.NGARCH	2014-07-20	USDCNY.Lo	6.19500	1.194381e+01	-589.430373	-589.348203	-589.431406	-589.397340	1.927975e+00	1
USDCNY	fGARCH.NGARCH	2014-07-22	USDCNY.Lo	6.18900	1.945038e+01	-591.466725	-591.384782	-591.467750	-591.433786	3.142734e+00	1
USDCNY	fGARCH.NGARCH	2014-07-23	USDCNY.Lo	6.18200	-3.637318e+01	-588.553531	-588.471588	-588.554557	-588.520593	5.883724e+00	1
USDCNY	fGARCH.NGARCH	2014-07-27	USDCNY.Lo	6.17600	4.872521e+01	-587.187420	-587.105250	-587.188453	-587.154387	7.889444e+00	1
USDCNY	fGARCH.NGARCH	2014-07-31	USDCNY.Lo	6.16300	2.769268e+01	-590.455881	-590.373938	-590.456907	-590.422943	4.493377e+00	1
USDCNY	fGARCH.NGARCH	2014-08-03	USDCNY.Lo	6.16800	3.201427e+01	-587.733648	-587.651478	-587.734681	-587.700615	5.190381e+00	1
USDCNY	fGARCH.NGARCH	2014-08-05	USDCNY.Lo	6.15300	1.853196e+01	-589.664961	-589.583018	-589.665987	-589.632023	3.011858e+00	1
USDCNY	fGARCH.NGARCH	2014-08-06	USDCNY.Lo	6.14700	2.635122e+01	-591.728569	-591.646626	-591.729595	-591.695631	4.286842e+00	1
USDCNY	fGARCH.NGARCH	2014-08-10	USDCNY.Lo	6.14400	5.336958e+01	-588.785684	-588.703514	-588.786717	-588.752651	8.686456e+00	1
USDCNY	fGARCH.NGARCH	2014-08-12	USDCNY.Lo	6.14400	4.740305e+01	-587.300349	-587.218406	-587.301374	-587.267410	7.715340e+00	1
USDCNY	fGARCH.NGARCH	2014-08-13	USDCNY.Lo	6.14200	8.825968e+00	-589.224653	-589.142710	-589.225679	-589.191715	1.436986e+00	1
USDCNY	fGARCH.NGARCH	2014-08-14	USDCNY.Lo	6.13600	4.872331e+01	-586.351874	-586.269931	-586.352899	-586.318935	7.940565e+00	1
USDCNY	fGARCH.NGARCH	2014-08-19	USDCNY.Lo	6.13000	-1.240483e+01	-590.789977	-590.708034	-590.791003	-590.757039	2.023627e+00	1
USDCNY	fGARCH.NGARCH	2014-08-20	USDCNY.Lo	6.13000	9.161532e+00	-592.227353	-592.145410	-592.228379	-592.194415	1.494540e+00	1
USDCNY	fGARCH.NGARCH	2014-08-21	USDCNY.Lo	6.14100	-1.525661e+01	-590.144127	-590.062184	-590.145153	-590.111189	2.484385e+00	1
USDCNY	fGARCH.NGARCH	2014-08-24	USDCNY.Lo	6.14000	-3.247607e+01	-589.174302	-589.092132	-589.175335	-589.141269	5.289262e+00	1
USDCNY	fGARCH.NGARCH	2014-08-25	USDCNY.Lo	6.14200	6.174800e+01	-572.956479	-572.874536	-572.957505	-572.923541	1.005340e+01	1
USDCNY	fGARCH.NGARCH	2014-08-26	USDCNY.Lo	6.13300	9.738678e+01	-587.251542	-587.169599	-587.252568	-587.218604	1.587914e+01	1
USDCNY	fGARCH.NGARCH	2014-08-31	USDCNY.Lo	6.12900	2.545583e+02	-584.923023	-584.840853	-584.924056	-584.889989	4.153341e+01	1
USDCNY	fGARCH.NGARCH	2014-09-01	USDCNY.Lo	6.13200	1.596999e+02	-584.161053	-584.079110	-584.162079	-584.128115	2.604369e+01	1
USDCNY	fGARCH.NGARCH	2014-09-02	USDCNY.Lo	6.13100	-1.989882e+01	-589.399865	-589.317922	-589.400891	-589.366927	3.245608e+00	1
USDCNY	fGARCH.NGARCH	2014-09-04	USDCNY.Lo	6.12800	-2.866168e+01	-585.515480	-585.433537	-585.516505	-585.482541	4.677168e+00	1
USDCNY	fGARCH.NGARCH	2014-09-08	USDCNY.Lo	6.12200	-2.517129e+01	-587.872377	-587.790434	-587.873402	-587.839438	4.111612e+00	1
USDCNY	fGARCH.NGARCH	2014-09-11	USDCNY.Lo	6.12000	1.708482e+01	-588.380157	-588.298214	-588.381183	-588.347219	2.791637e+00	1
USDCNY	fGARCH.NGARCH	2014-09-14	USDCNY.Lo	6.12500	-7.626137e+01	-589.072288	-588.990119	-589.073322	-589.039255	1.245084e+01	1
USDCNY	fGARCH.NGARCH	2014-09-16	USDCNY.Lo	6.12900	-1.759094e+02	-585.597533	-585.515590	-585.598558	-585.564594	2.870116e+01	1
USDCNY	fGARCH.NGARCH	2014-09-21	USDCNY.Lo	6.12800	-2.039517e+01	-588.488512	-588.406343	-588.489546	-588.455479	3.328194e+00	1
USDCNY	fGARCH.NGARCH	2014-09-23	USDCNY.Lo	6.12400	1.512941e+01	-590.152856	-590.070913	-590.153882	-590.119918	2.470511e+00	1
USDCNY	fGARCH.NGARCH	2014-10-01	USDCNY.Lo	6.12800	-1.146657e+02	-584.091459	-584.009516	-584.092485	-584.058521	1.871177e+01	1
USDCNY	fGARCH.NGARCH	2014-10-06	USDCNY.Lo	6.12900	-2.283202e+01	-579.908511	-579.826568	-579.909537	-579.875573	3.725243e+00	1
USDCNY	fGARCH.NGARCH	2014-10-07	USDCNY.Lo	6.12500	5.146397e+01	-565.845084	-565.763141	-565.846110	-565.812146	8.402281e+00	1
USDCNY	fGARCH.NGARCH	2014-10-09	USDCNY.Lo	6.12000	6.182692e+01	-583.758544	-583.676826	-583.759562	-583.725700	1.010244e+01	1
USDCNY	fGARCH.NGARCH	2014-11-26	USDCNY.Lo	6.12300	6.187566e+01	-583.601907	-583.520189	-583.602924	-583.569062	1.010545e+01	1
USDCNY	fGARCH.NGARCH	2017-06-15	USDCNY.Op	6.80600	-1.649282e+44	-461.947546	-461.824970	-461.949803	-461.898280	2.423276e+43	1
USDCNY	fGARCH.NAGARCH	2014-07-10	USDCNY.Lo	2.20100	2.977219e+00	-4.669064	-4.573464	-4.670453	-4.630636	1.352666e+00	1
USDCNY	fGARCH.NAGARCH	2014-07-24	USDCNY.Lo	6.18200	-3.603032e+02	14.561667	14.643610	14.560642	14.594606	5.828262e+01	1
USDCNY	fGARCH.NAGARCH	2014-07-29	USDCNY.Lo	6.16200	-3.579216e+02	14.548624	14.630567	14.547598	14.581562	5.808530e+01	1
USDCNY	fGARCH.NAGARCH	2014-07-31	USDCNY.Lo	6.16300	-3.531901e+02	14.522470	14.604413	14.521444	14.555409	5.730814e+01	1
USDCNY	fGARCH.NAGARCH	2014-08-04	USDCNY.Lo	6.16100	-3.492923e+02	14.548440	14.630382	14.547414	14.581378	5.669409e+01	1
USDCNY	fGARCH.NAGARCH	2014-08-26	USDCNY.Lo	6.13300	4.865151e+00	104.667516	104.749459	104.666490	104.700454	7.932742e-01	1
USDCNY	fGARCH.NAGARCH	2014-09-04	USDCNY.Lo	6.12800	4.796821e+02	172.167572	172.249515	172.166546	172.200510	7.827710e+01	1
USDCNY	fGARCH.NAGARCH	2014-10-19	USDCNY.Lo	6.11300	-3.344848e+02	98.972743	99.054686	98.971717	99.005682	5.471696e+01	1
USDCNY	fGARCH.APARCH	2013-10-29	USDCNY.Hi	6.13400	2.876649e+25	-526.990144	-526.826258	-526.994129	-526.924267	4.689679e+24	1
USDCNY	fGARCH.APARCH	2013-11-07	USDCNY.Hi	6.14400	-8.647337e+68	-406.983178	-406.819292	-406.987163	-406.917301	1.407444e+68	1
USDCNY	fGARCH.APARCH	2014-06-19	USDCNY.Hi	6.22100	-7.210200e+39	-479.345003	-479.181117	-479.348988	-479.279126	1.159010e+39	1
USDCNY	fGARCH.APARCH	2014-07-15	USDCNY.Lo	6.19400	2.096796e+01	-591.356584	-591.260983	-591.357973	-591.318155	3.385206e+00	1
USDCNY	fGARCH.APARCH	2014-07-24	USDCNY.Lo	6.18200	2.156616e+01	103.442134	103.537734	103.440745	103.480562	3.488541e+00	1
USDCNY	fGARCH.APARCH	2014-08-18	USDCNY.Lo	6.12700	4.686359e+01	-590.025600	-589.930000	-590.026990	-589.987172	7.648701e+00	1
USDCNY	fGARCH.APARCH	2014-08-20	USDCNY.Lo	6.13000	-1.738365e+02	-587.118563	-587.022963	-587.119952	-587.080135	2.835831e+01	1
USDCNY	fGARCH.APARCH	2014-09-22	USDCNY.Lo	6.12800	2.649730e+02	-583.798821	-583.703221	-583.800210	-583.760393	4.323972e+01	1
USDCNY	fGARCH.APARCH	2014-11-20	USDCNY.Lo	6.10900	-1.204425e+02	-584.497904	-584.402566	-584.499282	-584.459586	1.971558e+01	1
USDCNY	fGARCH.APARCH	2014-11-26	USDCNY.Lo	6.12300	1.763058e+02	-584.737735	-584.642398	-584.739114	-584.699417	2.879403e+01	1
USDCNY	fGARCH.APARCH	2014-12-19	USDCNY.Lo	6.20500	1.811908e+02	-585.237794	-585.142457	-585.239173	-585.199476	2.920077e+01	1
USDCNY	fGARCH.GJRGARCH	2014-07-10	USDCNY.Lo	2.20100	2.979918e+00	-4.677596	-4.581996	-4.678985	-4.639168	1.353893e+00	1
USDCNY	fGARCH.GJRGARCH	2014-09-01	USDCNY.Lo	6.13200	1.263740e+01	98.054293	98.136236	98.053267	98.087231	2.060893e+00	1
USDCNY	fGARCH.GJRGARCH	2014-11-12	USDCNY.Lo	6.11400	-3.508494e+01	94.016565	94.098283	94.015548	94.049410	5.738460e+00	1
USDCNY	fGARCH.ALLGARCH	2013-03-19	USDCNY.Op	6.21400	1.851958e+30	-506.919310	-506.755875	-506.923266	-506.853622	2.980300e+29	1
USDCNY	fGARCH.ALLGARCH	2014-07-10	USDCNY.Lo	2.20100	2.966190e+00	-4.732654	-4.609740	-4.734928	-4.683247	1.347655e+00	1
USDCNY	fGARCH.ALLGARCH	2014-07-16	USDCNY.Lo	6.19100	-3.928444e+01	-582.734556	-582.625298	-582.736361	-582.690638	6.345410e+00	1
USDCNY	fGARCH.ALLGARCH	2014-07-17	USDCNY.Lo	6.19200	1.616838e+02	-583.779418	-583.670160	-583.781223	-583.735500	2.611173e+01	1
USDCNY	fGARCH.ALLGARCH	2014-07-20	USDCNY.Lo	6.19500	3.493327e+01	-587.564830	-587.455270	-587.566649	-587.520785	5.638946e+00	1
USDCNY	fGARCH.ALLGARCH	2014-07-21	USDCNY.Lo	6.19300	2.379018e+02	-582.588057	-582.478800	-582.589863	-582.544139	3.841462e+01	1
USDCNY	fGARCH.ALLGARCH	2014-07-27	USDCNY.Lo	6.17600	6.750841e+01	-588.539587	-588.430027	-588.541406	-588.495542	1.093077e+01	1
USDCNY	fGARCH.ALLGARCH	2014-07-31	USDCNY.Lo	6.16300	-1.535570e+01	-587.168301	-587.059044	-587.170107	-587.124384	2.491595e+00	1
USDCNY	fGARCH.ALLGARCH	2014-08-03	USDCNY.Lo	6.16800	-1.336380e+01	-588.926648	-588.817089	-588.928467	-588.882604	2.166635e+00	1
USDCNY	fGARCH.ALLGARCH	2014-08-05	USDCNY.Lo	6.15300	6.028594e+02	19.084869	19.194126	19.083063	19.128787	9.797812e+01	1
USDCNY	fGARCH.ALLGARCH	2014-08-06	USDCNY.Lo	6.14700	2.980786e+01	-588.051008	-587.941750	-588.052813	-588.007090	4.849171e+00	1
USDCNY	fGARCH.ALLGARCH	2014-08-07	USDCNY.Lo	6.14600	-7.094383e+01	-586.949487	-586.840229	-586.951292	-586.905569	1.154309e+01	1
USDCNY	fGARCH.ALLGARCH	2014-08-11	USDCNY.Lo	6.14400	2.489838e+01	-587.776345	-587.667088	-587.778151	-587.732427	4.052471e+00	1
USDCNY	fGARCH.ALLGARCH	2014-08-12	USDCNY.Lo	6.14400	6.297337e+01	-587.294543	-587.185286	-587.296349	-587.250625	1.024957e+01	1
USDCNY	fGARCH.ALLGARCH	2014-08-13	USDCNY.Lo	6.14200	-2.219940e+01	-590.296221	-590.186964	-590.298027	-590.252303	3.614361e+00	1
USDCNY	fGARCH.ALLGARCH	2014-08-14	USDCNY.Lo	6.13600	-1.404711e+02	-587.700902	-587.591645	-587.702708	-587.656984	2.289295e+01	1
USDCNY	fGARCH.ALLGARCH	2014-08-17	USDCNY.Lo	6.13300	5.944981e+02	109.501754	109.611314	109.499935	109.545799	9.693430e+01	1
USDCNY	fGARCH.ALLGARCH	2014-08-19	USDCNY.Lo	6.13000	-5.155929e+01	-585.152751	-585.043494	-585.154557	-585.108833	8.410978e+00	1
USDCNY	fGARCH.ALLGARCH	2014-08-20	USDCNY.Lo	6.13000	-1.929233e+02	-586.176906	-586.067649	-586.178711	-586.132988	3.147199e+01	1
USDCNY	fGARCH.ALLGARCH	2014-08-24	USDCNY.Lo	6.14000	1.671067e+01	-588.414218	-588.304658	-588.416037	-588.370173	2.721608e+00	1
USDCNY	fGARCH.ALLGARCH	2014-08-25	USDCNY.Lo	6.14200	2.016595e+01	-590.032967	-589.923710	-590.034773	-589.989049	3.283287e+00	1
USDCNY	fGARCH.ALLGARCH	2014-08-26	USDCNY.Lo	6.13300	-9.193458e+00	-592.028938	-591.919680	-592.030743	-591.985020	1.499015e+00	1
USDCNY	fGARCH.ALLGARCH	2014-08-27	USDCNY.Lo	6.13200	9.527845e+01	-586.491601	-586.382343	-586.493406	-586.447683	1.553791e+01	1
USDCNY	fGARCH.ALLGARCH	2014-09-03	USDCNY.Lo	6.12500	-3.275840e+02	13.412488	13.521745	13.410682	13.456406	5.348311e+01	1
USDCNY	fGARCH.ALLGARCH	2014-09-10	USDCNY.Lo	6.11900	3.412713e+01	-588.214319	-588.105062	-588.216125	-588.170401	5.577240e+00	1
USDCNY	fGARCH.ALLGARCH	2014-09-11	USDCNY.Lo	6.12000	1.713551e+02	-585.306314	-585.197057	-585.308120	-585.262397	2.799920e+01	1
USDCNY	fGARCH.ALLGARCH	2014-09-14	USDCNY.Lo	6.12500	-1.143873e+01	-591.115129	-591.005570	-591.116949	-591.071085	1.867548e+00	1
USDCNY	fGARCH.ALLGARCH	2014-09-15	USDCNY.Lo	6.13200	6.270890e+01	-587.125551	-587.016294	-587.127357	-587.081633	1.022650e+01	1
USDCNY	fGARCH.ALLGARCH	2014-09-17	USDCNY.Lo	6.12900	1.185828e+01	-590.965879	-590.856622	-590.967685	-590.921961	1.934781e+00	1
USDCNY	fGARCH.ALLGARCH	2014-09-18	USDCNY.Lo	6.12700	5.849842e+01	-586.243193	-586.133936	-586.244999	-586.199275	9.547645e+00	1
USDCNY	fGARCH.ALLGARCH	2014-09-22	USDCNY.Lo	6.12800	-7.554483e+01	-585.523762	-585.414505	-585.525568	-585.479844	1.232781e+01	1
USDCNY	fGARCH.ALLGARCH	2014-09-23	USDCNY.Lo	6.12400	6.743292e+01	-586.611629	-586.502371	-586.613434	-586.567711	1.101125e+01	1
USDCNY	fGARCH.ALLGARCH	2014-09-24	USDCNY.Lo	6.12500	-1.361419e+02	-583.665628	-583.556371	-583.667434	-583.621710	2.222725e+01	1
USDCNY	fGARCH.ALLGARCH	2014-09-28	USDCNY.Lo	6.11700	-1.470848e+00	-589.397050	-589.287490	-589.398869	-589.353005	2.404524e-01	1
USDCNY	fGARCH.ALLGARCH	2014-10-02	USDCNY.Lo	6.12800	-1.655563e+01	-586.788690	-586.679433	-586.790496	-586.744772	2.701636e+00	1
USDCNY	fGARCH.ALLGARCH	2014-10-05	USDCNY.Lo	6.12900	1.461850e+01	-590.597425	-590.487865	-590.599244	-590.553380	2.385136e+00	1
USDCNY	fGARCH.ALLGARCH	2014-10-07	USDCNY.Lo	6.12500	-2.893222e+00	-592.477892	-592.368634	-592.479697	-592.433974	4.723629e-01	1
USDCNY	fGARCH.ALLGARCH	2014-10-13	USDCNY.Lo	6.11300	6.047961e+01	-587.057935	-586.948978	-587.059727	-587.014143	9.893606e+00	1
USDCNY	fGARCH.ALLGARCH	2014-10-15	USDCNY.Lo	6.11200	-2.322660e+02	-584.723325	-584.614368	-584.725117	-584.679533	3.800164e+01	1
USDCNY	fGARCH.ALLGARCH	2014-10-28	USDCNY.Lo	6.10300	5.800710e+01	-589.031088	-588.922131	-589.032880	-588.987295	9.504686e+00	1
USDCNY	fGARCH.ALLGARCH	2014-11-04	USDCNY.Lo	6.10500	-1.520227e+02	-585.103628	-584.994670	-585.105420	-585.059835	2.490134e+01	1
USDCNY	fGARCH.ALLGARCH	2014-11-07	USDCNY.Lo	6.10200	3.102281e+01	-590.154705	-590.045748	-590.156497	-590.110913	5.084040e+00	1
USDCNY	fGARCH.ALLGARCH	2014-11-10	USDCNY.Lo	6.10500	-1.387418e+02	-584.273462	-584.164205	-584.275268	-584.229544	2.272592e+01	1
USDCNY	fGARCH.ALLGARCH	2014-11-20	USDCNY.Lo	6.10900	-4.671149e+01	-588.176614	-588.067656	-588.178406	-588.132821	7.646340e+00	1
USDCNY	fGARCH.ALLGARCH	2014-11-25	USDCNY.Lo	6.12600	-3.509017e+01	-588.097661	-587.988704	-588.099453	-588.053869	5.728072e+00	1
USDCNY	fGARCH.ALLGARCH	2014-11-27	USDCNY.Lo	6.12500	-4.766673e+01	-589.227416	-589.118459	-589.229208	-589.183624	7.782323e+00	1
USDCNY	fGARCH.ALLGARCH	2014-12-02	USDCNY.Lo	6.13700	-3.559250e+01	-586.845104	-586.736147	-586.846896	-586.801311	5.799658e+00	1
USDCNY	fGARCH.ALLGARCH	2014-12-05	USDCNY.Lo	6.14000	-1.335011e+00	-590.219456	-590.110499	-590.221248	-590.175664	2.174285e-01	1
USDCNY	fGARCH.ALLGARCH	2014-12-18	USDCNY.Lo	6.18700	2.127975e+01	-591.310725	-591.201768	-591.312518	-591.266933	3.439430e+00	1
USDCNY	fGARCH.ALLGARCH	2014-12-19	USDCNY.Lo	6.20500	1.828485e+01	-589.889033	-589.780075	-589.890825	-589.845240	2.946793e+00	1
USDCNY	eGARCH	2014-07-10	USDCNY.Lo	2.20100	2.758887e+00	-4.752441	-4.656841	-4.753830	-4.714013	1.253470e+00	1
USDCNY	gjrGARCH	2014-07-10	USDCNY.Lo	2.20100	2.894085e+00	-4.702450	-4.606850	-4.703839	-4.664022	1.314895e+00	1
USDCNY	iGARCH	2014-07-10	USDCNY.Lo	2.20100	2.988228e+00	-4.673441	-4.605156	-4.674157	-4.645993	1.357668e+00	1
USDCNY	csGARCH	2014-03-19	USDCNY.Op	6.18200	-4.743008e+149	761.606011	761.769897	761.602025	761.671888	7.672287e+148	1
USDJPY	fGARCH.TGARCH	2013-03-31	USDJPY.Op	94.26200	-5.215159e+89	433.750440	433.914326	433.746455	433.816317	5.532621e+87	1
USDJPY	fGARCH.NGARCH	2013-05-20	USDJPY.Hi	102.87200	1.639729e+20	126.895461	127.031657	126.892687	126.950201	1.593951e+18	1
USDJPY	fGARCH.NGARCH	2013-06-16	USDJPY.Hi	95.10600	-2.728130e+05	179.131969	179.268541	179.129175	179.186867	2.868516e+03	1
USDJPY	fGARCH.NGARCH	2013-06-17	USDJPY.Hi	95.75300	3.511368e+02	10.570756	10.706952	10.567983	10.625496	3.667111e+00	1
USDJPY	fGARCH.NGARCH	2013-06-19	USDJPY.Hi	98.23900	4.076553e+124	740.361014	740.497210	740.358240	740.415754	4.149628e+122	1
USDJPY	fGARCH.NGARCH	2013-07-01	USDJPY.Hi	100.43800	4.397652e+23	-244.819452	-244.683255	-244.822225	-244.764711	4.378474e+21	1
USDJPY	fGARCH.NGARCH	2013-07-22	USDJPY.Hi	100.17000	-7.099425e+16	107.520826	107.657022	107.518052	107.575566	7.087376e+14	1
USDJPY	fGARCH.APARCH	2013-02-07	USDJPY.Lo	93.09300	-3.970675e+14	-210.537651	-210.401828	-210.540404	-210.483067	4.265278e+12	1
USDJPY	fGARCH.APARCH	2013-03-29	USDJPY.Hi	94.25500	1.067074e+03	-571.141577	-570.936720	-571.147717	-571.059231	1.132114e+01	1
USDJPY	fGARCH.APARCH	2013-05-13	USDJPY.Hi	102.26100	1.875536e+63	-401.564171	-401.441594	-401.566428	-401.514904	1.834068e+61	1
USDJPY	fGARCH.APARCH	2013-06-12	USDJPY.Hi	95.93000	-1.338837e+49	118.941807	119.091623	118.938467	119.002021	1.395639e+47	1
USDJPY	fGARCH.ALLGARCH	2013-04-08	USDJPY.Lo	98.63900	2.419383e+10	-45.341071	-45.164015	-45.345691	-45.269908	2.452765e+08	1
USDJPY	fGARCH.ALLGARCH	2013-04-14	USDJPY.Lo	97.62300	1.365824e+02	9.689241	9.866784	9.684586	9.760608	1.399080e+00	1
USDJPY	fGARCH.ALLGARCH	2013-05-15	USDJPY.Lo	101.85000	1.719010e+30	-497.287445	-497.124010	-497.291401	-497.221757	1.687786e+28	1
USDJPY	fGARCH.ALLGARCH	2013-05-15	USDJPY.Cl	102.25800	6.921087e+61	309.378416	309.555471	309.373795	309.449578	6.768259e+59	1
USDJPY	fGARCH.ALLGARCH	2013-06-19	USDJPY.Lo	96.21100	-8.650911e+03	78.994799	79.117376	78.992542	79.044066	8.991603e+01	1
USDJPY	fGARCH.ALLGARCH	2013-12-03	USDJPY.Hi	103.36900	3.656304e+138	-201.516514	-201.352628	-201.520499	-201.450637	3.537137e+136	1
USDJPY	fGARCH.ALLGARCH	2013-12-12	USDJPY.Hi	103.07700	-3.572408e+44	285.951103	286.128646	285.946448	286.022470	3.465767e+42	1
USDJPY	eGARCH	2013-03-19	USDJPY.Lo	94.77000	2.936350e+60	155.742660	155.919716	155.738040	155.813823	3.098396e+58	1
USDJPY	eGARCH	2013-04-07	USDJPY.Hi	99.01600	-1.249428e+80	167.045855	167.196083	167.042490	167.106242	1.261845e+78	1
USDJPY	eGARCH	2013-04-14	USDJPY.Lo	97.62300	-5.344121e+15	115.987973	116.138202	115.984609	116.048361	5.474244e+13	1
USDJPY	eGARCH	2013-05-13	USDJPY.Hi	102.26100	1.483098e+63	161.813922	161.922879	161.812130	161.857714	1.450307e+61	1
USDJPY	eGARCH	2013-06-16	USDJPY.Hi	95.10600	2.867306e+54	123.668672	123.805244	123.665878	123.723570	3.014853e+52	1
USDJPY	eGARCH	2013-11-18	USDJPY.Hi	100.33300	-1.192013e+13	283.354744	283.491693	283.351929	283.409799	1.188057e+11	1
USDJPY	apARCH	2013-01-29	USDJPY.Hi	90.99000	-1.175138e+50	-1305.505004	-1305.341568	-1305.508959	-1305.439315	1.291503e+48	1
USDJPY	apARCH	2013-03-15	USDJPY.Lo	95.16000	-1.758223e+61	315.688639	315.824835	315.685866	315.743379	1.847649e+59	1
USDJPY	apARCH	2013-04-04	USDJPY.Lo	95.81700	6.156224e+02	8.903971	9.094646	8.898637	8.980607	6.424981e+00	1
USDJPY	apARCH	2013-04-09	USDJPY.Hi	99.69400	-7.412985e+02	-1357.528473	-1357.392277	-1357.531246	-1357.473733	7.435739e+00	1
USDJPY	apARCH	2013-04-17	USDJPY.Lo	97.64000	-4.147166e+22	-1334.100214	-1333.950398	-1334.103553	-1334.039999	4.247405e+20	1
USDJPY	apARCH	2013-05-06	USDJPY.Op	99.36400	-2.666861e+24	223.445230	223.595046	223.441891	223.505445	2.683931e+22	1
USDJPY	apARCH	2013-05-09	USDJPY.Hi	101.94900	-3.960522e+122	494.605046	494.727623	494.602789	494.654312	3.884807e+120	1
USDJPY	apARCH	2013-05-14	USDJPY.Hi	102.76000	6.892843e+01	-1352.815761	-1352.652325	-1352.819717	-1352.750072	6.707710e-01	1
USDJPY	apARCH	2013-05-15	USDJPY.Cl	102.25800	-4.614626e+04	12.698392	12.861828	12.694436	12.764081	4.512728e+02	1

6.1.1.1D : Table Contain Bias dataset.

Above table shows the details of prediction result which bias. Based on above table, we can know every single wrong prediction result or wrong AIC/BIC. You can know which model predict which currency for which date is wrong or bias.

Now we try to filter the dataset which contain OHLC of 7 currecies.

## Bias which contain OHLC of 7 currencies.
acc <- fx %>% dplyr::filter(Date %in% ntimeID2) %>% 
  ddply(.(.id, Model), summarise, 
        MSE = mean((Price.T1 - Price)^2), 
        n = length(Price), 
        AIC.MSE = (-2*MSE)/n+2*4/n, 
        MSE.AIC = mean((Akaike - mean(Akaike))^2),
        Akaike = mean(Akaike), 
        Bayes = mean(Bayes), 
        Shibata = mean(Shibata), 
        Hannan.Quinn = mean(Hannan.Quinn)) %>% 
  tbl_df %>% mutate(MSE = round(MSE, 7))

Group Table Summary

.id	Model	MSE	n	AIC.MSE	MSE.AIC	Akaike	Bayes	Shibata	Hannan.Quinn
USD/AUD
USDAUD	sGARCH	0.0000000	4	2.000000	0.0042571	-7.7157954	-7.6442923	-7.7165827	-7.6870568
USDAUD	fGARCH.GARCH	0.0000000	4	2.000000	0.0042571	-7.7157308	-7.6442277	-7.7165180	-7.6869921
USDAUD	fGARCH.TGARCH	0.0000000	4	2.000000	0.0040899	-7.7115975	-7.6264748	-7.7127056	-7.6773848
USDAUD	fGARCH.AVGARCH	0.0000000	4	2.000000	0.0046426	-7.7096123	-7.6108700	-7.7110944	-7.6699256
USDAUD	fGARCH.NGARCH	0.0000000	4	2.000000	0.0042573	-7.7086240	-7.6235013	-7.7097321	-7.6744113
USDAUD	fGARCH.NAGARCH	0.0000000	4	2.000000	0.0044076	-7.7252460	-7.6401232	-7.7263541	-7.6910333
USDAUD	fGARCH.APARCH	0.0000000	4	2.000000	0.0045248	-7.7121329	-7.6133905	-7.7136150	-7.6724462
USDAUD	fGARCH.GJRGARCH	0.0000000	4	2.000000	0.0045302	-7.7194559	-7.6343332	-7.7205640	-7.6852432
USDAUD	fGARCH.ALLGARCH	0.0000000	4	2.000000	0.0046029	-7.7114799	-7.5991179	-7.7133882	-7.6663191
USDAUD	eGARCH	0.0000000	4	2.000000	0.0043887	-7.7275210	-7.6423983	-7.7286292	-7.6933084
USDAUD	gjrGARCH	0.0000000	4	2.000000	0.0045379	-7.7195102	-7.6343875	-7.7206184	-7.6852975
USDAUD	apARCH	0.0000000	4	2.000000	0.0045312	-7.7121916	-7.6134493	-7.7136737	-7.6725049
USDAUD	iGARCH	0.0000000	4	2.000000	0.0041693	-7.7214244	-7.6635410	-7.7219447	-7.6981598
USDAUD	csGARCH	0.0000000	4	2.000000	0.0045144	-7.7006430	-7.6019007	-7.7021251	-7.6609563
USD/CAD
USDEUR	sGARCH	0.0000000	4	2.000000	0.6050811	-7.6998813	-7.5943291	-7.7017000	-7.6574575
USDEUR	fGARCH.GARCH	0.0000000	4	2.000000	0.6048705	-7.6997431	-7.5941909	-7.7015618	-7.6573194
USDEUR	fGARCH.TGARCH	0.0000000	4	2.000000	0.2397655	-7.6699895	-7.5508176	-7.6722585	-7.6220917
USDEUR	fGARCH.AVGARCH	0.0000001	4	2.000000	0.3127196	-7.8253571	-7.6925656	-7.8281276	-7.7719853
USDEUR	fGARCH.NGARCH	0.0000001	4	2.000000	0.2303104	-7.8613915	-7.7422197	-7.8636606	-7.8134938
USDEUR	fGARCH.NAGARCH	0.0000000	4	2.000000	0.4971729	-7.7737017	-7.6545298	-7.7759707	-7.7258039
USDEUR	fGARCH.APARCH	0.0000000	4	2.000000	0.3255517	-7.8170471	-7.6842556	-7.8198177	-7.7636753
USDEUR	fGARCH.GJRGARCH	0.0000000	4	2.000000	0.6011446	-7.7266217	-7.6074498	-7.7288907	-7.6787239
USDEUR	fGARCH.ALLGARCH	0.0000001	4	2.000000	0.2042237	-7.8817577	-7.7353466	-7.8850803	-7.8229118
USDEUR	eGARCH	0.0000000	4	2.000000	0.0294717	-8.1069604	-7.9877886	-8.1092294	-8.0590626
USDEUR	gjrGARCH	0.0000001	4	2.000000	0.6060193	-7.7316377	-7.6124659	-7.7339067	-7.6837399
USDEUR	apARCH	0.0000000	4	2.000000	0.2455494	-7.8656406	-7.7328491	-7.8684111	-7.8122688
USDEUR	iGARCH	0.0000000	4	2.000000	0.5011615	-7.7435079	-7.6515754	-7.7449283	-7.7065582
USDEUR	csGARCH	0.0000000	4	2.000000	0.0428158	-8.0263288	-7.8935374	-8.0290994	-7.9729571
USD/CHF
USDGBP	sGARCH	0.0000001	4	2.000000	0.8403505	-8.7045263	-8.6332190	-8.7053077	-8.6758696
USDGBP	fGARCH.GARCH	0.0000001	4	2.000000	0.8403599	-8.7045383	-8.6332310	-8.7053197	-8.6758816
USDGBP	fGARCH.TGARCH	0.0000000	4	2.000000	0.5772550	-8.6611404	-8.5762508	-8.6622403	-8.6270253
USDGBP	fGARCH.AVGARCH	0.0000000	4	2.000000	0.4602830	-8.4926470	-8.3941751	-8.4941180	-8.4530735
USDGBP	fGARCH.NGARCH	0.0000000	4	2.000000	0.6589618	-8.7556480	-8.6707584	-8.7567478	-8.7215329
USDGBP	fGARCH.NAGARCH	0.0000000	4	2.000000	0.0812317	-9.0784271	-8.9935375	-9.0795270	-9.0443120
USDGBP	fGARCH.APARCH	0.0000000	4	2.000000	0.6407555	-8.7652475	-8.6667756	-8.7667186	-8.7256740
USDGBP	fGARCH.GJRGARCH	0.0000000	4	2.000000	0.8314076	-8.7097255	-8.6248359	-8.7108253	-8.6756104
USDGBP	fGARCH.ALLGARCH	0.0000000	4	2.000000	0.0625439	-9.0894691	-8.9774148	-9.0913632	-9.0444371
USDGBP	eGARCH	0.0000000	4	2.000000	0.0688022	-9.1094499	-9.0245603	-9.1105498	-9.0753348
USDGBP	gjrGARCH	0.0000000	4	2.000000	0.0753793	-9.0831765	-8.9982869	-9.0842764	-9.0490614
USDGBP	apARCH	0.0000000	4	2.000000	0.5934160	-8.7853142	-8.6868422	-8.7867852	-8.7457406
USDGBP	iGARCH	0.0000000	4	2.000000	0.9567749	-8.6735138	-8.6157889	-8.6740302	-8.6503156
USDGBP	csGARCH	0.0000000	4	2.000000	0.1128146	-9.0261227	-8.9276507	-9.0275937	-8.9865491
USD/CNY
USDCHF	sGARCH	0.0000001	4	2.000000	0.0237947	-7.8898857	-7.7905975	-7.8915229	-7.8499705
USDCHF	fGARCH.GARCH	0.0000001	4	2.000000	0.0238168	-7.8898457	-7.7905575	-7.8914829	-7.8499305
USDCHF	fGARCH.TGARCH	0.0000000	4	2.000000	0.0232968	-7.7798803	-7.6668972	-7.7819483	-7.7344596
USDCHF	fGARCH.AVGARCH	0.0000001	4	2.000000	0.0224723	-7.8728367	-7.7461586	-7.8753878	-7.8219104
USDCHF	fGARCH.NGARCH	0.0000003	4	2.000000	0.0219593	-7.8762987	-7.7633156	-7.8783667	-7.8308780
USDCHF	fGARCH.NAGARCH	0.0000001	4	2.000000	0.0217284	-7.8960491	-7.7830660	-7.8981171	-7.8506284
USDCHF	fGARCH.APARCH	0.0000001	4	2.000000	0.0194777	-7.7981621	-7.6714840	-7.8007132	-7.7472358
USDCHF	fGARCH.GJRGARCH	0.0000001	4	2.000000	0.0214671	-7.8973560	-7.7843728	-7.8994240	-7.8519353
USDCHF	fGARCH.ALLGARCH	0.0000002	4	2.000000	0.0184411	-7.8761116	-7.7357386	-7.8791975	-7.8196798
USDCHF	eGARCH	0.0000001	4	2.000000	0.0194239	-7.9009921	-7.7880089	-7.9030600	-7.8555713
USDCHF	gjrGARCH	0.0000003	4	2.000000	0.0176093	-7.8932971	-7.7803140	-7.8953651	-7.8478764
USDCHF	apARCH	0.0000002	4	2.000000	0.0175526	-7.8837665	-7.7570884	-7.8863176	-7.8328402
USDCHF	iGARCH	0.0000003	4	2.000000	0.0198707	-7.8801376	-7.7945442	-7.8813971	-7.8457279
USDCHF	csGARCH	0.0000001	4	2.000000	0.0201152	-7.8635773	-7.7368992	-7.8661284	-7.8126510
USD/EUR
USDCAD	sGARCH	0.0000000	4	2.000000	0.0049855	-8.2818931	-8.2069851	-8.2827573	-8.2517860
USDCAD	fGARCH.GARCH	0.0000000	4	2.000000	0.0049738	-8.2817294	-8.2068214	-8.2825936	-8.2516222
USDCAD	fGARCH.TGARCH	0.0000000	4	2.000000	0.0051920	-8.2981108	-8.2095831	-8.2993091	-8.2625296
USDCAD	fGARCH.AVGARCH	0.0000000	4	2.000000	0.0929052	-8.1148285	-8.0126812	-8.1164139	-8.0737733
USDCAD	fGARCH.NGARCH	0.0000000	4	2.000000	0.0048273	-8.2735840	-8.1850564	-8.2747824	-8.2380029
USDCAD	fGARCH.NAGARCH	0.0000000	4	2.000000	0.0037520	-8.2868248	-8.1982972	-8.2880231	-8.2512436
USDCAD	fGARCH.APARCH	0.0000000	4	2.000000	0.0508286	-8.1477858	-8.0456386	-8.1493712	-8.1067306
USDCAD	fGARCH.GJRGARCH	0.0000000	4	2.000000	0.0032447	-8.2888576	-8.2003299	-8.2900559	-8.2532764
USDCAD	fGARCH.ALLGARCH	0.0000001	4	2.000000	0.0040514	-8.2748314	-8.1590645	-8.2768561	-8.2283022
USDCAD	eGARCH	0.0000001	4	2.000000	0.0050232	-8.2940264	-8.2054988	-8.2952247	-8.2584452
USDCAD	gjrGARCH	0.0000000	4	2.000000	0.0032165	-8.2887046	-8.2001769	-8.2899029	-8.2531234
USDCAD	apARCH	0.0000000	4	2.000000	0.0037201	-8.2824580	-8.1803107	-8.2840434	-8.2414028
USDCAD	iGARCH	0.0000000	4	2.000000	0.0046769	-8.2861995	-8.2249111	-8.2867831	-8.2615663
USDCAD	csGARCH	0.0000000	4	2.000000	0.0049357	-8.2689115	-8.1667643	-8.2704970	-8.2278563
USD/GBP
USDCNY	sGARCH	0.0000005	4	2.000000	0.0055601	-6.9273647	-6.8356839	-6.9286566	-6.8905204
USDCNY	fGARCH.GARCH	0.0000005	4	2.000000	0.0055601	-6.9273648	-6.8356840	-6.9286567	-6.8905205
USDCNY	fGARCH.TGARCH	0.0000008	4	2.000000	0.0048566	-6.8925111	-6.7872481	-6.8942002	-6.8502084
USDCNY	fGARCH.AVGARCH	0.0000005	4	2.000000	0.0111231	-6.9095713	-6.7907259	-6.9117090	-6.8618102
USDCNY	fGARCH.NGARCH	0.0000004	4	2.000000	0.0048438	-6.9226063	-6.8173432	-6.9242953	-6.8803036
USDCNY	fGARCH.NAGARCH	0.0000005	4	2.000000	0.0050575	-6.9179916	-6.8127285	-6.9196806	-6.8756888
USDCNY	fGARCH.APARCH	0.0000004	4	2.000000	0.0048932	-6.9185218	-6.7996764	-6.9206595	-6.8707607
USDCNY	fGARCH.GJRGARCH	0.0000005	4	2.000000	0.0049980	-6.9182496	-6.8129865	-6.9199386	-6.8759469
USDCNY	fGARCH.ALLGARCH	0.0000006	4	2.000000	0.0049341	-6.9226321	-6.7902043	-6.9252692	-6.8694125
USDCNY	eGARCH	0.0000004	4	2.000000	0.0044761	-6.8891119	-6.7838488	-6.8908009	-6.8468092
USDCNY	gjrGARCH	0.0000005	4	2.000000	0.0049979	-6.9182497	-6.8129866	-6.9199387	-6.8759470
USDCNY	apARCH	0.0000004	4	2.000000	0.0050421	-6.9182851	-6.7994396	-6.9204227	-6.8705239
USDCNY	iGARCH	0.0000006	4	2.000000	0.0051785	-6.9005154	-6.8224169	-6.9014626	-6.8691295
USDCNY	csGARCH	0.0000005	4	2.000000	0.0055494	-6.9114237	-6.7925783	-6.9135614	-6.8636626
USD/JPY
USDJPY	sGARCH	0.0043414	4	1.997829	0.0272442	0.8165514	0.9014410	0.8154383	0.8506665
USDJPY	fGARCH.GARCH	0.0043414	4	1.997829	0.0272442	0.8165514	0.9014410	0.8154383	0.8506665
USDJPY	fGARCH.TGARCH	0.0042872	4	1.997856	0.0280165	0.7848311	0.8833030	0.7833470	0.8244046
USDJPY	fGARCH.AVGARCH	0.0043247	4	1.997838	0.0250116	0.7776130	0.8896673	0.7757060	0.8226450
USDJPY	fGARCH.NGARCH	0.0043057	4	1.997847	0.0311397	0.8114503	0.9099222	0.8099662	0.8510238
USDJPY	fGARCH.NAGARCH	0.0048188	4	1.997591	0.0260458	0.7715537	0.8700256	0.7700696	0.8111272
USDJPY	fGARCH.APARCH	0.0045436	4	1.997728	0.0297432	0.7888246	0.9008789	0.7869176	0.8338565
USDJPY	fGARCH.GJRGARCH	0.0043442	4	1.997828	0.0268770	0.7971652	0.8956372	0.7956812	0.8367387
USDJPY	fGARCH.ALLGARCH	0.0019024	4	1.999049	0.0263061	0.7644200	0.8900566	0.7620388	0.8149104
USDJPY	eGARCH	0.0041875	4	1.997906	0.0278439	0.7416013	0.8400733	0.7401173	0.7811748
USDJPY	gjrGARCH	0.0047415	4	1.997629	0.0263785	0.7701763	0.8686482	0.7686922	0.8097498
USDJPY	apARCH	0.0051226	4	1.997439	0.0298260	0.7886781	0.9007324	0.7867711	0.8337100
USDJPY	iGARCH	0.0043089	4	1.997845	0.0271791	0.8196221	0.8909294	0.8188273	0.8482788
USDJPY	csGARCH	0.0042846	4	1.997858	0.0272044	0.8340534	0.9461076	0.8321463	0.8790853

6.1.1.2A : Table summary

Due to different currency different standard deviation and mean value, therefore above table 6.1.1.2A compares the accuracy of the models which contain all currencies.

Table Summary Contain OHLC of 7 Currencies

Model	MSE	n	AIC.MSE	MSE.AIC	Akaike	Bayes	Shibata	Hannan.Quinn
sGARCH	0.0006203	28	0.2856700	9.713449	-6.628971	-6.543381	-6.630156	-6.594571
fGARCH.GARCH	0.0006203	28	0.2856700	9.713274	-6.628914	-6.543324	-6.630099	-6.594514
fGARCH.TGARCH	0.0006126	28	0.2856705	9.486882	-6.604057	-6.504853	-6.605616	-6.564185
fGARCH.AVGARCH	0.0006179	28	0.2856701	9.383348	-6.592463	-6.479644	-6.594449	-6.547119
fGARCH.NGARCH	0.0006152	28	0.2856703	9.695058	-6.655243	-6.556039	-6.656803	-6.615371
fGARCH.NAGARCH	0.0006885	28	0.2856651	9.760064	-6.700955	-6.601751	-6.702515	-6.661083
fGARCH.APARCH	0.0006492	28	0.2856679	9.572200	-6.624296	-6.511477	-6.626283	-6.578952
fGARCH.GJRGARCH	0.0006207	28	0.2856700	9.687413	-6.637586	-6.538382	-6.639145	-6.597714
fGARCH.ALLGARCH	0.0002719	28	0.2856949	9.726224	-6.713123	-6.586690	-6.715588	-6.662307
eGARCH	0.0005983	28	0.2856716	9.767911	-6.755209	-6.656004	-6.756768	-6.715337
gjrGARCH	0.0006775	28	0.2856659	9.760039	-6.694914	-6.595710	-6.696474	-6.655042
apARCH	0.0007319	28	0.2856620	9.665221	-6.665568	-6.552750	-6.667555	-6.620224
iGARCH	0.0006157	28	0.2856703	9.714553	-6.626525	-6.554550	-6.627388	-6.597597
csGARCH	0.0006122	28	0.2856706	9.858674	-6.708993	-6.596175	-6.710980	-6.663650

6.1.1.2B : Table summary

table 6.1.1.2B same with table 6.1.1.2A but not breakdown the currency. The number of n will be 7xn of table 6.1.1.2A due to 7 currencies.

Table Summary of Bias

Model	n

6.1.1.2C : Table summary number of errors.

Above table shows the number of bias.

Table Contains Bias Contain OHLC of 7 Currencies

.id	Model	Date	Type	Price	Price.T1	Akaike	Bayes	Shibata	Hannan.Quinn	diff	se

6.1.1.2D : Table Contain Bias dataset.

Table above list down all details which bias.

Lastly, we filter all bias data and look at the comparison of mse of OHLC of 7 currencies.

## contain OHLC of 7 currencies without bias.
acc <- fx %>% dplyr::filter(Date %in% ntimeID2 & !Date %in% ntimeID) %>% 
  ddply(.(.id, Model), summarise, 
        MSE = mean((Price.T1 - Price)^2), 
        n = length(Price), 
        AIC.MSE = (-2*MSE)/n+2*4/n, 
        MSE.AIC = mean((Akaike - mean(Akaike))^2),
        Akaike = mean(Akaike), 
        Bayes = mean(Bayes), 
        Shibata = mean(Shibata), 
        Hannan.Quinn = mean(Hannan.Quinn)) %>% 
  tbl_df %>% mutate(MSE = round(MSE, 7))

Group Table Summary Contain OHLC of 7 Currencies without Bias

.id	Model	MSE	n	AIC.MSE	MSE.AIC	Akaike	Bayes	Shibata	Hannan.Quinn
USD/AUD
USDAUD	sGARCH	0.0000000	4	2.000000	0.0042571	-7.7157954	-7.6442923	-7.7165827	-7.6870568
USDAUD	fGARCH.GARCH	0.0000000	4	2.000000	0.0042571	-7.7157308	-7.6442277	-7.7165180	-7.6869921
USDAUD	fGARCH.TGARCH	0.0000000	4	2.000000	0.0040899	-7.7115975	-7.6264748	-7.7127056	-7.6773848
USDAUD	fGARCH.AVGARCH	0.0000000	4	2.000000	0.0046426	-7.7096123	-7.6108700	-7.7110944	-7.6699256
USDAUD	fGARCH.NGARCH	0.0000000	4	2.000000	0.0042573	-7.7086240	-7.6235013	-7.7097321	-7.6744113
USDAUD	fGARCH.NAGARCH	0.0000000	4	2.000000	0.0044076	-7.7252460	-7.6401232	-7.7263541	-7.6910333
USDAUD	fGARCH.APARCH	0.0000000	4	2.000000	0.0045248	-7.7121329	-7.6133905	-7.7136150	-7.6724462
USDAUD	fGARCH.GJRGARCH	0.0000000	4	2.000000	0.0045302	-7.7194559	-7.6343332	-7.7205640	-7.6852432
USDAUD	fGARCH.ALLGARCH	0.0000000	4	2.000000	0.0046029	-7.7114799	-7.5991179	-7.7133882	-7.6663191
USDAUD	eGARCH	0.0000000	4	2.000000	0.0043887	-7.7275210	-7.6423983	-7.7286292	-7.6933084
USDAUD	gjrGARCH	0.0000000	4	2.000000	0.0045379	-7.7195102	-7.6343875	-7.7206184	-7.6852975
USDAUD	apARCH	0.0000000	4	2.000000	0.0045312	-7.7121916	-7.6134493	-7.7136737	-7.6725049
USDAUD	iGARCH	0.0000000	4	2.000000	0.0041693	-7.7214244	-7.6635410	-7.7219447	-7.6981598
USDAUD	csGARCH	0.0000000	4	2.000000	0.0045144	-7.7006430	-7.6019007	-7.7021251	-7.6609563
USD/CAD
USDEUR	sGARCH	0.0000000	4	2.000000	0.6050811	-7.6998813	-7.5943291	-7.7017000	-7.6574575
USDEUR	fGARCH.GARCH	0.0000000	4	2.000000	0.6048705	-7.6997431	-7.5941909	-7.7015618	-7.6573194
USDEUR	fGARCH.TGARCH	0.0000000	4	2.000000	0.2397655	-7.6699895	-7.5508176	-7.6722585	-7.6220917
USDEUR	fGARCH.AVGARCH	0.0000001	4	2.000000	0.3127196	-7.8253571	-7.6925656	-7.8281276	-7.7719853
USDEUR	fGARCH.NGARCH	0.0000001	4	2.000000	0.2303104	-7.8613915	-7.7422197	-7.8636606	-7.8134938
USDEUR	fGARCH.NAGARCH	0.0000000	4	2.000000	0.4971729	-7.7737017	-7.6545298	-7.7759707	-7.7258039
USDEUR	fGARCH.APARCH	0.0000000	4	2.000000	0.3255517	-7.8170471	-7.6842556	-7.8198177	-7.7636753
USDEUR	fGARCH.GJRGARCH	0.0000000	4	2.000000	0.6011446	-7.7266217	-7.6074498	-7.7288907	-7.6787239
USDEUR	fGARCH.ALLGARCH	0.0000001	4	2.000000	0.2042237	-7.8817577	-7.7353466	-7.8850803	-7.8229118
USDEUR	eGARCH	0.0000000	4	2.000000	0.0294717	-8.1069604	-7.9877886	-8.1092294	-8.0590626
USDEUR	gjrGARCH	0.0000001	4	2.000000	0.6060193	-7.7316377	-7.6124659	-7.7339067	-7.6837399
USDEUR	apARCH	0.0000000	4	2.000000	0.2455494	-7.8656406	-7.7328491	-7.8684111	-7.8122688
USDEUR	iGARCH	0.0000000	4	2.000000	0.5011615	-7.7435079	-7.6515754	-7.7449283	-7.7065582
USDEUR	csGARCH	0.0000000	4	2.000000	0.0428158	-8.0263288	-7.8935374	-8.0290994	-7.9729571
USD/CHF
USDGBP	sGARCH	0.0000001	4	2.000000	0.8403505	-8.7045263	-8.6332190	-8.7053077	-8.6758696
USDGBP	fGARCH.GARCH	0.0000001	4	2.000000	0.8403599	-8.7045383	-8.6332310	-8.7053197	-8.6758816
USDGBP	fGARCH.TGARCH	0.0000000	4	2.000000	0.5772550	-8.6611404	-8.5762508	-8.6622403	-8.6270253
USDGBP	fGARCH.AVGARCH	0.0000000	4	2.000000	0.4602830	-8.4926470	-8.3941751	-8.4941180	-8.4530735
USDGBP	fGARCH.NGARCH	0.0000000	4	2.000000	0.6589618	-8.7556480	-8.6707584	-8.7567478	-8.7215329
USDGBP	fGARCH.NAGARCH	0.0000000	4	2.000000	0.0812317	-9.0784271	-8.9935375	-9.0795270	-9.0443120
USDGBP	fGARCH.APARCH	0.0000000	4	2.000000	0.6407555	-8.7652475	-8.6667756	-8.7667186	-8.7256740
USDGBP	fGARCH.GJRGARCH	0.0000000	4	2.000000	0.8314076	-8.7097255	-8.6248359	-8.7108253	-8.6756104
USDGBP	fGARCH.ALLGARCH	0.0000000	4	2.000000	0.0625439	-9.0894691	-8.9774148	-9.0913632	-9.0444371
USDGBP	eGARCH	0.0000000	4	2.000000	0.0688022	-9.1094499	-9.0245603	-9.1105498	-9.0753348
USDGBP	gjrGARCH	0.0000000	4	2.000000	0.0753793	-9.0831765	-8.9982869	-9.0842764	-9.0490614
USDGBP	apARCH	0.0000000	4	2.000000	0.5934160	-8.7853142	-8.6868422	-8.7867852	-8.7457406
USDGBP	iGARCH	0.0000000	4	2.000000	0.9567749	-8.6735138	-8.6157889	-8.6740302	-8.6503156
USDGBP	csGARCH	0.0000000	4	2.000000	0.1128146	-9.0261227	-8.9276507	-9.0275937	-8.9865491
USD/CNY
USDCHF	sGARCH	0.0000001	4	2.000000	0.0237947	-7.8898857	-7.7905975	-7.8915229	-7.8499705
USDCHF	fGARCH.GARCH	0.0000001	4	2.000000	0.0238168	-7.8898457	-7.7905575	-7.8914829	-7.8499305
USDCHF	fGARCH.TGARCH	0.0000000	4	2.000000	0.0232968	-7.7798803	-7.6668972	-7.7819483	-7.7344596
USDCHF	fGARCH.AVGARCH	0.0000001	4	2.000000	0.0224723	-7.8728367	-7.7461586	-7.8753878	-7.8219104
USDCHF	fGARCH.NGARCH	0.0000003	4	2.000000	0.0219593	-7.8762987	-7.7633156	-7.8783667	-7.8308780
USDCHF	fGARCH.NAGARCH	0.0000001	4	2.000000	0.0217284	-7.8960491	-7.7830660	-7.8981171	-7.8506284
USDCHF	fGARCH.APARCH	0.0000001	4	2.000000	0.0194777	-7.7981621	-7.6714840	-7.8007132	-7.7472358
USDCHF	fGARCH.GJRGARCH	0.0000001	4	2.000000	0.0214671	-7.8973560	-7.7843728	-7.8994240	-7.8519353
USDCHF	fGARCH.ALLGARCH	0.0000002	4	2.000000	0.0184411	-7.8761116	-7.7357386	-7.8791975	-7.8196798
USDCHF	eGARCH	0.0000001	4	2.000000	0.0194239	-7.9009921	-7.7880089	-7.9030600	-7.8555713
USDCHF	gjrGARCH	0.0000003	4	2.000000	0.0176093	-7.8932971	-7.7803140	-7.8953651	-7.8478764
USDCHF	apARCH	0.0000002	4	2.000000	0.0175526	-7.8837665	-7.7570884	-7.8863176	-7.8328402
USDCHF	iGARCH	0.0000003	4	2.000000	0.0198707	-7.8801376	-7.7945442	-7.8813971	-7.8457279
USDCHF	csGARCH	0.0000001	4	2.000000	0.0201152	-7.8635773	-7.7368992	-7.8661284	-7.8126510
USD/EUR
USDCAD	sGARCH	0.0000000	4	2.000000	0.0049855	-8.2818931	-8.2069851	-8.2827573	-8.2517860
USDCAD	fGARCH.GARCH	0.0000000	4	2.000000	0.0049738	-8.2817294	-8.2068214	-8.2825936	-8.2516222
USDCAD	fGARCH.TGARCH	0.0000000	4	2.000000	0.0051920	-8.2981108	-8.2095831	-8.2993091	-8.2625296
USDCAD	fGARCH.AVGARCH	0.0000000	4	2.000000	0.0929052	-8.1148285	-8.0126812	-8.1164139	-8.0737733
USDCAD	fGARCH.NGARCH	0.0000000	4	2.000000	0.0048273	-8.2735840	-8.1850564	-8.2747824	-8.2380029
USDCAD	fGARCH.NAGARCH	0.0000000	4	2.000000	0.0037520	-8.2868248	-8.1982972	-8.2880231	-8.2512436
USDCAD	fGARCH.APARCH	0.0000000	4	2.000000	0.0508286	-8.1477858	-8.0456386	-8.1493712	-8.1067306
USDCAD	fGARCH.GJRGARCH	0.0000000	4	2.000000	0.0032447	-8.2888576	-8.2003299	-8.2900559	-8.2532764
USDCAD	fGARCH.ALLGARCH	0.0000001	4	2.000000	0.0040514	-8.2748314	-8.1590645	-8.2768561	-8.2283022
USDCAD	eGARCH	0.0000001	4	2.000000	0.0050232	-8.2940264	-8.2054988	-8.2952247	-8.2584452
USDCAD	gjrGARCH	0.0000000	4	2.000000	0.0032165	-8.2887046	-8.2001769	-8.2899029	-8.2531234
USDCAD	apARCH	0.0000000	4	2.000000	0.0037201	-8.2824580	-8.1803107	-8.2840434	-8.2414028
USDCAD	iGARCH	0.0000000	4	2.000000	0.0046769	-8.2861995	-8.2249111	-8.2867831	-8.2615663
USDCAD	csGARCH	0.0000000	4	2.000000	0.0049357	-8.2689115	-8.1667643	-8.2704970	-8.2278563
USD/GBP
USDCNY	sGARCH	0.0000005	4	2.000000	0.0055601	-6.9273647	-6.8356839	-6.9286566	-6.8905204
USDCNY	fGARCH.GARCH	0.0000005	4	2.000000	0.0055601	-6.9273648	-6.8356840	-6.9286567	-6.8905205
USDCNY	fGARCH.TGARCH	0.0000008	4	2.000000	0.0048566	-6.8925111	-6.7872481	-6.8942002	-6.8502084
USDCNY	fGARCH.AVGARCH	0.0000005	4	2.000000	0.0111231	-6.9095713	-6.7907259	-6.9117090	-6.8618102
USDCNY	fGARCH.NGARCH	0.0000004	4	2.000000	0.0048438	-6.9226063	-6.8173432	-6.9242953	-6.8803036
USDCNY	fGARCH.NAGARCH	0.0000005	4	2.000000	0.0050575	-6.9179916	-6.8127285	-6.9196806	-6.8756888
USDCNY	fGARCH.APARCH	0.0000004	4	2.000000	0.0048932	-6.9185218	-6.7996764	-6.9206595	-6.8707607
USDCNY	fGARCH.GJRGARCH	0.0000005	4	2.000000	0.0049980	-6.9182496	-6.8129865	-6.9199386	-6.8759469
USDCNY	fGARCH.ALLGARCH	0.0000006	4	2.000000	0.0049341	-6.9226321	-6.7902043	-6.9252692	-6.8694125
USDCNY	eGARCH	0.0000004	4	2.000000	0.0044761	-6.8891119	-6.7838488	-6.8908009	-6.8468092
USDCNY	gjrGARCH	0.0000005	4	2.000000	0.0049979	-6.9182497	-6.8129866	-6.9199387	-6.8759470
USDCNY	apARCH	0.0000004	4	2.000000	0.0050421	-6.9182851	-6.7994396	-6.9204227	-6.8705239
USDCNY	iGARCH	0.0000006	4	2.000000	0.0051785	-6.9005154	-6.8224169	-6.9014626	-6.8691295
USDCNY	csGARCH	0.0000005	4	2.000000	0.0055494	-6.9114237	-6.7925783	-6.9135614	-6.8636626
USD/JPY
USDJPY	sGARCH	0.0043414	4	1.997829	0.0272442	0.8165514	0.9014410	0.8154383	0.8506665
USDJPY	fGARCH.GARCH	0.0043414	4	1.997829	0.0272442	0.8165514	0.9014410	0.8154383	0.8506665
USDJPY	fGARCH.TGARCH	0.0042872	4	1.997856	0.0280165	0.7848311	0.8833030	0.7833470	0.8244046
USDJPY	fGARCH.AVGARCH	0.0043247	4	1.997838	0.0250116	0.7776130	0.8896673	0.7757060	0.8226450
USDJPY	fGARCH.NGARCH	0.0043057	4	1.997847	0.0311397	0.8114503	0.9099222	0.8099662	0.8510238
USDJPY	fGARCH.NAGARCH	0.0048188	4	1.997591	0.0260458	0.7715537	0.8700256	0.7700696	0.8111272
USDJPY	fGARCH.APARCH	0.0045436	4	1.997728	0.0297432	0.7888246	0.9008789	0.7869176	0.8338565
USDJPY	fGARCH.GJRGARCH	0.0043442	4	1.997828	0.0268770	0.7971652	0.8956372	0.7956812	0.8367387
USDJPY	fGARCH.ALLGARCH	0.0019024	4	1.999049	0.0263061	0.7644200	0.8900566	0.7620388	0.8149104
USDJPY	eGARCH	0.0041875	4	1.997906	0.0278439	0.7416013	0.8400733	0.7401173	0.7811748
USDJPY	gjrGARCH	0.0047415	4	1.997629	0.0263785	0.7701763	0.8686482	0.7686922	0.8097498
USDJPY	apARCH	0.0051226	4	1.997439	0.0298260	0.7886781	0.9007324	0.7867711	0.8337100
USDJPY	iGARCH	0.0043089	4	1.997845	0.0271791	0.8196221	0.8909294	0.8188273	0.8482788
USDJPY	csGARCH	0.0042846	4	1.997858	0.0272044	0.8340534	0.9461076	0.8321463	0.8790853

6.1.1.3A : Table summary

Table Summary Contain OHLC of 7 Currencies without Bias

Model	MSE	n	AIC.MSE	MSE.AIC	Akaike	Bayes	Shibata	Hannan.Quinn
sGARCH	0.0006203	28	0.2856700	9.713449	-6.628971	-6.543381	-6.630156	-6.594571
fGARCH.GARCH	0.0006203	28	0.2856700	9.713274	-6.628914	-6.543324	-6.630099	-6.594514
fGARCH.TGARCH	0.0006126	28	0.2856705	9.486882	-6.604057	-6.504853	-6.605616	-6.564185
fGARCH.AVGARCH	0.0006179	28	0.2856701	9.383348	-6.592463	-6.479644	-6.594449	-6.547119
fGARCH.NGARCH	0.0006152	28	0.2856703	9.695058	-6.655243	-6.556039	-6.656803	-6.615371
fGARCH.NAGARCH	0.0006885	28	0.2856651	9.760064	-6.700955	-6.601751	-6.702515	-6.661083
fGARCH.APARCH	0.0006492	28	0.2856679	9.572200	-6.624296	-6.511477	-6.626283	-6.578952
fGARCH.GJRGARCH	0.0006207	28	0.2856700	9.687413	-6.637586	-6.538382	-6.639145	-6.597714
fGARCH.ALLGARCH	0.0002719	28	0.2856949	9.726224	-6.713123	-6.586690	-6.715588	-6.662307
eGARCH	0.0005983	28	0.2856716	9.767911	-6.755209	-6.656004	-6.756768	-6.715337
gjrGARCH	0.0006775	28	0.2856659	9.760039	-6.694914	-6.595710	-6.696474	-6.655042
apARCH	0.0007319	28	0.2856620	9.665221	-6.665568	-6.552750	-6.667555	-6.620224
iGARCH	0.0006157	28	0.2856703	9.714553	-6.626525	-6.554550	-6.627388	-6.597597
csGARCH	0.0006122	28	0.2856706	9.858674	-6.708993	-6.596175	-6.710980	-6.663650

6.1.1.3B : Table summary

6.1.2 Selected Models

Now I select 9 models which almost run all data from 2013-01-01 to 2017-08-30. More observations will be able to know the best model. The models includes :

• sGARCH
• fGARCH.GARCH
• fGARCH.TGARCH
• fGARCH.NGARCH
• fGARCH.NAGARCH
• fGARCH.GJRGARCH
• gjrGARCH
• iGARCH
• csGARCH

## filter gmds
gmds2 <- c('sGARCH', 'fGARCH.GARCH', 'fGARCH.TGARCH', 'fGARCH.NGARCH', 'fGARCH.NAGARCH', 'fGARCH.GJRGARCH', 'gjrGARCH', 'iGARCH', 'csGARCH')

## check completed dataset.
mdate <- fx %>% dplyr::filter(Model %in% gmds2) %>% 
  dplyr::count(Date, Model)

##filter 7 currency and OHLC data.
united.dateID <- mdate %>% dplyr::filter(n == 28) %>% 
  .$Date %>% unique %>% sort

united.fx <- fx %>% dplyr::filter(Model %in% gmds2 & Date %in% united.dateID) %>% 
  mutate(Model = factor(Model))

## filter all predictive error where sd >= 20%.
notID <- united.fx %>% 
  mutate(diff = abs(Price.T1/Price), 
         se = ifelse(diff <= 0.8 | diff >= 1.25, 1, 0)) %>% 
  dplyr::filter(se == 1)

ntimeID <- notID %>% .$Date %>% unique %>% sort

acc <- united.fx %>% dplyr::filter(!Date %in% ntimeID) %>% 
  ddply(.(.id, Model), summarise, 
        MSE = mean((Price.T1 - Price)^2), 
        n = length(Price), 
        AIC.MSE = (-2*MSE)/n+2*4/n, 
        MSE.AIC = mean((Akaike - mean(Akaike))^2),
        Akaike = mean(Akaike), 
        Bayes = mean(Bayes), 
        Shibata = mean(Shibata), 
        Hannan.Quinn = mean(Hannan.Quinn)) %>% 
  tbl_df %>% mutate(MSE = round(MSE, 7))

Group Table Summary

.id	Model	MSE	n	AIC.MSE	MSE.AIC	Akaike	Bayes	Shibata	Hannan.Quinn
USD/AUD
USDAUD	sGARCH	0.0000005	4477	0.0017869	0.2702696	-7.073117	-6.994153	-7.074109	-7.041377
USDAUD	fGARCH.GARCH	0.0000005	4476	0.0017873	0.2697114	-7.072178	-6.993226	-7.073169	-7.040443
USDAUD	fGARCH.TGARCH	0.0000026	4432	0.0018051	0.5511541	-6.882550	-6.789963	-6.883892	-6.845334
USDAUD	fGARCH.NGARCH	0.0000039	4460	0.0017937	4311.5762280	-14.898208	-14.805639	-14.899550	-14.861000
USDAUD	fGARCH.NAGARCH	0.0000011	3824	0.0020920	15.7702280	-7.119684	-7.026074	-7.121056	-7.082058
USDAUD	fGARCH.GJRGARCH	0.0000006	3064	0.0026110	0.2597132	-7.253154	-7.160961	-7.254486	-7.216096
USDAUD	gjrGARCH	0.0000010	4480	0.0017857	0.2817553	-7.076009	-6.983385	-7.077352	-7.038779
USDAUD	iGARCH	0.0000006	4480	0.0017857	0.2712321	-7.075498	-7.010165	-7.076193	-7.049237
USDAUD	csGARCH	0.0000007	4460	0.0017937	0.2721160	-7.058751	-6.952446	-7.060499	-7.016021
USD/CAD
USDEUR	sGARCH	0.0000004	4480	0.0017857	0.3056961	-8.068736	-7.987479	-8.069793	-8.036074
USDEUR	fGARCH.GARCH	0.0000004	4480	0.0017857	0.3056818	-8.068722	-7.987465	-8.069779	-8.036060
USDEUR	fGARCH.TGARCH	0.0000007	4184	0.0019120	0.4702677	-7.924146	-7.828933	-7.925571	-7.885875
USDEUR	fGARCH.NGARCH	0.0000017	4476	0.0017873	5254.5707416	-16.746107	-16.651202	-16.747524	-16.707960
USDEUR	fGARCH.NAGARCH	0.0000004	3724	0.0021482	18.5925989	-8.056686	-7.960835	-8.058131	-8.018158
USDEUR	fGARCH.GJRGARCH	0.0000003	4296	0.0018622	0.3112483	-8.085018	-7.989973	-8.086438	-8.046814
USDEUR	gjrGARCH	0.0000003	4480	0.0017857	0.3151286	-8.086419	-7.991516	-8.087835	-8.048272
USDEUR	iGARCH	0.0000003	4480	0.0017857	0.3082212	-8.062245	-7.994634	-8.062996	-8.035069
USDEUR	csGARCH	0.0000023	4480	0.0017857	0.3005422	-8.053816	-7.945267	-8.055645	-8.010184
USD/CHF
USDGBP	sGARCH	0.0000007	4480	0.0017857	0.4173150	-8.598410	-8.515175	-8.599531	-8.564955
USDGBP	fGARCH.GARCH	0.0000007	4476	0.0017873	0.4171185	-8.597814	-8.514608	-8.598935	-8.564371
USDGBP	fGARCH.TGARCH	0.0000008	4424	0.0018083	0.6565235	-8.376277	-8.279363	-8.377766	-8.337324
USDGBP	fGARCH.NGARCH	0.0000016	4468	0.0017905	3738.2833345	-14.491818	-14.394961	-14.493305	-14.452888
USDGBP	fGARCH.NAGARCH	0.0000005	4212	0.0018993	53.8487935	-8.319973	-8.223698	-8.321443	-8.281277
USDGBP	fGARCH.GJRGARCH	0.0000007	4452	0.0017969	0.4150860	-8.613077	-8.516209	-8.614565	-8.574143
USDGBP	gjrGARCH	0.0000009	4480	0.0017857	0.4153488	-8.623688	-8.526823	-8.625176	-8.584755
USDGBP	iGARCH	0.0000009	4480	0.0017857	0.4165171	-8.598660	-8.529054	-8.599468	-8.570683
USDGBP	csGARCH	0.0000009	4480	0.0017857	0.4063786	-8.584948	-8.474453	-8.586854	-8.540536
USD/CNY
USDCHF	sGARCH	0.0000027	4476	0.0017873	0.3046351	-7.607386	-7.527338	-7.608410	-7.575210
USDCHF	fGARCH.GARCH	0.0000027	4480	0.0017857	0.3048075	-7.607278	-7.527228	-7.608302	-7.575102
USDCHF	fGARCH.TGARCH	0.0000016	4348	0.0018399	0.4039605	-7.526386	-7.432499	-7.527771	-7.488647
USDCHF	fGARCH.NGARCH	0.0000022	4480	0.0017857	3579.4227695	-13.978433	-13.884736	-13.979813	-13.940771
USDCHF	fGARCH.NAGARCH	0.0000021	3112	0.0025707	103.9285031	-7.009464	-6.915413	-7.010853	-6.971660
USDCHF	fGARCH.GJRGARCH	0.0000017	4324	0.0018501	0.2866458	-7.626157	-7.532331	-7.627540	-7.588443
USDCHF	gjrGARCH	0.0000019	4480	0.0017857	0.2873851	-7.645792	-7.552095	-7.647171	-7.608130
USDCHF	iGARCH	0.0000363	4480	0.0017857	0.4019555	-7.554560	-7.488158	-7.555283	-7.527869
USDCHF	csGARCH	0.0000112	4476	0.0017873	0.3142188	-7.584671	-7.477328	-7.586458	-7.541524
USD/EUR
USDCAD	sGARCH	0.0000009	4480	0.0017857	0.3538086	-7.672449	-7.590516	-7.673534	-7.639516
USDCAD	fGARCH.GARCH	0.0000009	4480	0.0017857	0.3538725	-7.672451	-7.590517	-7.673535	-7.639517
USDCAD	fGARCH.TGARCH	0.0000020	4356	0.0018365	0.7269497	-7.449761	-7.354053	-7.451212	-7.411291
USDCAD	fGARCH.NGARCH	0.0000059	4452	0.0017969	5384.5041279	-17.639763	-17.544174	-17.641210	-17.601340
USDCAD	fGARCH.NAGARCH	0.0000004	4164	0.0019212	3.1598109	-7.689223	-7.593755	-7.690666	-7.650849
USDCAD	fGARCH.GJRGARCH	0.0000010	4396	0.0018198	0.3597302	-7.680388	-7.584782	-7.681836	-7.641959
USDCAD	gjrGARCH	0.0000015	4480	0.0017857	0.3592903	-7.677063	-7.581481	-7.678510	-7.638643
USDCAD	iGARCH	0.0000007	4480	0.0017857	0.3555405	-7.671354	-7.603070	-7.672130	-7.643906
USDCAD	csGARCH	0.0000005	4464	0.0017921	0.3528473	-7.657667	-7.548412	-7.659530	-7.613751
USD/GBP
USDCNY	sGARCH	0.0003941	4476	0.0017871	1.0919412	-6.153136	-6.064309	-6.154380	-6.117433
USDCNY	fGARCH.GARCH	0.0002750	4476	0.0017872	1.0909033	-6.153294	-6.064460	-6.154538	-6.117587
USDCNY	fGARCH.TGARCH	0.0010651	4400	0.0018177	5.6886561	-5.861617	-5.759209	-5.863248	-5.820455
USDCNY	fGARCH.NGARCH	0.0626842	4480	0.0017577	3686.0317228	-13.654720	-13.552264	-13.656353	-13.613539
USDCNY	fGARCH.NAGARCH	0.0001943	4360	0.0018348	14.6467463	-6.021891	-5.919355	-6.023526	-5.980677
USDCNY	fGARCH.GJRGARCH	0.0003234	3308	0.0024182	1.0209684	-6.459293	-6.356085	-6.460948	-6.417809
USDCNY	gjrGARCH	0.0002988	4472	0.0017888	1.1447509	-6.195280	-6.092809	-6.196913	-6.154092
USDCNY	iGARCH	0.0004613	4480	0.0017855	1.2332516	-6.082386	-6.007206	-6.083294	-6.052167
USDCNY	csGARCH	0.0005630	4480	0.0017855	1.2253906	-6.125356	-6.009262	-6.127430	-6.078693
USD/JPY
USDJPY	sGARCH	0.0094989	4480	0.0017815	0.2102541	1.847171	1.932058	1.846003	1.881291
USDJPY	fGARCH.GARCH	0.0095258	4480	0.0017815	0.2097379	1.847129	1.932017	1.845962	1.881249
USDJPY	fGARCH.TGARCH	0.0103159	4472	0.0017843	0.2240196	1.855281	1.953776	1.853741	1.894871
USDJPY	fGARCH.NGARCH	0.0392135	4460	0.0017761	4868.9215412	-7.520947	-7.422480	-7.522485	-7.481369
USDJPY	fGARCH.NAGARCH	0.0070418	4384	0.0018216	0.2165974	1.827884	1.926309	1.826347	1.867445
USDJPY	fGARCH.GJRGARCH	0.0079776	4432	0.0018015	0.2131285	1.839769	1.938374	1.838226	1.879403
USDJPY	gjrGARCH	0.0076362	4480	0.0017823	0.2175053	1.836628	1.935154	1.835087	1.876230
USDJPY	iGARCH	0.0095254	4480	0.0017815	0.2142725	1.849941	1.921190	1.849093	1.878579
USDJPY	csGARCH	0.0664766	4480	0.0017560	0.2101829	1.857461	1.969625	1.855495	1.902545

6.1.2.1A : Table summary

Summary

Model	MSE	n	AIC.MSE	MSE.AIC	Akaike	Bayes	Shibata	Hannan.Quinn
sGARCH	0.0014145	31349	0.0002551	11.69900	-6.189177	-6.106441	-6.190276	-6.155921
fGARCH.GARCH	0.0014014	31348	0.0002551	11.69775	-6.188814	-6.106083	-6.189913	-6.155561
fGARCH.TGARCH	0.0016610	30616	0.0002612	12.33038	-5.989839	-5.893365	-5.991306	-5.951062
fGARCH.NGARCH	0.0145730	31276	0.0002549	4411.45911	-14.132984	-14.036619	-14.134447	-14.094250
fGARCH.NAGARCH	0.0011424	27780	0.0002879	39.03730	-5.915978	-5.819175	-5.917455	-5.877068
fGARCH.GJRGARCH	0.0012891	28272	0.0002829	12.76305	-6.198864	-6.102428	-6.200331	-6.160102
gjrGARCH	0.0011346	31352	0.0002551	11.72844	-6.209664	-6.113285	-6.211128	-6.170925
iGARCH	0.0014322	31360	0.0002550	11.71401	-6.170680	-6.101585	-6.171467	-6.142907
csGARCH	0.0095915	31320	0.0002548	11.71392	-6.171030	-6.060998	-6.172912	-6.126803

6.1.2.1B : Table summary

Summary

Model	n
sGARCH	2
fGARCH.GARCH	5
fGARCH.TGARCH	5
fGARCH.NGARCH	69
fGARCH.NAGARCH	14
fGARCH.GJRGARCH	4
gjrGARCH	3
iGARCH	10
csGARCH	5

6.1.2.1C : Table summary

Summary

.id	Model	Date	Type	Price	Price.T1	Akaike	Bayes	Shibata	Hannan.Quinn	diff	se
USDAUD	fGARCH.TGARCH	2013-06-03	USDAUD.Op	1.02600	-7.365624e+01	24.941247	25.064162	24.938973	24.990655	7.178971e+01	1
USDAUD	fGARCH.NGARCH	2013-06-27	USDAUD.Lo	1.07700	2.542027e+00	-590.320340	-590.197426	-590.322615	-590.270933	2.360285e+00	1
USDAUD	fGARCH.NGARCH	2013-08-04	USDAUD.Op	1.12300	1.260885e+39	-299.194470	-299.084911	-299.196290	-299.150426	1.122783e+39	1
USDAUD	fGARCH.NGARCH	2013-08-04	USDAUD.Cl	1.12290	9.147871e+10	192.689015	192.798574	192.687195	192.733059	8.146648e+10	1
USDAUD	fGARCH.NGARCH	2014-04-14	USDAUD.Op	1.06200	1.419924e+09	-416.149142	-416.012570	-416.151936	-416.094244	1.337028e+09	1
USDAUD	fGARCH.NGARCH	2017-03-26	USDAUD.Lo	1.30700	1.111220e-02	-586.980288	-586.857373	-586.982562	-586.930880	8.502100e-03	1
USDAUD	fGARCH.NAGARCH	2015-02-09	USDAUD.Op	1.28800	9.042209e+09	101.921621	102.058192	101.918826	101.976518	7.020349e+09	1
USDAUD	fGARCH.NAGARCH	2015-02-10	USDAUD.Op	1.28300	-9.623617e+31	153.814604	153.950801	153.811831	153.869344	7.500870e+31	1
USDAUD	iGARCH	2014-10-15	USDAUD.Cl	1.13730	2.310843e+145	738.699064	738.808021	738.697272	738.742856	2.031868e+145	1
USDEUR	fGARCH.GARCH	2015-02-05	USDEUR.Hi	0.88400	2.683682e+92	412.262447	412.385024	412.260190	412.311713	3.035839e+92	1
USDEUR	fGARCH.GARCH	2017-06-18	USDEUR.Cl	0.89220	6.667688e+68	356.680437	356.817009	356.677643	356.735335	7.473311e+68	1
USDEUR	fGARCH.NGARCH	2014-10-14	USDEUR.Lo	0.77900	-2.018651e+51	-468.909622	-468.759806	-468.912961	-468.849407	2.591336e+51	1
USDEUR	fGARCH.NGARCH	2015-03-02	USDEUR.Lo	0.89000	-4.015994e+07	83.346290	83.510176	83.342305	83.412167	4.512353e+07	1
USDEUR	fGARCH.NGARCH	2015-06-04	USDEUR.Lo	0.88700	-1.394863e+18	-545.380537	-545.244340	-545.383310	-545.325796	1.572562e+18	1
USDEUR	fGARCH.NGARCH	2015-06-24	USDEUR.Lo	0.89100	1.892803e+10	77.586765	77.722962	77.583992	77.641506	2.124358e+10	1
USDEUR	fGARCH.NGARCH	2016-04-28	USDEUR.Hi	0.88000	4.510825e-01	-594.671515	-594.535319	-594.674288	-594.616775	5.125938e-01	1
USDGBP	fGARCH.TGARCH	2014-06-19	USDGBP.Lo	0.58600	-3.465523e+73	364.832355	365.037213	364.826216	364.914701	5.913861e+73	1
USDGBP	fGARCH.NGARCH	2014-03-31	USDGBP.Cl	0.60001	-1.642110e+04	-444.661563	-444.524991	-444.664357	-444.606666	2.736805e+04	1
USDGBP	fGARCH.NGARCH	2014-05-01	USDGBP.Cl	0.59188	9.637298e-01	-516.051131	-515.914560	-516.053925	-515.996234	1.628252e+00	1
USDGBP	fGARCH.NGARCH	2014-06-19	USDGBP.Lo	0.58600	4.316118e-01	-160.018385	-159.813528	-160.024525	-159.936039	7.365389e-01	1
USDGBP	fGARCH.NGARCH	2015-04-16	USDGBP.Cl	0.67016	1.865748e+15	-556.647438	-556.511242	-556.650211	-556.592698	2.784033e+15	1
USDGBP	fGARCH.NGARCH	2015-04-21	USDGBP.Op	0.67000	-1.002521e+06	-574.983967	-574.847770	-574.986740	-574.929227	1.496300e+06	1
USDGBP	fGARCH.NGARCH	2015-06-08	USDGBP.Op	0.65200	5.022905e+36	-490.210255	-490.087678	-490.212512	-490.160989	7.703841e+36	1
USDGBP	fGARCH.NGARCH	2015-06-16	USDGBP.Op	0.63900	1.392346e+72	349.939882	350.048839	349.938090	349.983675	2.178945e+72	1
USDGBP	fGARCH.NGARCH	2016-07-19	USDGBP.Cl	0.76287	-6.365327e+09	114.898499	115.034323	114.895747	114.953084	8.343921e+09	1
USDGBP	fGARCH.NGARCH	2016-07-20	USDGBP.Hi	0.75900	7.366569e+74	-405.810489	-405.701830	-405.812268	-405.766822	9.705624e+74	1
USDGBP	csGARCH	2014-12-05	USDGBP.Lo	0.63700	9.285102e+149	758.957433	759.107249	758.954093	759.017647	1.457630e+150	1
USDCHF	sGARCH	2015-01-16	USDCHF.Lo	0.85000	1.189676e+00	-6.687989	-6.606271	-6.689007	-6.655145	1.399619e+00	1
USDCHF	fGARCH.GARCH	2014-05-25	USDCHF.Hi	0.89700	-3.484066e+62	366.067877	366.273301	366.061692	366.150461	3.884132e+62	1
USDCHF	fGARCH.GARCH	2015-01-16	USDCHF.Lo	0.85000	1.189676e+00	-6.687989	-6.606271	-6.689007	-6.655145	1.399619e+00	1
USDCHF	fGARCH.TGARCH	2015-01-16	USDCHF.Lo	0.85000	1.182560e+00	-6.882116	-6.786779	-6.883495	-6.843798	1.391247e+00	1
USDCHF	fGARCH.NGARCH	2013-12-12	USDCHF.Op	0.88700	-3.879205e+00	-432.539483	-432.402912	-432.542277	-432.484586	4.373400e+00	1
USDCHF	fGARCH.NGARCH	2015-01-16	USDCHF.Lo	0.85000	1.182556e+00	-6.811955	-6.716617	-6.813334	-6.773637	1.391243e+00	1
USDCHF	fGARCH.NGARCH	2015-09-07	USDCHF.Lo	0.97000	-8.823318e+01	-587.029347	-586.920390	-587.031140	-586.985555	9.096204e+01	1
USDCHF	fGARCH.NGARCH	2015-10-30	USDCHF.Hi	0.99100	-1.889325e+01	-584.267632	-584.158374	-584.269437	-584.223714	1.906483e+01	1
USDCHF	fGARCH.NAGARCH	2013-12-05	USDCHF.Op	0.90200	4.359195e+145	731.450007	731.586578	731.447212	731.504904	4.832810e+145	1
USDCHF	fGARCH.NAGARCH	2013-12-16	USDCHF.Op	0.89000	2.195181e+145	732.215372	732.352321	732.212557	732.270427	2.466495e+145	1
USDCHF	fGARCH.NAGARCH	2015-01-09	USDCHF.Op	1.01800	-1.228938e+24	226.375920	226.539355	226.371964	226.441608	1.207208e+24	1
USDCHF	fGARCH.NAGARCH	2015-01-16	USDCHF.Lo	0.85000	1.188451e+00	-6.758750	-6.663413	-6.760129	-6.720432	1.398178e+00	1
USDCHF	fGARCH.GJRGARCH	2015-01-16	USDCHF.Lo	0.85000	1.189203e+00	-6.775060	-6.679723	-6.776439	-6.736742	1.399062e+00	1
USDCHF	gjrGARCH	2015-01-16	USDCHF.Lo	0.85000	1.187461e+00	-6.834457	-6.739119	-6.835835	-6.796138	1.397013e+00	1
USDCHF	gjrGARCH	2015-01-19	USDCHF.Lo	0.85700	5.503465e-01	-6.799206	-6.703606	-6.800595	-6.760778	6.421780e-01	1
USDCHF	iGARCH	2015-01-16	USDCHF.Lo	0.85000	1.189656e+00	-6.696311	-6.628212	-6.697021	-6.668940	1.399595e+00	1
USDCHF	iGARCH	2015-01-19	USDCHF.Lo	0.85700	5.467194e-01	-6.659730	-6.591444	-6.660445	-6.632281	6.379457e-01	1
USDCHF	iGARCH	2015-01-20	USDCHF.Lo	0.86900	1.169574e+00	-6.632037	-6.563939	-6.632748	-6.604667	1.345885e+00	1
USDCHF	iGARCH	2015-01-21	USDCHF.Lo	0.85100	5.536845e-01	-6.599117	-6.531019	-6.599827	-6.571747	6.506281e-01	1
USDCHF	iGARCH	2015-01-22	USDCHF.Lo	0.85300	1.132264e+00	-6.569994	-6.501896	-6.570705	-6.542624	1.327390e+00	1
USDCHF	iGARCH	2015-01-26	USDCHF.Lo	0.87600	1.153558e+00	-6.519110	-6.450824	-6.519825	-6.491661	1.316847e+00	1
USDCHF	iGARCH	2015-01-27	USDCHF.Lo	0.89400	6.896106e-01	-6.470927	-6.402829	-6.471637	-6.443557	7.713765e-01	1
USDCHF	iGARCH	2015-02-02	USDCHF.Lo	0.92000	7.319616e-01	-6.350835	-6.255235	-6.352225	-6.312407	7.956105e-01	1
USDCHF	csGARCH	2015-01-16	USDCHF.Lo	0.85000	1.193636e+00	-6.688153	-6.579196	-6.689945	-6.644361	1.404278e+00	1
USDCHF	csGARCH	2015-01-22	USDCHF.Lo	0.85300	1.141360e+00	-6.534724	-6.425767	-6.536516	-6.490932	1.338054e+00	1
USDCHF	csGARCH	2015-01-23	USDCHF.Lo	0.86800	6.200740e-01	-6.493151	-6.384194	-6.494943	-6.449359	7.143710e-01	1
USDCAD	fGARCH.NGARCH	2015-02-05	USDCAD.Hi	1.25800	-2.752758e+42	-487.602382	-487.425326	-487.607002	-487.531219	2.188202e+42	1
USDCAD	fGARCH.NGARCH	2015-02-09	USDCAD.Cl	1.25170	-7.979335e+22	142.673774	142.783031	142.671968	142.717692	6.374798e+22	1
USDCAD	fGARCH.NGARCH	2015-03-29	USDCAD.Hi	1.27000	-6.542943e+22	-529.240306	-529.131049	-529.242112	-529.196389	5.151924e+22	1
USDCAD	fGARCH.NGARCH	2015-07-21	USDCAD.Hi	1.30500	4.139802e+61	-435.142670	-435.006474	-435.145443	-435.087930	3.172262e+61	1
USDCAD	fGARCH.NGARCH	2016-05-02	USDCAD.Hi	1.27000	2.847428e+37	-493.891329	-493.741100	-493.894693	-493.830942	2.242069e+37	1
USDCNY	sGARCH	2014-07-10	USDCNY.Lo	2.20100	2.987751e+00	-4.665480	-4.583537	-4.666505	-4.632541	1.357452e+00	1
USDCNY	fGARCH.GARCH	2014-07-10	USDCNY.Lo	2.20100	2.987874e+00	-4.665479	-4.583536	-4.666505	-4.632541	1.357508e+00	1
USDCNY	fGARCH.TGARCH	2013-10-09	USDCNY.Op	6.11100	5.483283e+03	60.013013	60.135928	60.010739	60.062421	8.972808e+02	1
USDCNY	fGARCH.NGARCH	2014-07-17	USDCNY.Lo	6.19200	-5.016306e+02	-585.712986	-585.631043	-585.714011	-585.680047	8.101269e+01	1
USDCNY	fGARCH.NGARCH	2014-07-20	USDCNY.Lo	6.19500	1.194381e+01	-589.430373	-589.348203	-589.431406	-589.397340	1.927975e+00	1
USDCNY	fGARCH.NGARCH	2014-07-22	USDCNY.Lo	6.18900	1.945038e+01	-591.466725	-591.384782	-591.467750	-591.433786	3.142734e+00	1
USDCNY	fGARCH.NGARCH	2014-07-23	USDCNY.Lo	6.18200	-3.637318e+01	-588.553531	-588.471588	-588.554557	-588.520593	5.883724e+00	1
USDCNY	fGARCH.NGARCH	2014-07-27	USDCNY.Lo	6.17600	4.872521e+01	-587.187420	-587.105250	-587.188453	-587.154387	7.889444e+00	1
USDCNY	fGARCH.NGARCH	2014-07-31	USDCNY.Lo	6.16300	2.769268e+01	-590.455881	-590.373938	-590.456907	-590.422943	4.493377e+00	1
USDCNY	fGARCH.NGARCH	2014-08-03	USDCNY.Lo	6.16800	3.201427e+01	-587.733648	-587.651478	-587.734681	-587.700615	5.190381e+00	1
USDCNY	fGARCH.NGARCH	2014-08-05	USDCNY.Lo	6.15300	1.853196e+01	-589.664961	-589.583018	-589.665987	-589.632023	3.011858e+00	1
USDCNY	fGARCH.NGARCH	2014-08-06	USDCNY.Lo	6.14700	2.635122e+01	-591.728569	-591.646626	-591.729595	-591.695631	4.286842e+00	1
USDCNY	fGARCH.NGARCH	2014-08-10	USDCNY.Lo	6.14400	5.336958e+01	-588.785684	-588.703514	-588.786717	-588.752651	8.686456e+00	1
USDCNY	fGARCH.NGARCH	2014-08-12	USDCNY.Lo	6.14400	4.740305e+01	-587.300349	-587.218406	-587.301374	-587.267410	7.715340e+00	1
USDCNY	fGARCH.NGARCH	2014-08-13	USDCNY.Lo	6.14200	8.825968e+00	-589.224653	-589.142710	-589.225679	-589.191715	1.436986e+00	1
USDCNY	fGARCH.NGARCH	2014-08-14	USDCNY.Lo	6.13600	4.872331e+01	-586.351874	-586.269931	-586.352899	-586.318935	7.940565e+00	1
USDCNY	fGARCH.NGARCH	2014-08-19	USDCNY.Lo	6.13000	-1.240483e+01	-590.789977	-590.708034	-590.791003	-590.757039	2.023627e+00	1
USDCNY	fGARCH.NGARCH	2014-08-20	USDCNY.Lo	6.13000	9.161532e+00	-592.227353	-592.145410	-592.228379	-592.194415	1.494540e+00	1
USDCNY	fGARCH.NGARCH	2014-08-21	USDCNY.Lo	6.14100	-1.525661e+01	-590.144127	-590.062184	-590.145153	-590.111189	2.484385e+00	1
USDCNY	fGARCH.NGARCH	2014-08-24	USDCNY.Lo	6.14000	-3.247607e+01	-589.174302	-589.092132	-589.175335	-589.141269	5.289262e+00	1
USDCNY	fGARCH.NGARCH	2014-08-25	USDCNY.Lo	6.14200	6.174800e+01	-572.956479	-572.874536	-572.957505	-572.923541	1.005340e+01	1
USDCNY	fGARCH.NGARCH	2014-08-26	USDCNY.Lo	6.13300	9.738678e+01	-587.251542	-587.169599	-587.252568	-587.218604	1.587914e+01	1
USDCNY	fGARCH.NGARCH	2014-08-31	USDCNY.Lo	6.12900	2.545583e+02	-584.923023	-584.840853	-584.924056	-584.889989	4.153341e+01	1
USDCNY	fGARCH.NGARCH	2014-09-01	USDCNY.Lo	6.13200	1.596999e+02	-584.161053	-584.079110	-584.162079	-584.128115	2.604369e+01	1
USDCNY	fGARCH.NGARCH	2014-09-02	USDCNY.Lo	6.13100	-1.989882e+01	-589.399865	-589.317922	-589.400891	-589.366927	3.245608e+00	1
USDCNY	fGARCH.NGARCH	2014-09-04	USDCNY.Lo	6.12800	-2.866168e+01	-585.515480	-585.433537	-585.516505	-585.482541	4.677168e+00	1
USDCNY	fGARCH.NGARCH	2014-09-08	USDCNY.Lo	6.12200	-2.517129e+01	-587.872377	-587.790434	-587.873402	-587.839438	4.111612e+00	1
USDCNY	fGARCH.NGARCH	2014-09-11	USDCNY.Lo	6.12000	1.708482e+01	-588.380157	-588.298214	-588.381183	-588.347219	2.791637e+00	1
USDCNY	fGARCH.NGARCH	2014-09-14	USDCNY.Lo	6.12500	-7.626137e+01	-589.072288	-588.990119	-589.073322	-589.039255	1.245084e+01	1
USDCNY	fGARCH.NGARCH	2014-09-16	USDCNY.Lo	6.12900	-1.759094e+02	-585.597533	-585.515590	-585.598558	-585.564594	2.870116e+01	1
USDCNY	fGARCH.NGARCH	2014-09-21	USDCNY.Lo	6.12800	-2.039517e+01	-588.488512	-588.406343	-588.489546	-588.455479	3.328194e+00	1
USDCNY	fGARCH.NGARCH	2014-09-23	USDCNY.Lo	6.12400	1.512941e+01	-590.152856	-590.070913	-590.153882	-590.119918	2.470511e+00	1
USDCNY	fGARCH.NGARCH	2014-10-01	USDCNY.Lo	6.12800	-1.146657e+02	-584.091459	-584.009516	-584.092485	-584.058521	1.871177e+01	1
USDCNY	fGARCH.NGARCH	2014-10-06	USDCNY.Lo	6.12900	-2.283202e+01	-579.908511	-579.826568	-579.909537	-579.875573	3.725243e+00	1
USDCNY	fGARCH.NGARCH	2014-10-07	USDCNY.Lo	6.12500	5.146397e+01	-565.845084	-565.763141	-565.846110	-565.812146	8.402281e+00	1
USDCNY	fGARCH.NGARCH	2014-10-09	USDCNY.Lo	6.12000	6.182692e+01	-583.758544	-583.676826	-583.759562	-583.725700	1.010244e+01	1
USDCNY	fGARCH.NGARCH	2014-11-26	USDCNY.Lo	6.12300	6.187566e+01	-583.601907	-583.520189	-583.602924	-583.569062	1.010545e+01	1
USDCNY	fGARCH.NGARCH	2017-06-15	USDCNY.Op	6.80600	-1.649282e+44	-461.947546	-461.824970	-461.949803	-461.898280	2.423276e+43	1
USDCNY	fGARCH.NAGARCH	2014-07-10	USDCNY.Lo	2.20100	2.977219e+00	-4.669064	-4.573464	-4.670453	-4.630636	1.352666e+00	1
USDCNY	fGARCH.NAGARCH	2014-07-24	USDCNY.Lo	6.18200	-3.603032e+02	14.561667	14.643610	14.560642	14.594606	5.828262e+01	1
USDCNY	fGARCH.NAGARCH	2014-07-29	USDCNY.Lo	6.16200	-3.579216e+02	14.548624	14.630567	14.547598	14.581562	5.808530e+01	1
USDCNY	fGARCH.NAGARCH	2014-07-31	USDCNY.Lo	6.16300	-3.531901e+02	14.522470	14.604413	14.521444	14.555409	5.730814e+01	1
USDCNY	fGARCH.NAGARCH	2014-08-04	USDCNY.Lo	6.16100	-3.492923e+02	14.548440	14.630382	14.547414	14.581378	5.669409e+01	1
USDCNY	fGARCH.NAGARCH	2014-08-26	USDCNY.Lo	6.13300	4.865151e+00	104.667516	104.749459	104.666490	104.700454	7.932742e-01	1
USDCNY	fGARCH.NAGARCH	2014-09-04	USDCNY.Lo	6.12800	4.796821e+02	172.167572	172.249515	172.166546	172.200510	7.827710e+01	1
USDCNY	fGARCH.NAGARCH	2014-10-19	USDCNY.Lo	6.11300	-3.344848e+02	98.972743	99.054686	98.971717	99.005682	5.471696e+01	1
USDCNY	fGARCH.GJRGARCH	2014-07-10	USDCNY.Lo	2.20100	2.979918e+00	-4.677596	-4.581996	-4.678985	-4.639168	1.353893e+00	1
USDCNY	fGARCH.GJRGARCH	2014-09-01	USDCNY.Lo	6.13200	1.263740e+01	98.054293	98.136236	98.053267	98.087231	2.060893e+00	1
USDCNY	fGARCH.GJRGARCH	2014-11-12	USDCNY.Lo	6.11400	-3.508494e+01	94.016565	94.098283	94.015548	94.049410	5.738460e+00	1
USDCNY	gjrGARCH	2014-07-10	USDCNY.Lo	2.20100	2.894085e+00	-4.702450	-4.606850	-4.703839	-4.664022	1.314895e+00	1
USDCNY	iGARCH	2014-07-10	USDCNY.Lo	2.20100	2.988228e+00	-4.673441	-4.605156	-4.674157	-4.645993	1.357668e+00	1
USDCNY	csGARCH	2014-03-19	USDCNY.Op	6.18200	-4.743008e+149	761.606011	761.769897	761.602025	761.671888	7.672287e+148	1
USDJPY	fGARCH.TGARCH	2013-03-31	USDJPY.Op	94.26200	-5.215159e+89	433.750440	433.914326	433.746455	433.816317	5.532621e+87	1
USDJPY	fGARCH.NGARCH	2013-05-20	USDJPY.Hi	102.87200	1.639729e+20	126.895461	127.031657	126.892687	126.950201	1.593951e+18	1
USDJPY	fGARCH.NGARCH	2013-06-16	USDJPY.Hi	95.10600	-2.728130e+05	179.131969	179.268541	179.129175	179.186867	2.868516e+03	1
USDJPY	fGARCH.NGARCH	2013-06-17	USDJPY.Hi	95.75300	3.511368e+02	10.570756	10.706952	10.567983	10.625496	3.667111e+00	1
USDJPY	fGARCH.NGARCH	2013-06-19	USDJPY.Hi	98.23900	4.076553e+124	740.361014	740.497210	740.358240	740.415754	4.149628e+122	1
USDJPY	fGARCH.NGARCH	2013-07-01	USDJPY.Hi	100.43800	4.397652e+23	-244.819452	-244.683255	-244.822225	-244.764711	4.378474e+21	1
USDJPY	fGARCH.NGARCH	2013-07-22	USDJPY.Hi	100.17000	-7.099425e+16	107.520826	107.657022	107.518052	107.575566	7.087376e+14	1

6.1.2.1D : Table summary

Now I try to filter the dataset again. Below table summarise all dataset which excludes bias but contain OHLC of 7 currencies.

## filter all date which contain OHLC of 7 currencies.
ntimeID2 <- united.fx %>% dplyr::count(Date) %>% 
    dplyr::filter(n == 252) %>% .$Date %>% sort #9 models x 7 currencies x OHLC 4 types = 252 observations per day.

united.fx2 <- united.fx %>% dplyr::filter(Date %in% ntimeID2)

## filter all predictive error where sd >= 20%.
notID <- united.fx2 %>% 
  mutate(diff = abs(Price.T1/Price), 
         se = ifelse(diff <= 0.8 | diff >= 1.25, 1, 0)) %>% 
  dplyr::filter(se == 1)

acc <- united.fx2 %>% 
  ddply(.(.id, Model), summarise, 
        MSE = mean((Price.T1 - Price)^2), 
        n = length(Price), 
        AIC.MSE = (-2*MSE)/n+2*4/n, 
        MSE.AIC = mean((Akaike - mean(Akaike))^2),
        Akaike = mean(Akaike), 
        Bayes = mean(Bayes), 
        Shibata = mean(Shibata), 
        Hannan.Quinn = mean(Hannan.Quinn)) %>% 
  tbl_df %>% mutate(MSE = round(MSE, 7))

Group Table Summary

.id	Model	MSE	n	AIC.MSE	MSE.AIC	Akaike	Bayes	Shibata	Hannan.Quinn
USD/AUD
USDAUD	sGARCH	6.000000e-07	2236	3.577800e-03	0.1625351	-7.368950	-7.288749	-7.369979	-7.336712
USDAUD	fGARCH.GARCH	6.000000e-07	2236	3.577800e-03	0.1624570	-7.368979	-7.288779	-7.370009	-7.336742
USDAUD	fGARCH.TGARCH	2.494384e+00	2236	1.346700e-03	1.0768079	-7.120062	-7.026208	-7.121447	-7.082336
USDAUD	fGARCH.NGARCH	9.016917e+14	2236	-8.065221e+11	8250.0079154	-22.405061	-22.311208	-22.406446	-22.367336
USDAUD	fGARCH.NAGARCH	4.141950e+60	2236	-3.704785e+57	43.6941028	-7.147520	-7.053666	-7.148905	-7.109794
USDAUD	fGARCH.GJRGARCH	8.000000e-07	2236	3.577800e-03	0.1693578	-7.369940	-7.276086	-7.371325	-7.332214
USDAUD	gjrGARCH	8.000000e-07	2236	3.577800e-03	0.1713696	-7.376728	-7.282875	-7.378113	-7.339003
USDAUD	iGARCH	2.388192e+287	2236	-2.136129e+284	248.9905666	-7.037625	-6.971078	-7.038352	-7.010876
USDAUD	csGARCH	8.000000e-07	2236	3.577800e-03	0.1681670	-7.351422	-7.243915	-7.353216	-7.308208
USD/CAD
USDEUR	sGARCH	5.000000e-07	2236	3.577800e-03	0.3248276	-8.375734	-8.292899	-8.376828	-8.342438
USDEUR	fGARCH.GARCH	5.000000e-07	2236	3.577800e-03	0.3244428	-8.375693	-8.292858	-8.376787	-8.342397
USDEUR	fGARCH.TGARCH	1.100000e-06	2236	3.577800e-03	0.5189860	-8.230733	-8.134244	-8.232193	-8.191948
USDEUR	fGARCH.NGARCH	8.701438e+32	2236	-7.783040e+29	8704.1660980	-22.676244	-22.579756	-22.677705	-22.637460
USDEUR	fGARCH.NAGARCH	4.000000e-07	2236	3.577800e-03	30.6842331	-8.266987	-8.170499	-8.268448	-8.228203
USDEUR	fGARCH.GJRGARCH	4.000000e-07	2236	3.577800e-03	0.3266558	-8.383353	-8.286864	-8.384813	-8.344568
USDEUR	gjrGARCH	4.000000e-07	2236	3.577800e-03	0.3272131	-8.399480	-8.302992	-8.400941	-8.360696
USDEUR	iGARCH	6.000000e-07	2236	3.577800e-03	0.3242069	-8.374202	-8.305020	-8.374983	-8.346393
USDEUR	csGARCH	6.000000e-07	2236	3.577800e-03	0.3111112	-8.360968	-8.250826	-8.362847	-8.316695
USD/CHF
USDGBP	sGARCH	1.000000e-07	2236	3.577800e-03	0.1141396	-9.053570	-8.971985	-9.054654	-9.020777
USDGBP	fGARCH.GARCH	1.000000e-07	2236	3.577800e-03	0.1142206	-9.053111	-8.971526	-9.054195	-9.020318
USDGBP	fGARCH.TGARCH	5.371130e+143	2236	-4.804231e+140	62.8726733	-8.613631	-8.518406	-8.615076	-8.575356
USDGBP	fGARCH.NGARCH	1.128335e+70	2236	-1.009244e+67	3895.7815123	-15.234293	-15.139068	-15.235738	-15.196017
USDGBP	fGARCH.NAGARCH	1.000000e-07	2236	3.577800e-03	47.7249662	-8.782240	-8.687015	-8.783685	-8.743965
USDGBP	fGARCH.GJRGARCH	1.000000e-07	2236	3.577800e-03	0.1173539	-9.066730	-8.971505	-9.068174	-9.028454
USDGBP	gjrGARCH	1.000000e-07	2236	3.577800e-03	0.1149523	-9.079875	-8.984651	-9.081320	-9.041600
USDGBP	iGARCH	1.000000e-07	2236	3.577800e-03	0.1144318	-9.053292	-8.985346	-9.054069	-9.025981
USDGBP	csGARCH	1.000000e-07	2236	3.577800e-03	0.1014799	-9.038237	-8.929373	-9.040095	-8.994480
USD/CNY
USDCHF	sGARCH	5.620000e-05	2236	3.577800e-03	0.4628833	-7.598820	-7.516889	-7.599894	-7.565887
USDCHF	fGARCH.GARCH	5.630000e-05	2236	3.577800e-03	0.4633472	-7.598326	-7.516395	-7.599400	-7.565392
USDCHF	fGARCH.TGARCH	5.200000e-05	2236	3.577800e-03	0.5703948	-7.597254	-7.501667	-7.598691	-7.558832
USDCHF	fGARCH.NGARCH	3.745718e+00	2236	2.274000e-04	6266.4845818	-19.427313	-19.331726	-19.428750	-19.388890
USDCHF	fGARCH.NAGARCH	2.155107e+287	2236	-1.927645e+284	358.5205739	-6.527131	-6.431544	-6.528568	-6.488708
USDCHF	fGARCH.GJRGARCH	5.430000e-05	2236	3.577800e-03	0.4260898	-7.635906	-7.540319	-7.637343	-7.597483
USDCHF	gjrGARCH	5.410000e-05	2236	3.577800e-03	0.4277262	-7.658412	-7.562825	-7.659849	-7.619989
USDCHF	iGARCH	2.713000e-04	2236	3.577600e-03	0.5951953	-7.524153	-7.455878	-7.524918	-7.496709
USDCHF	csGARCH	1.391000e-04	2236	3.577700e-03	0.5033270	-7.557460	-7.448218	-7.559313	-7.513548
USD/EUR
USDCAD	sGARCH	4.000000e-07	2236	3.577800e-03	0.1874770	-8.057212	-7.975944	-8.058271	-8.024546
USDCAD	fGARCH.GARCH	4.000000e-07	2236	3.577800e-03	0.1875521	-8.057192	-7.975923	-8.058251	-8.024525
USDCAD	fGARCH.TGARCH	1.200000e-06	2236	3.577800e-03	0.6410392	-7.831225	-7.736303	-7.832644	-7.793070
USDCAD	fGARCH.NGARCH	7.664560e+119	2236	-6.855600e+116	8460.2378875	-24.265468	-24.170547	-24.266887	-24.227313
USDCAD	fGARCH.NAGARCH	3.000000e-07	2236	3.577800e-03	0.1870218	-8.065685	-7.970763	-8.067104	-8.027530
USDCAD	fGARCH.GJRGARCH	3.000000e-07	2236	3.577800e-03	0.1876002	-8.060906	-7.965984	-8.062325	-8.022751
USDCAD	gjrGARCH	3.000000e-07	2236	3.577800e-03	0.1860144	-8.066548	-7.971626	-8.067967	-8.028393
USDCAD	iGARCH	5.000000e-07	2236	3.577800e-03	0.1891828	-8.056657	-7.989041	-8.057409	-8.029478
USDCAD	csGARCH	4.000000e-07	2236	3.577800e-03	0.1854206	-8.041441	-7.932866	-8.043273	-7.997798
USD/GBP
USDCNY	sGARCH	5.853000e-04	2236	3.577300e-03	1.2136315	-6.543910	-6.454648	-6.545171	-6.508031
USDCNY	fGARCH.GARCH	3.669000e-04	2236	3.577500e-03	1.2155462	-6.543360	-6.454098	-6.544621	-6.507481
USDCNY	fGARCH.TGARCH	1.341655e+04	2236	-1.199692e+01	4.0387293	-6.265960	-6.163056	-6.267612	-6.224598
USDCNY	fGARCH.NGARCH	1.935781e+02	2236	-1.695690e-01	6667.3821629	-18.332871	-18.229967	-18.334523	-18.291508
USDCNY	fGARCH.NAGARCH	3.265008e+02	2236	-2.884623e-01	26.8084491	-6.353122	-6.250217	-6.354774	-6.311759
USDCNY	fGARCH.GJRGARCH	1.944250e-02	2236	3.560400e-03	6.2854180	-6.497338	-6.394434	-6.498990	-6.455976
USDCNY	gjrGARCH	5.185000e-04	2236	3.577400e-03	1.2006618	-6.583577	-6.480672	-6.585229	-6.542214
USDCNY	iGARCH	7.443000e-04	2236	3.577200e-03	1.3212583	-6.506358	-6.430739	-6.507282	-6.475962
USDCNY	csGARCH	6.272000e-04	2236	3.577300e-03	1.3686447	-6.531051	-6.414504	-6.533146	-6.484205
USD/JPY
USDJPY	sGARCH	1.121510e-02	2236	3.567800e-03	0.1881739	1.589979	1.678876	1.588700	1.625711
USDJPY	fGARCH.GARCH	1.113200e-02	2236	3.567900e-03	0.1879695	1.590212	1.679109	1.588933	1.625944
USDJPY	fGARCH.TGARCH	1.216363e+176	2236	-1.087982e+173	83.7014653	1.799893	1.902432	1.798225	1.841109
USDJPY	fGARCH.NGARCH	7.432149e+245	2236	-6.647719e+242	7663.4907412	-12.386898	-12.284358	-12.388566	-12.345682
USDJPY	fGARCH.NAGARCH	7.675100e-03	2236	3.571000e-03	0.1976159	1.574545	1.677085	1.572877	1.615761
USDJPY	fGARCH.GJRGARCH	9.290300e-03	2236	3.569500e-03	0.1930752	1.585747	1.688286	1.584078	1.626962
USDJPY	gjrGARCH	8.264100e-03	2236	3.570400e-03	0.1998324	1.576720	1.679259	1.575052	1.617936
USDJPY	iGARCH	1.114260e-02	2236	3.567900e-03	0.1899926	1.587496	1.662750	1.586552	1.617744
USDJPY	csGARCH	1.373920e-02	2236	3.565500e-03	0.1841325	1.597237	1.713419	1.595128	1.643936

6.1.2.2A : Table summary

Summarised Table Excludes Bias and Contain OHLC of 7 Currencies

Model	MSE	n	AIC.MSE	MSE.AIC	Akaike	Bayes	Shibata	Hannan.Quinn
sGARCH	1.694000e-03	15652	5.109000e-04	11.78981	-6.486888	-6.403177	-6.488014	-6.453240
fGARCH.GARCH	1.651000e-03	15652	5.109000e-04	11.79008	-6.486636	-6.402924	-6.487761	-6.452987
fGARCH.TGARCH	1.737662e+175	15652	-2.220371e+171	33.25741	-6.265567	-6.168208	-6.267062	-6.226433
fGARCH.NGARCH	1.061736e+245	15652	-1.356677e+241	7145.49999	-19.246878	-19.149518	-19.248373	-19.207744
fGARCH.NAGARCH	3.078724e+286	15652	-3.933969e+282	83.38656	-6.224020	-6.126660	-6.225515	-6.184886
fGARCH.GJRGARCH	4.112700e-03	15652	5.106000e-04	12.52896	-6.489775	-6.392415	-6.491270	-6.450641
gjrGARCH	1.262600e-03	15652	5.110000e-04	11.81364	-6.512557	-6.415197	-6.514052	-6.473423
iGARCH	3.411703e+286	15652	-4.359446e+282	47.26923	-6.423541	-6.353479	-6.424352	-6.395379
csGARCH	2.072500e-03	15652	5.109000e-04	11.78669	-6.469049	-6.358040	-6.470966	-6.424428

6.1.2.2B : Table summary

Summary

.id	Model	Date	Type	Price	Price.T1	Akaike	Bayes	Shibata	Hannan.Quinn	diff	se
USDAUD	fGARCH.TGARCH	2013-06-03	USDAUD.Op	1.02600	-7.365624e+01	24.941247	25.064162	24.938973	24.990655	7.178971e+01	1
USDAUD	fGARCH.NGARCH	2013-06-27	USDAUD.Lo	1.07700	2.542027e+00	-590.320340	-590.197426	-590.322615	-590.270933	2.360285e+00	1
USDAUD	fGARCH.NGARCH	2014-04-14	USDAUD.Op	1.06200	1.419924e+09	-416.149142	-416.012570	-416.151936	-416.094244	1.337028e+09	1
USDAUD	fGARCH.NAGARCH	2015-02-09	USDAUD.Op	1.28800	9.042209e+09	101.921621	102.058192	101.918826	101.976518	7.020349e+09	1
USDAUD	fGARCH.NAGARCH	2015-02-10	USDAUD.Op	1.28300	-9.623617e+31	153.814604	153.950801	153.811831	153.869344	7.500870e+31	1
USDAUD	iGARCH	2014-10-15	USDAUD.Cl	1.13730	2.310843e+145	738.699064	738.808021	738.697272	738.742856	2.031868e+145	1
USDEUR	fGARCH.NGARCH	2015-03-02	USDEUR.Lo	0.89000	-4.015994e+07	83.346290	83.510176	83.342305	83.412167	4.512353e+07	1
USDEUR	fGARCH.NGARCH	2015-06-04	USDEUR.Lo	0.88700	-1.394863e+18	-545.380537	-545.244340	-545.383310	-545.325796	1.572562e+18	1
USDEUR	fGARCH.NGARCH	2015-06-24	USDEUR.Lo	0.89100	1.892803e+10	77.586765	77.722962	77.583992	77.641506	2.124358e+10	1
USDGBP	fGARCH.TGARCH	2014-06-19	USDGBP.Lo	0.58600	-3.465523e+73	364.832355	365.037213	364.826216	364.914701	5.913861e+73	1
USDGBP	fGARCH.NGARCH	2014-03-31	USDGBP.Cl	0.60001	-1.642110e+04	-444.661563	-444.524991	-444.664357	-444.606666	2.736805e+04	1
USDGBP	fGARCH.NGARCH	2014-06-19	USDGBP.Lo	0.58600	4.316118e-01	-160.018385	-159.813528	-160.024525	-159.936039	7.365389e-01	1
USDGBP	fGARCH.NGARCH	2015-04-16	USDGBP.Cl	0.67016	1.865748e+15	-556.647438	-556.511242	-556.650211	-556.592698	2.784033e+15	1
USDGBP	fGARCH.NGARCH	2015-04-21	USDGBP.Op	0.67000	-1.002521e+06	-574.983967	-574.847770	-574.986740	-574.929227	1.496300e+06	1
USDGBP	fGARCH.NGARCH	2015-06-08	USDGBP.Op	0.65200	5.022905e+36	-490.210255	-490.087678	-490.212512	-490.160989	7.703841e+36	1
USDCHF	sGARCH	2015-01-16	USDCHF.Lo	0.85000	1.189676e+00	-6.687989	-6.606271	-6.689007	-6.655145	1.399619e+00	1
USDCHF	fGARCH.GARCH	2015-01-16	USDCHF.Lo	0.85000	1.189676e+00	-6.687989	-6.606271	-6.689007	-6.655145	1.399619e+00	1
USDCHF	fGARCH.TGARCH	2015-01-16	USDCHF.Lo	0.85000	1.182560e+00	-6.882116	-6.786779	-6.883495	-6.843798	1.391247e+00	1
USDCHF	fGARCH.NGARCH	2013-12-12	USDCHF.Op	0.88700	-3.879205e+00	-432.539483	-432.402912	-432.542277	-432.484586	4.373400e+00	1
USDCHF	fGARCH.NGARCH	2015-01-16	USDCHF.Lo	0.85000	1.182556e+00	-6.811955	-6.716617	-6.813334	-6.773637	1.391243e+00	1
USDCHF	fGARCH.NGARCH	2015-09-07	USDCHF.Lo	0.97000	-8.823318e+01	-587.029347	-586.920390	-587.031140	-586.985555	9.096204e+01	1
USDCHF	fGARCH.NGARCH	2015-10-30	USDCHF.Hi	0.99100	-1.889325e+01	-584.267632	-584.158374	-584.269437	-584.223714	1.906483e+01	1
USDCHF	fGARCH.NAGARCH	2013-12-16	USDCHF.Op	0.89000	2.195181e+145	732.215372	732.352321	732.212557	732.270427	2.466495e+145	1
USDCHF	fGARCH.NAGARCH	2015-01-09	USDCHF.Op	1.01800	-1.228938e+24	226.375920	226.539355	226.371964	226.441608	1.207208e+24	1
USDCHF	fGARCH.NAGARCH	2015-01-16	USDCHF.Lo	0.85000	1.188451e+00	-6.758750	-6.663413	-6.760129	-6.720432	1.398178e+00	1
USDCHF	fGARCH.GJRGARCH	2015-01-16	USDCHF.Lo	0.85000	1.189203e+00	-6.775060	-6.679723	-6.776439	-6.736742	1.399062e+00	1
USDCHF	gjrGARCH	2015-01-16	USDCHF.Lo	0.85000	1.187461e+00	-6.834457	-6.739119	-6.835835	-6.796138	1.397013e+00	1
USDCHF	iGARCH	2015-01-16	USDCHF.Lo	0.85000	1.189656e+00	-6.696311	-6.628212	-6.697021	-6.668940	1.399595e+00	1
USDCHF	iGARCH	2015-01-20	USDCHF.Lo	0.86900	1.169574e+00	-6.632037	-6.563939	-6.632748	-6.604667	1.345885e+00	1
USDCHF	iGARCH	2015-01-21	USDCHF.Lo	0.85100	5.536845e-01	-6.599117	-6.531019	-6.599827	-6.571747	6.506281e-01	1
USDCHF	iGARCH	2015-01-22	USDCHF.Lo	0.85300	1.132264e+00	-6.569994	-6.501896	-6.570705	-6.542624	1.327390e+00	1
USDCHF	iGARCH	2015-01-27	USDCHF.Lo	0.89400	6.896106e-01	-6.470927	-6.402829	-6.471637	-6.443557	7.713765e-01	1
USDCHF	iGARCH	2015-02-02	USDCHF.Lo	0.92000	7.319616e-01	-6.350835	-6.255235	-6.352225	-6.312407	7.956105e-01	1
USDCHF	csGARCH	2015-01-16	USDCHF.Lo	0.85000	1.193636e+00	-6.688153	-6.579196	-6.689945	-6.644361	1.404278e+00	1
USDCHF	csGARCH	2015-01-22	USDCHF.Lo	0.85300	1.141360e+00	-6.534724	-6.425767	-6.536516	-6.490932	1.338054e+00	1
USDCHF	csGARCH	2015-01-23	USDCHF.Lo	0.86800	6.200740e-01	-6.493151	-6.384194	-6.494943	-6.449359	7.143710e-01	1
USDCAD	fGARCH.NGARCH	2015-02-09	USDCAD.Cl	1.25170	-7.979335e+22	142.673774	142.783031	142.671968	142.717692	6.374798e+22	1
USDCAD	fGARCH.NGARCH	2015-03-29	USDCAD.Hi	1.27000	-6.542943e+22	-529.240306	-529.131049	-529.242112	-529.196389	5.151924e+22	1
USDCAD	fGARCH.NGARCH	2015-07-21	USDCAD.Hi	1.30500	4.139802e+61	-435.142670	-435.006474	-435.145443	-435.087930	3.172262e+61	1
USDCNY	fGARCH.TGARCH	2013-10-09	USDCNY.Op	6.11100	5.483283e+03	60.013013	60.135928	60.010739	60.062421	8.972808e+02	1
USDCNY	fGARCH.NGARCH	2014-07-17	USDCNY.Lo	6.19200	-5.016306e+02	-585.712986	-585.631043	-585.714011	-585.680047	8.101269e+01	1
USDCNY	fGARCH.NGARCH	2014-07-20	USDCNY.Lo	6.19500	1.194381e+01	-589.430373	-589.348203	-589.431406	-589.397340	1.927975e+00	1
USDCNY	fGARCH.NGARCH	2014-07-22	USDCNY.Lo	6.18900	1.945038e+01	-591.466725	-591.384782	-591.467750	-591.433786	3.142734e+00	1
USDCNY	fGARCH.NGARCH	2014-07-23	USDCNY.Lo	6.18200	-3.637318e+01	-588.553531	-588.471588	-588.554557	-588.520593	5.883724e+00	1
USDCNY	fGARCH.NGARCH	2014-07-27	USDCNY.Lo	6.17600	4.872521e+01	-587.187420	-587.105250	-587.188453	-587.154387	7.889444e+00	1
USDCNY	fGARCH.NGARCH	2014-07-31	USDCNY.Lo	6.16300	2.769268e+01	-590.455881	-590.373938	-590.456907	-590.422943	4.493377e+00	1
USDCNY	fGARCH.NGARCH	2014-08-03	USDCNY.Lo	6.16800	3.201427e+01	-587.733648	-587.651478	-587.734681	-587.700615	5.190381e+00	1
USDCNY	fGARCH.NGARCH	2014-08-05	USDCNY.Lo	6.15300	1.853196e+01	-589.664961	-589.583018	-589.665987	-589.632023	3.011858e+00	1
USDCNY	fGARCH.NGARCH	2014-08-06	USDCNY.Lo	6.14700	2.635122e+01	-591.728569	-591.646626	-591.729595	-591.695631	4.286842e+00	1
USDCNY	fGARCH.NGARCH	2014-08-12	USDCNY.Lo	6.14400	4.740305e+01	-587.300349	-587.218406	-587.301374	-587.267410	7.715340e+00	1
USDCNY	fGARCH.NGARCH	2014-08-13	USDCNY.Lo	6.14200	8.825968e+00	-589.224653	-589.142710	-589.225679	-589.191715	1.436986e+00	1
USDCNY	fGARCH.NGARCH	2014-08-14	USDCNY.Lo	6.13600	4.872331e+01	-586.351874	-586.269931	-586.352899	-586.318935	7.940565e+00	1
USDCNY	fGARCH.NGARCH	2014-08-19	USDCNY.Lo	6.13000	-1.240483e+01	-590.789977	-590.708034	-590.791003	-590.757039	2.023627e+00	1
USDCNY	fGARCH.NGARCH	2014-08-20	USDCNY.Lo	6.13000	9.161532e+00	-592.227353	-592.145410	-592.228379	-592.194415	1.494540e+00	1
USDCNY	fGARCH.NGARCH	2014-08-21	USDCNY.Lo	6.14100	-1.525661e+01	-590.144127	-590.062184	-590.145153	-590.111189	2.484385e+00	1
USDCNY	fGARCH.NGARCH	2014-08-24	USDCNY.Lo	6.14000	-3.247607e+01	-589.174302	-589.092132	-589.175335	-589.141269	5.289262e+00	1
USDCNY	fGARCH.NGARCH	2014-08-25	USDCNY.Lo	6.14200	6.174800e+01	-572.956479	-572.874536	-572.957505	-572.923541	1.005340e+01	1
USDCNY	fGARCH.NGARCH	2014-08-26	USDCNY.Lo	6.13300	9.738678e+01	-587.251542	-587.169599	-587.252568	-587.218604	1.587914e+01	1
USDCNY	fGARCH.NGARCH	2014-08-31	USDCNY.Lo	6.12900	2.545583e+02	-584.923023	-584.840853	-584.924056	-584.889989	4.153341e+01	1
USDCNY	fGARCH.NGARCH	2014-09-01	USDCNY.Lo	6.13200	1.596999e+02	-584.161053	-584.079110	-584.162079	-584.128115	2.604369e+01	1
USDCNY	fGARCH.NGARCH	2014-09-02	USDCNY.Lo	6.13100	-1.989882e+01	-589.399865	-589.317922	-589.400891	-589.366927	3.245608e+00	1
USDCNY	fGARCH.NGARCH	2014-09-04	USDCNY.Lo	6.12800	-2.866168e+01	-585.515480	-585.433537	-585.516505	-585.482541	4.677168e+00	1
USDCNY	fGARCH.NGARCH	2014-09-08	USDCNY.Lo	6.12200	-2.517129e+01	-587.872377	-587.790434	-587.873402	-587.839438	4.111612e+00	1
USDCNY	fGARCH.NGARCH	2014-09-11	USDCNY.Lo	6.12000	1.708482e+01	-588.380157	-588.298214	-588.381183	-588.347219	2.791637e+00	1
USDCNY	fGARCH.NGARCH	2014-09-14	USDCNY.Lo	6.12500	-7.626137e+01	-589.072288	-588.990119	-589.073322	-589.039255	1.245084e+01	1
USDCNY	fGARCH.NGARCH	2014-09-16	USDCNY.Lo	6.12900	-1.759094e+02	-585.597533	-585.515590	-585.598558	-585.564594	2.870116e+01	1
USDCNY	fGARCH.NGARCH	2014-10-01	USDCNY.Lo	6.12800	-1.146657e+02	-584.091459	-584.009516	-584.092485	-584.058521	1.871177e+01	1
USDCNY	fGARCH.NGARCH	2014-10-06	USDCNY.Lo	6.12900	-2.283202e+01	-579.908511	-579.826568	-579.909537	-579.875573	3.725243e+00	1
USDCNY	fGARCH.NGARCH	2014-10-07	USDCNY.Lo	6.12500	5.146397e+01	-565.845084	-565.763141	-565.846110	-565.812146	8.402281e+00	1
USDCNY	fGARCH.NGARCH	2014-10-09	USDCNY.Lo	6.12000	6.182692e+01	-583.758544	-583.676826	-583.759562	-583.725700	1.010244e+01	1
USDCNY	fGARCH.NGARCH	2014-11-26	USDCNY.Lo	6.12300	6.187566e+01	-583.601907	-583.520189	-583.602924	-583.569062	1.010545e+01	1
USDCNY	fGARCH.NAGARCH	2014-07-24	USDCNY.Lo	6.18200	-3.603032e+02	14.561667	14.643610	14.560642	14.594606	5.828262e+01	1
USDCNY	fGARCH.NAGARCH	2014-07-31	USDCNY.Lo	6.16300	-3.531901e+02	14.522470	14.604413	14.521444	14.555409	5.730814e+01	1
USDCNY	fGARCH.NAGARCH	2014-08-04	USDCNY.Lo	6.16100	-3.492923e+02	14.548440	14.630382	14.547414	14.581378	5.669409e+01	1
USDCNY	fGARCH.NAGARCH	2014-08-26	USDCNY.Lo	6.13300	4.865151e+00	104.667516	104.749459	104.666490	104.700454	7.932742e-01	1
USDCNY	fGARCH.NAGARCH	2014-09-04	USDCNY.Lo	6.12800	4.796821e+02	172.167572	172.249515	172.166546	172.200510	7.827710e+01	1
USDCNY	fGARCH.NAGARCH	2014-10-19	USDCNY.Lo	6.11300	-3.344848e+02	98.972743	99.054686	98.971717	99.005682	5.471696e+01	1
USDCNY	fGARCH.GJRGARCH	2014-09-01	USDCNY.Lo	6.13200	1.263740e+01	98.054293	98.136236	98.053267	98.087231	2.060893e+00	1
USDJPY	fGARCH.TGARCH	2013-03-31	USDJPY.Op	94.26200	-5.215159e+89	433.750440	433.914326	433.746455	433.816317	5.532621e+87	1
USDJPY	fGARCH.NGARCH	2013-05-20	USDJPY.Hi	102.87200	1.639729e+20	126.895461	127.031657	126.892687	126.950201	1.593951e+18	1
USDJPY	fGARCH.NGARCH	2013-06-16	USDJPY.Hi	95.10600	-2.728130e+05	179.131969	179.268541	179.129175	179.186867	2.868516e+03	1
USDJPY	fGARCH.NGARCH	2013-06-19	USDJPY.Hi	98.23900	4.076553e+124	740.361014	740.497210	740.358240	740.415754	4.149628e+122	1
USDJPY	fGARCH.NGARCH	2013-07-22	USDJPY.Hi	100.17000	-7.099425e+16	107.520826	107.657022	107.518052	107.575566	7.087376e+14	1

6.1.2.2C : Table summary

Lastly, we filter all bias data and look at the comparison of mse of OHLC of 7 currencies.

## filter all date which excludes bias and also contain OHLC of 7 currencies.
united.fx3 <- united.fx2 %>% dplyr::filter(!Date %in% ntimeID)

acc <- united.fx3 %>% 
  ddply(.(.id, Model), summarise, 
        MSE = mean((Price.T1 - Price)^2), 
        n = length(Price), 
        AIC.MSE = (-2*MSE)/n+2*4/n, 
        MSE.AIC = mean((Akaike - mean(Akaike))^2),
        Akaike = mean(Akaike), 
        Bayes = mean(Bayes), 
        Shibata = mean(Shibata), 
        Hannan.Quinn = mean(Hannan.Quinn)) %>% 
  tbl_df %>% mutate(MSE = round(MSE, 7))

6.1.2.3A : Table summary

Group Table Summary Contain OHLC of 7 Currencies without Bias

.id	Model	MSE	n	AIC.MSE	MSE.AIC	Akaike	Bayes	Shibata	Hannan.Quinn
USD/AUD
USDAUD	sGARCH	0.0000006	1964	0.0040733	0.1704839	-7.348481	-7.269185	-7.349482	-7.316607
USDAUD	fGARCH.GARCH	0.0000006	1964	0.0040733	0.1704050	-7.348536	-7.269241	-7.349537	-7.316662
USDAUD	fGARCH.TGARCH	0.0000031	1964	0.0040733	0.6415224	-7.105799	-7.012850	-7.107153	-7.068437
USDAUD	fGARCH.NGARCH	0.0000060	1964	0.0040733	8429.7696048	-22.993951	-22.901002	-22.995305	-22.956589
USDAUD	fGARCH.NAGARCH	0.0000006	1964	0.0040733	30.4577459	-7.232584	-7.139635	-7.233937	-7.195222
USDAUD	fGARCH.GJRGARCH	0.0000008	1964	0.0040733	0.1780224	-7.349209	-7.256260	-7.350563	-7.311847
USDAUD	gjrGARCH	0.0000008	1964	0.0040733	0.1802683	-7.356035	-7.263086	-7.357389	-7.318673
USDAUD	iGARCH	0.0000008	1964	0.0040733	0.1744092	-7.350949	-7.285307	-7.351652	-7.324563
USDAUD	csGARCH	0.0000008	1964	0.0040733	0.1766085	-7.330955	-7.224352	-7.332714	-7.288105
USD/CAD
USDEUR	sGARCH	0.0000004	1964	0.0040733	0.3016021	-8.314447	-8.231956	-8.315531	-8.281289
USDEUR	fGARCH.GARCH	0.0000004	1964	0.0040733	0.3013892	-8.314567	-8.232076	-8.315651	-8.281409
USDEUR	fGARCH.TGARCH	0.0000010	1964	0.0040733	0.5009938	-8.164153	-8.068009	-8.165602	-8.125507
USDEUR	fGARCH.NGARCH	0.0000029	1964	0.0040733	9002.7971698	-23.129780	-23.033635	-23.131228	-23.091133
USDEUR	fGARCH.NAGARCH	0.0000004	1964	0.0040733	34.8478527	-8.190174	-8.094030	-8.191623	-8.151528
USDEUR	fGARCH.GJRGARCH	0.0000004	1964	0.0040733	0.3046646	-8.322888	-8.226743	-8.324337	-8.284241
USDEUR	gjrGARCH	0.0000004	1964	0.0040733	0.3068970	-8.340332	-8.244188	-8.341781	-8.301686
USDEUR	iGARCH	0.0000004	1964	0.0040733	0.3008728	-8.313577	-8.244740	-8.314350	-8.285907
USDEUR	csGARCH	0.0000005	1964	0.0040733	0.2879457	-8.301212	-8.191414	-8.303078	-8.257077
USD/CHF
USDGBP	sGARCH	0.0000001	1964	0.0040733	0.1053306	-9.015116	-8.934469	-9.016172	-8.982700
USDGBP	fGARCH.GARCH	0.0000001	1964	0.0040733	0.1050917	-9.015254	-8.934607	-9.016311	-8.982839
USDGBP	fGARCH.TGARCH	0.0000002	1964	0.0040733	0.4531749	-8.745162	-8.650876	-8.746575	-8.707265
USDGBP	fGARCH.NGARCH	0.0000004	1964	0.0040733	3554.5406689	-14.406021	-14.311735	-14.407434	-14.368123
USDGBP	fGARCH.NAGARCH	0.0000001	1964	0.0040733	22.3878180	-8.834433	-8.740147	-8.835845	-8.796535
USDGBP	fGARCH.GJRGARCH	0.0000001	1964	0.0040733	0.1091998	-9.028451	-8.934166	-9.029864	-8.990554
USDGBP	gjrGARCH	0.0000001	1964	0.0040733	0.1065263	-9.041778	-8.947492	-9.043191	-9.003880
USDGBP	iGARCH	0.0000001	1964	0.0040733	0.1054963	-9.015574	-8.948566	-9.016327	-8.988640
USDGBP	csGARCH	0.0000001	1964	0.0040733	0.0918052	-9.001129	-8.893204	-9.002951	-8.957749
USD/CNY
USDCHF	sGARCH	0.0000050	1964	0.0040733	0.4360335	-7.556341	-7.474477	-7.557410	-7.523434
USDCHF	fGARCH.GARCH	0.0000050	1964	0.0040733	0.4365744	-7.555830	-7.473967	-7.556900	-7.522924
USDCHF	fGARCH.TGARCH	0.0000029	1964	0.0040733	0.5861093	-7.550472	-7.454952	-7.551904	-7.512076
USDCHF	fGARCH.NGARCH	0.0000040	1964	0.0040733	6175.8773918	-18.988818	-18.893299	-18.990250	-18.950422
USDCHF	fGARCH.NAGARCH	0.0000026	1964	0.0040733	75.7828723	-6.946425	-6.850905	-6.947857	-6.908029
USDCHF	fGARCH.GJRGARCH	0.0000030	1964	0.0040733	0.4032531	-7.593545	-7.498025	-7.594977	-7.555149
USDCHF	gjrGARCH	0.0000034	1964	0.0040733	0.4108477	-7.613690	-7.518171	-7.615123	-7.575295
USDCHF	iGARCH	0.0000796	1964	0.0040732	0.5694475	-7.479379	-7.411172	-7.480139	-7.451962
USDCHF	csGARCH	0.0000243	1964	0.0040733	0.4709379	-7.517801	-7.408626	-7.519649	-7.473916
USD/EUR
USDCAD	sGARCH	0.0000004	1964	0.0040733	0.1946121	-8.036072	-7.955282	-8.037116	-8.003597
USDCAD	fGARCH.GARCH	0.0000004	1964	0.0040733	0.1947232	-8.036130	-7.955340	-8.037175	-8.003656
USDCAD	fGARCH.TGARCH	0.0000013	1964	0.0040733	0.6797914	-7.799262	-7.704818	-7.800664	-7.761299
USDCAD	fGARCH.NGARCH	0.0000089	1964	0.0040733	8785.5565821	-25.027626	-24.933183	-25.029029	-24.989663
USDCAD	fGARCH.NAGARCH	0.0000003	1964	0.0040733	0.1940495	-8.044102	-7.949659	-8.045505	-8.006139
USDCAD	fGARCH.GJRGARCH	0.0000003	1964	0.0040733	0.1950460	-8.040065	-7.945622	-8.041468	-8.002103
USDCAD	gjrGARCH	0.0000003	1964	0.0040733	0.1932222	-8.045696	-7.951252	-8.047098	-8.007733
USDCAD	iGARCH	0.0000004	1964	0.0040733	0.1967645	-8.035456	-7.968319	-8.036196	-8.008469
USDCAD	csGARCH	0.0000004	1964	0.0040733	0.1925457	-8.020174	-7.912078	-8.021988	-7.976724
USD/GBP
USDCNY	sGARCH	0.0005846	1964	0.0040727	0.9851124	-6.594331	-6.504166	-6.595617	-6.558089
USDCNY	fGARCH.GARCH	0.0003402	1964	0.0040730	0.9836548	-6.594248	-6.504084	-6.595535	-6.558007
USDCNY	fGARCH.TGARCH	0.0010341	1964	0.0040723	2.0081608	-6.338085	-6.234279	-6.339766	-6.296360
USDCNY	fGARCH.NGARCH	0.1420922	1964	0.0039286	2083.0907734	-10.205374	-10.101568	-10.207055	-10.163649
USDCNY	fGARCH.NAGARCH	0.0002175	1964	0.0040731	1.2126230	-6.604923	-6.501117	-6.606604	-6.563198
USDCNY	fGARCH.GJRGARCH	0.0004765	1964	0.0040728	1.1551500	-6.594711	-6.490905	-6.596392	-6.552987
USDCNY	gjrGARCH	0.0005059	1964	0.0040728	0.9731173	-6.636100	-6.532294	-6.637780	-6.594375
USDCNY	iGARCH	0.0006407	1964	0.0040727	1.1136171	-6.553609	-6.477087	-6.554555	-6.522851
USDCNY	csGARCH	0.0006482	1964	0.0040727	1.1517611	-6.579058	-6.461610	-6.581185	-6.531850
USD/JPY
USDJPY	sGARCH	0.0119944	1964	0.0040611	0.1837680	1.628464	1.717233	1.627188	1.664144
USDJPY	fGARCH.GARCH	0.0118018	1964	0.0040613	0.1835890	1.628656	1.717425	1.627380	1.664336
USDJPY	fGARCH.TGARCH	0.0137016	1964	0.0040594	0.2188039	1.645614	1.748025	1.643950	1.686778
USDJPY	fGARCH.NGARCH	0.0712931	1964	0.0040007	7516.7405061	-13.098092	-12.995681	-13.099756	-13.056928
USDJPY	fGARCH.NAGARCH	0.0079408	1964	0.0040652	0.1933607	1.613558	1.715969	1.611894	1.654722
USDJPY	fGARCH.GJRGARCH	0.0096504	1964	0.0040635	0.1885072	1.624642	1.727053	1.622977	1.665806
USDJPY	gjrGARCH	0.0086481	1964	0.0040645	0.1950242	1.616392	1.718803	1.614728	1.657556
USDJPY	iGARCH	0.0118972	1964	0.0040612	0.1854706	1.626329	1.701457	1.625388	1.656527
USDJPY	csGARCH	0.0150696	1964	0.0040580	0.1796248	1.635637	1.751690	1.633532	1.682284

6.1.2.3B : Table summary

Table Summary Contain OHLC of 7 Currencies without Bias

Model	MSE	n	AIC.MSE	MSE.AIC	Akaike	Bayes	Shibata	Hannan.Quinn
sGARCH	0.0017979	13748	0.0005816	11.75159	-6.462332	-6.378900	-6.463449	-6.428796
fGARCH.GARCH	0.0017355	13748	0.0005817	11.75186	-6.462273	-6.378841	-6.463390	-6.428737
fGARCH.TGARCH	0.0021063	13748	0.0005816	11.73389	-6.293903	-6.196823	-6.295388	-6.254881
fGARCH.NGARCH	0.0304868	13748	0.0005775	6535.31500	-18.264237	-18.167158	-18.265722	-18.225216
fGARCH.NAGARCH	0.0011660	13748	0.0005817	34.58807	-6.319869	-6.222789	-6.321354	-6.280847
fGARCH.GJRGARCH	0.0014474	13748	0.0005817	11.79313	-6.472033	-6.374953	-6.473518	-6.433011
gjrGARCH	0.0013084	13748	0.0005817	11.78129	-6.488177	-6.391097	-6.489662	-6.449155
iGARCH	0.0018028	13748	0.0005816	11.76056	-6.446031	-6.376248	-6.446833	-6.417981
csGARCH	0.0022491	13748	0.0005816	11.75174	-6.444956	-6.334228	-6.446862	-6.400448

6.1.2.3C : Table summary

6.2 Open Price

6.2.1 All Models

## filtered bias closing price.
op <- fx %>% separate(Type, c('Cur', 'Type')) %>% 
  dplyr::filter(Type == 'Op') %>% 
  dplyr::select(-Cur, -Type)

ntmID <- op %>% dplyr::filter(se == 1) %>% .$Date %>% unlist %>% sort

acc <- op %>% dplyr::filter(!Date %in% ntmID & Date %in% ntimeID2) %>% 
  ddply(.(.id, Model), summarise, 
        MSE = mean((Price.T1 - Price)^2), 
        n = length(Price), 
        AIC.MSE = (-2*MSE)/n+2*4/n, 
        MSE.AIC = mean((Akaike - mean(Akaike))^2),
        Akaike = mean(Akaike), 
        Bayes = mean(Bayes), 
        Shibata = mean(Shibata), 
        Hannan.Quinn = mean(Hannan.Quinn)) %>% 
  tbl_df %>% mutate(MSE = round(MSE, 7))

Open Price Summary : All Models

.id	Model	MSE	n	AIC.MSE	MSE.AIC	Akaike	Bayes	Shibata	Hannan.Quinn
USD/AUD
USDAUD	sGARCH	0.0000010	543	0.0147330	1.498536e-01	-7.273287	-7.191877	-7.274345	-7.240563
USDAUD	fGARCH.GARCH	0.0000011	543	0.0147330	1.496184e-01	-7.273028	-7.191618	-7.274087	-7.240305
USDAUD	fGARCH.TGARCH	0.0000027	543	0.0147330	4.394660e-01	-7.098187	-7.003124	-7.099606	-7.059976
USDAUD	fGARCH.AVGARCH	0.0000002	52	0.1538461	4.323170e-02	-7.644820	-7.531890	-7.646799	-7.599426
USDAUD	fGARCH.NGARCH	0.0000040	543	0.0147330	4.978345e+03	-16.268829	-16.173766	-16.270248	-16.230617
USDAUD	fGARCH.NAGARCH	0.0000009	543	0.0147330	1.566873e-01	-7.284149	-7.189086	-7.285568	-7.245938
USDAUD	fGARCH.APARCH	0.0000005	351	0.0227920	1.085739e+03	-9.402868	-9.296290	-9.404638	-9.360026
USDAUD	fGARCH.GJRGARCH	0.0000010	543	0.0147330	1.522789e-01	-7.277452	-7.182389	-7.278871	-7.239240
USDAUD	fGARCH.ALLGARCH	0.0000012	265	0.0301887	2.884090e+02	-8.554293	-8.426976	-8.556794	-8.503117
USDAUD	eGARCH	0.0000013	492	0.0162602	1.107478e-01	-7.338778	-7.243300	-7.340212	-7.300400
USDAUD	gjrGARCH	0.0000010	543	0.0147330	1.547929e-01	-7.285277	-7.190214	-7.286696	-7.247065
USDAUD	apARCH	0.0000005	89	0.0898876	3.089500e-03	-7.725827	-7.606726	-7.728035	-7.677952
USDAUD	iGARCH	0.0000011	543	0.0147330	1.489983e-01	-7.278051	-7.210294	-7.278802	-7.250815
USDAUD	csGARCH	0.0000013	543	0.0147330	1.527615e-01	-7.255735	-7.147019	-7.257568	-7.212035
USD/CAD
USDEUR	sGARCH	0.0000004	543	0.0147330	3.288031e-01	-8.257352	-8.174005	-8.258455	-8.223850
USDEUR	fGARCH.GARCH	0.0000004	543	0.0147330	3.288435e-01	-8.257300	-8.173953	-8.258403	-8.223798
USDEUR	fGARCH.TGARCH	0.0000006	543	0.0147330	5.512540e-01	-8.128269	-8.031269	-8.129740	-8.089279
USDEUR	fGARCH.AVGARCH	0.0000000	26	0.3076923	8.860980e-02	-7.884639	-7.783841	-7.886225	-7.844123
USDEUR	fGARCH.NGARCH	0.0000010	543	0.0147330	4.770952e+03	-15.398501	-15.301502	-15.399973	-15.359511
USDEUR	fGARCH.NAGARCH	0.0000004	543	0.0147330	3.341634e-01	-8.263886	-8.166886	-8.265357	-8.224896
USDEUR	fGARCH.APARCH	0.0000010	127	0.0629921	7.348679e+02	-10.130251	-10.021392	-10.132112	-10.086494
USDEUR	fGARCH.GJRGARCH	0.0000003	543	0.0147330	3.365995e-01	-8.267377	-8.170377	-8.268848	-8.228387
USDEUR	fGARCH.ALLGARCH	0.0000005	375	0.0213333	2.758547e+03	-13.216209	-13.090285	-13.218638	-13.165591
USDEUR	eGARCH	0.0000016	494	0.0161943	6.493540e-01	-8.301821	-8.203523	-8.303331	-8.262309
USDEUR	gjrGARCH	0.0000003	543	0.0147330	3.414733e-01	-8.282342	-8.185343	-8.283813	-8.243352
USDEUR	apARCH	0.0000000	89	0.0898876	4.382000e-04	-8.065416	-7.966130	-8.066936	-8.025506
USDEUR	iGARCH	0.0000004	543	0.0147330	3.333370e-01	-8.256227	-8.186534	-8.257016	-8.228213
USDEUR	csGARCH	0.0000005	543	0.0147330	3.261404e-01	-8.236246	-8.125593	-8.238138	-8.191768
USD/CHF
USDGBP	sGARCH	0.0000001	543	0.0147330	1.038946e-01	-8.970309	-8.885876	-8.971473	-8.936371
USDGBP	fGARCH.GARCH	0.0000001	543	0.0147330	1.038977e-01	-8.970657	-8.886224	-8.971821	-8.936720
USDGBP	fGARCH.TGARCH	0.0000002	543	0.0147330	5.474029e-01	-8.665692	-8.567619	-8.667227	-8.626272
USDGBP	fGARCH.AVGARCH	0.0000000	34	0.2352941	2.962751e+01	-7.880450	-7.784713	-7.881841	-7.841971
USDGBP	fGARCH.NGARCH	0.0000002	543	0.0147330	4.856837e+03	-17.193027	-17.094954	-17.194562	-17.153607
USDGBP	fGARCH.NAGARCH	0.0000001	543	0.0147330	2.741967e+01	-8.756947	-8.658874	-8.758482	-8.717527
USDGBP	fGARCH.APARCH	0.0000000	352	0.0227273	9.465991e+02	-10.407965	-10.296301	-10.409934	-10.363081
USDGBP	fGARCH.GJRGARCH	0.0000002	543	0.0147330	1.092427e-01	-8.982736	-8.884664	-8.984271	-8.943316
USDGBP	fGARCH.ALLGARCH	0.0000000	377	0.0212202	2.658203e-01	-9.012428	-8.885996	-9.014916	-8.961608
USDGBP	eGARCH	0.0000002	491	0.0162933	7.086997e+00	-8.885864	-8.786425	-8.887443	-8.845895
USDGBP	gjrGARCH	0.0000001	543	0.0147330	1.126683e-01	-8.996081	-8.898009	-8.997616	-8.956661
USDGBP	apARCH	0.0000000	89	0.0898876	2.585700e-03	-9.066846	-8.969667	-9.068285	-9.027788
USDGBP	iGARCH	0.0000001	543	0.0147330	1.036423e-01	-8.970398	-8.899604	-8.971243	-8.941942
USDGBP	csGARCH	0.0000001	543	0.0147330	1.024553e-01	-8.949799	-8.838086	-8.951757	-8.904896
USD/CNY
USDCHF	sGARCH	0.0000039	543	0.0147330	4.919016e-01	-7.476076	-7.394413	-7.477152	-7.443250
USDCHF	fGARCH.GARCH	0.0000039	543	0.0147330	4.935157e-01	-7.473893	-7.392230	-7.474969	-7.441067
USDCHF	fGARCH.TGARCH	0.0000082	543	0.0147329	1.291667e+00	-7.426330	-7.331011	-7.427767	-7.388015
USDCHF	fGARCH.AVGARCH	0.0000002	16	0.5000000	2.541510e-02	-7.687590	-7.571104	-7.689769	-7.640760
USDCHF	fGARCH.NGARCH	0.0000027	543	0.0147330	6.592833e+03	-23.038598	-22.943279	-23.040035	-23.000283
USDCHF	fGARCH.NAGARCH	0.0000019	543	0.0147330	7.632188e+01	-6.816151	-6.720832	-6.817588	-6.777836
USDCHF	fGARCH.APARCH	0.0000002	350	0.0228571	9.739399e+02	-9.416715	-9.304375	-9.418694	-9.371557
USDCHF	fGARCH.GJRGARCH	0.0000024	543	0.0147330	4.619364e-01	-7.519177	-7.423859	-7.520614	-7.480862
USDCHF	fGARCH.ALLGARCH	0.0000009	374	0.0213904	7.224024e+03	-20.033994	-19.907915	-20.036455	-19.983313
USDCHF	eGARCH	0.0000006	494	0.0161943	3.717572e-01	-7.632103	-7.536873	-7.633542	-7.593824
USDCHF	gjrGARCH	0.0000024	543	0.0147330	4.579808e-01	-7.546094	-7.450776	-7.547532	-7.507779
USDCHF	apARCH	0.0000001	88	0.0909091	1.434400e-03	-7.782664	-7.680569	-7.784294	-7.741623
USDCHF	iGARCH	0.0000038	543	0.0147330	5.465868e-01	-7.451658	-7.383650	-7.452426	-7.424321
USDCHF	csGARCH	0.0000038	543	0.0147330	4.991954e-01	-7.456733	-7.347759	-7.458585	-7.412929
USD/EUR
USDCAD	sGARCH	0.0000002	543	0.0147330	1.858161e-01	-7.975405	-7.895423	-7.976432	-7.943255
USDCAD	fGARCH.GARCH	0.0000002	543	0.0147330	1.856532e-01	-7.975549	-7.895567	-7.976576	-7.943399
USDCAD	fGARCH.TGARCH	0.0000008	543	0.0147330	4.687355e-01	-7.773262	-7.679627	-7.774643	-7.735624
USDCAD	fGARCH.AVGARCH	0.0000001	40	0.2000000	3.721640e-02	-8.215637	-8.105027	-8.217508	-8.171176
USDCAD	fGARCH.NGARCH	0.0000007	543	0.0147330	3.740808e+03	-14.279807	-14.186173	-14.281189	-14.242170
USDCAD	fGARCH.NAGARCH	0.0000002	543	0.0147330	1.852753e-01	-7.982745	-7.889111	-7.984127	-7.945108
USDCAD	fGARCH.APARCH	0.0000007	350	0.0228571	1.319121e+03	-10.341593	-10.235881	-10.343324	-10.299099
USDCAD	fGARCH.GJRGARCH	0.0000002	543	0.0147330	1.894489e-01	-7.982292	-7.888657	-7.983674	-7.944655
USDCAD	fGARCH.ALLGARCH	0.0000001	376	0.0212766	1.080895e+03	-10.463258	-10.343115	-10.465472	-10.414964
USDCAD	eGARCH	0.0000002	488	0.0163934	1.482847e-01	-8.024710	-7.932527	-8.026043	-7.987656
USDCAD	gjrGARCH	0.0000002	543	0.0147330	1.875893e-01	-7.988993	-7.895358	-7.990375	-7.951355
USDCAD	apARCH	0.0000001	88	0.0909091	3.022700e-03	-8.297556	-8.186739	-8.299446	-8.253011
USDCAD	iGARCH	0.0000003	543	0.0147330	1.886790e-01	-7.973358	-7.907030	-7.974084	-7.946697
USDCAD	csGARCH	0.0000002	543	0.0147330	1.824291e-01	-7.960269	-7.852981	-7.962059	-7.917143
USD/GBP
USDCNY	sGARCH	0.0000059	543	0.0147329	1.995908e-01	-6.864431	-6.776764	-6.865644	-6.829193
USDCNY	fGARCH.GARCH	0.0000058	543	0.0147329	1.993972e-01	-6.863528	-6.775861	-6.864741	-6.828290
USDCNY	fGARCH.TGARCH	0.0000168	543	0.0147329	1.437177e+00	-6.503648	-6.402339	-6.505246	-6.462927
USDCNY	fGARCH.AVGARCH	0.0000005	12	0.6666666	3.583000e-04	-6.991135	-6.882277	-6.992923	-6.947384
USDCNY	fGARCH.NGARCH	0.0000088	543	0.0147329	3.141293e+03	-12.299544	-12.198235	-12.301142	-12.258823
USDCNY	fGARCH.NAGARCH	0.0000053	543	0.0147329	1.924556e-01	-6.899384	-6.798075	-6.900982	-6.858663
USDCNY	fGARCH.APARCH	0.0008172	349	0.0229180	2.700066e+04	-57.042188	-56.921593	-57.044415	-56.993714
USDCNY	fGARCH.GJRGARCH	0.0000062	543	0.0147329	1.887118e-01	-6.896163	-6.794854	-6.897761	-6.855442
USDCNY	fGARCH.ALLGARCH	0.0000299	376	0.0212764	1.809362e+03	-10.064395	-9.931495	-10.067081	-10.010976
USDCNY	eGARCH	0.0000097	491	0.0162932	2.626618e-01	-6.893326	-6.791439	-6.894945	-6.852373
USDCNY	gjrGARCH	0.0000066	543	0.0147329	1.784699e-01	-6.911417	-6.810108	-6.913015	-6.870696
USDCNY	apARCH	0.0000118	89	0.0898874	6.353630e-02	-6.738219	-6.621906	-6.740295	-6.691470
USDCNY	iGARCH	0.0000071	543	0.0147329	2.055216e-01	-6.852918	-6.778893	-6.853800	-6.823163
USDCNY	csGARCH	0.0000094	543	0.0147329	2.135969e-01	-6.886648	-6.771696	-6.888683	-6.840443
USD/JPY
USDJPY	sGARCH	0.0099659	543	0.0146963	1.733303e-01	1.719711	1.807160	1.718471	1.754861
USDJPY	fGARCH.GARCH	0.0093915	543	0.0146984	1.733284e-01	1.719789	1.807237	1.718549	1.754939
USDJPY	fGARCH.TGARCH	0.0056530	543	0.0147121	1.826058e-01	1.724055	1.825146	1.722432	1.764688
USDJPY	fGARCH.AVGARCH	0.1450546	40	0.1927473	1.221420e+00	1.313452	1.451011	1.310536	1.368740
USDJPY	fGARCH.NGARCH	0.0120539	543	0.0146886	1.012792e+04	-18.534436	-18.433345	-18.536059	-18.493803
USDJPY	fGARCH.NAGARCH	0.0049176	543	0.0147149	1.843351e-01	1.706950	1.808040	1.705326	1.747583
USDJPY	fGARCH.APARCH	0.0182964	131	0.0607894	1.198905e+04	-18.147979	-18.025689	-18.150340	-18.098828
USDJPY	fGARCH.GJRGARCH	0.0071971	543	0.0147065	1.796384e-01	1.715943	1.817034	1.714320	1.756576
USDJPY	fGARCH.ALLGARCH	0.0299952	199	0.0398995	8.797060e+03	-16.069967	-15.946816	-16.072338	-16.020467
USDJPY	eGARCH	0.0125981	492	0.0162090	2.659699e-01	1.748790	1.850811	1.747137	1.789797
USDJPY	gjrGARCH	0.0050117	543	0.0147145	1.889876e-01	1.702825	1.803916	1.701202	1.743458
USDJPY	apARCH	0.4214707	88	0.0813302	8.163543e+04	-55.866330	-55.737713	-55.868945	-55.814636
USDJPY	iGARCH	0.0098076	543	0.0146968	1.753304e-01	1.717299	1.791105	1.716388	1.746965
USDJPY	csGARCH	0.0090023	543	0.0146998	1.706387e-01	1.726386	1.841119	1.724327	1.772502

6.2.1.1 : Table summary

Above table shows the n excludes the bias dataset. If the open price of particular currency on particular date is bias, then the highest, lowest and close preice will also not in count due to filter by date.

Open Price Summary : All Models

Model	MSE	n	AIC.MSE	MSE.AIC	Akaike	Bayes	Shibata	Hannan.Quinn
sGARCH	0.0014254	3801	0.0021040	11.74639	-6.442450	-6.358743	-6.443576	-6.408803
fGARCH.GARCH	0.0013433	3801	0.0021040	11.74619	-6.442024	-6.358317	-6.443150	-6.408377
fGARCH.TGARCH	0.0008117	3801	0.0021043	11.76472	-6.267333	-6.169978	-6.268828	-6.228200
fGARCH.AVGARCH	0.0263737	220	0.0361239	17.29090	-6.152041	-6.039109	-6.154038	-6.106648
fGARCH.NGARCH	0.0017245	3801	0.0021038	5468.55402	-16.716106	-16.618751	-16.717601	-16.676973
fGARCH.NAGARCH	0.0007038	3801	0.0021043	26.17421	-6.328045	-6.230689	-6.329540	-6.288912
fGARCH.APARCH	0.0013347	2010	0.0039788	6584.86523	-18.632372	-18.520450	-18.634331	-18.587383
fGARCH.GJRGARCH	0.0010296	3801	0.0021042	11.77034	-6.458465	-6.361110	-6.459960	-6.419332
fGARCH.ALLGARCH	0.0025539	2342	0.0034137	2855.06098	-12.395255	-12.269110	-12.397708	-12.344549
eGARCH	0.0018027	3442	0.0023232	12.90935	-6.474513	-6.376718	-6.476023	-6.435204
gjrGARCH	0.0007175	3801	0.0021043	11.77250	-6.472483	-6.375127	-6.473978	-6.433350
apARCH	0.0598234	620	0.0127102	11867.07036	-14.747367	-14.636897	-14.749278	-14.702964
iGARCH	0.0014029	3801	0.0021040	11.74181	-6.437901	-6.367843	-6.438712	-6.409741
csGARCH	0.0012882	3801	0.0021040	11.72457	-6.431292	-6.320288	-6.433209	-6.386673

6.2.1.2 : Table summary

Similar with tabl 6.2.1.1 but without breakdown the currency.

Open Price Summary : All Models

Model	n
fGARCH.TGARCH	3
fGARCH.AVGARCH	1
fGARCH.NGARCH	7
fGARCH.NAGARCH	5
fGARCH.APARCH	1
fGARCH.ALLGARCH	6
eGARCH	1
apARCH	1
csGARCH	1

6.2.1.3 : Table summary

Hi-Lo Price Summary : Selected Models

.id	Model	Date	Price	Price.T1	Akaike	Bayes	Shibata	Hannan.Quinn	diff	se
USDAUD	fGARCH.TGARCH	2013-06-03	1.026	-7.365624e+01	24.94125	25.06416	24.93897	24.99066	7.178971e+01	1
USDAUD	fGARCH.AVGARCH	2013-04-11	0.948	-1.522796e+47	263.58733	263.76487	263.58267	263.65869	1.606325e+47	1
USDAUD	fGARCH.NGARCH	2013-08-04	1.123	1.260885e+39	-299.19447	-299.08491	-299.19629	-299.15043	1.122783e+39	1
USDAUD	fGARCH.NGARCH	2014-04-14	1.062	1.419924e+09	-416.14914	-416.01257	-416.15194	-416.09424	1.337028e+09	1
USDAUD	fGARCH.NAGARCH	2015-02-09	1.288	9.042209e+09	101.92162	102.05819	101.91883	101.97652	7.020349e+09	1
USDAUD	fGARCH.NAGARCH	2015-02-10	1.283	-9.623617e+31	153.81460	153.95080	153.81183	153.86934	7.500870e+31	1
USDAUD	fGARCH.ALLGARCH	2014-07-08	1.062	-3.075920e+11	-560.31931	-560.15543	-560.32330	-560.25344	2.896347e+11	1
USDGBP	fGARCH.NGARCH	2015-04-21	0.670	-1.002521e+06	-574.98397	-574.84777	-574.98674	-574.92923	1.496300e+06	1
USDGBP	fGARCH.NGARCH	2015-06-08	0.652	5.022905e+36	-490.21025	-490.08768	-490.21251	-490.16099	7.703841e+36	1
USDGBP	fGARCH.NGARCH	2015-06-16	0.639	1.392346e+72	349.93988	350.04884	349.93809	349.98367	2.178945e+72	1
USDGBP	fGARCH.ALLGARCH	2014-03-17	0.601	1.849141e+38	-496.80912	-496.64478	-496.81313	-496.74305	3.076773e+38	1
USDGBP	fGARCH.ALLGARCH	2014-04-06	0.603	-8.491069e+75	422.06222	422.24026	422.05753	422.13379	1.408138e+76	1
USDCHF	fGARCH.NGARCH	2013-12-12	0.887	-3.879205e+00	-432.53948	-432.40291	-432.54228	-432.48459	4.373400e+00	1
USDCHF	fGARCH.NAGARCH	2013-12-05	0.902	4.359195e+145	731.45001	731.58658	731.44721	731.50490	4.832810e+145	1
USDCHF	fGARCH.NAGARCH	2013-12-16	0.890	2.195181e+145	732.21537	732.35232	732.21256	732.27043	2.466495e+145	1
USDCHF	fGARCH.NAGARCH	2015-01-09	1.018	-1.228938e+24	226.37592	226.53936	226.37196	226.44161	1.207208e+24	1
USDCHF	fGARCH.APARCH	2014-07-28	0.904	-9.149533e+37	-500.11616	-499.92496	-500.12153	-500.03931	1.012116e+38	1
USDCHF	fGARCH.ALLGARCH	2014-03-13	0.874	1.402952e+08	-564.39523	-564.23134	-564.39921	-564.32935	1.605208e+08	1
USDCHF	eGARCH	2014-01-13	0.902	2.132004e+100	108.98449	109.12144	108.98168	109.03955	2.363641e+100	1
USDCAD	fGARCH.ALLGARCH	2015-02-09	1.252	1.586578e+17	110.07631	110.21288	110.07351	110.13120	1.267235e+17	1
USDCNY	fGARCH.TGARCH	2013-10-09	6.111	5.483283e+03	60.01301	60.13593	60.01074	60.06242	8.972808e+02	1
USDCNY	fGARCH.NGARCH	2017-06-15	6.806	-1.649282e+44	-461.94755	-461.82497	-461.94980	-461.89828	2.423276e+43	1
USDCNY	fGARCH.ALLGARCH	2013-03-19	6.214	1.851958e+30	-506.91931	-506.75587	-506.92327	-506.85362	2.980300e+29	1
USDCNY	csGARCH	2014-03-19	6.182	-4.743008e+149	761.60601	761.76990	761.60203	761.67189	7.672287e+148	1
USDJPY	fGARCH.TGARCH	2013-03-31	94.262	-5.215159e+89	433.75044	433.91433	433.74645	433.81632	5.532621e+87	1
USDJPY	apARCH	2013-05-06	99.364	-2.666861e+24	223.44523	223.59505	223.44189	223.50544	2.683931e+22	1

6.2.1.4 : Table summary

6.2.2 Selected Models

## selected models' filtered closing price.
op <- united.fx2 %>% 
  separate(Type, c('Cur', 'Type')) %>% 
  dplyr::filter(Type == 'Op') %>% dplyr::select(-Cur, -Type)

acc <- op %>% 
  ddply(.(.id, Model), summarise, 
        MSE = mean((Price.T1 - Price)^2), 
        n = length(Price), 
        AIC.MSE = (-2*MSE)/n+2*4/n, 
        MSE.AIC = mean((Akaike - mean(Akaike))^2),
        Akaike = mean(Akaike), 
        Bayes = mean(Bayes), 
        Shibata = mean(Shibata), 
        Hannan.Quinn = mean(Hannan.Quinn)) %>% 
  tbl_df %>% mutate(MSE = round(MSE, 7))

Open Price Summary : Selected Models

.id	Model	MSE	n	AIC.MSE	MSE.AIC	Akaike	Bayes	Shibata	Hannan.Quinn
USD/AUD
USDAUD	sGARCH	1.100000e-06	559	1.431130e-02	0.1475105	-7.275622	-7.193904	-7.276690	-7.242774
USDAUD	fGARCH.GARCH	1.100000e-06	559	1.431130e-02	0.1472847	-7.275369	-7.193651	-7.276437	-7.242522
USDAUD	fGARCH.TGARCH	9.977529e+00	559	-2.138650e-02	2.2663354	-7.043007	-6.947635	-7.044436	-7.004671
USDAUD	fGARCH.NGARCH	3.606767e+15	559	-1.290435e+13	5130.7079451	-16.650695	-16.555323	-16.652124	-16.612359
USDAUD	fGARCH.NAGARCH	1.656780e+61	559	-5.927656e+58	67.6839465	-6.802571	-6.707200	-6.804001	-6.764236
USDAUD	fGARCH.GJRGARCH	1.000000e-06	559	1.431130e-02	0.1499755	-7.279926	-7.184554	-7.281356	-7.241590
USDAUD	gjrGARCH	1.000000e-06	559	1.431130e-02	0.1524026	-7.287664	-7.192292	-7.289093	-7.249328
USDAUD	iGARCH	1.100000e-06	559	1.431130e-02	0.1467011	-7.280357	-7.212292	-7.281117	-7.252997
USDAUD	csGARCH	1.300000e-06	559	1.431130e-02	0.1507580	-7.256958	-7.147932	-7.258802	-7.213133
USD/CAD
USDEUR	sGARCH	4.000000e-07	559	1.431130e-02	0.3231024	-8.260904	-8.177451	-8.262010	-8.227360
USDEUR	fGARCH.GARCH	4.000000e-07	559	1.431130e-02	0.3231340	-8.260830	-8.177377	-8.261936	-8.227286
USDEUR	fGARCH.TGARCH	6.000000e-07	559	1.431130e-02	0.5406883	-8.136113	-8.039007	-8.137587	-8.097080
USDEUR	fGARCH.NGARCH	1.000000e-06	559	1.431130e-02	4635.7699223	-15.197491	-15.100385	-15.198966	-15.158458
USDEUR	fGARCH.NAGARCH	4.000000e-07	559	1.431130e-02	0.3283555	-8.267473	-8.170366	-8.268947	-8.228440
USDEUR	fGARCH.GJRGARCH	3.000000e-07	559	1.431130e-02	0.3307474	-8.271118	-8.174011	-8.272592	-8.232084
USDEUR	gjrGARCH	3.000000e-07	559	1.431130e-02	0.3354663	-8.286157	-8.189051	-8.287631	-8.247124
USDEUR	iGARCH	4.000000e-07	559	1.431130e-02	0.3275217	-8.259763	-8.189963	-8.260553	-8.231706
USDEUR	csGARCH	5.000000e-07	559	1.431130e-02	0.3204142	-8.239874	-8.129114	-8.241769	-8.195352
USD/CHF
USDGBP	sGARCH	1.000000e-07	559	1.431130e-02	0.1028412	-8.970168	-8.885417	-8.971342	-8.936103
USDGBP	fGARCH.GARCH	1.000000e-07	559	1.431130e-02	0.1028402	-8.970515	-8.885763	-8.971689	-8.936449
USDGBP	fGARCH.TGARCH	2.000000e-07	559	1.431130e-02	0.5417127	-8.667962	-8.569570	-8.669507	-8.628413
USDGBP	fGARCH.NGARCH	4.513340e+70	559	-1.614791e+68	5673.6774317	-18.831168	-18.732776	-18.832714	-18.791619
USDGBP	fGARCH.NAGARCH	1.000000e-07	559	1.431130e-02	26.6382034	-8.763450	-8.665059	-8.764996	-8.723902
USDGBP	fGARCH.GJRGARCH	2.000000e-07	559	1.431130e-02	0.1081367	-8.982733	-8.884342	-8.984279	-8.943185
USDGBP	gjrGARCH	1.000000e-07	559	1.431130e-02	0.1116630	-8.996274	-8.897882	-8.997820	-8.956726
USDGBP	iGARCH	1.000000e-07	559	1.431130e-02	0.1025959	-8.970351	-8.899239	-8.971205	-8.941767
USDGBP	csGARCH	1.000000e-07	559	1.431130e-02	0.1014585	-8.949646	-8.837615	-8.951617	-8.904616
USD/CNY
USDCHF	sGARCH	3.800000e-06	559	1.431130e-02	0.4886477	-7.476419	-7.394283	-7.477510	-7.443403
USDCHF	fGARCH.GARCH	3.800000e-06	559	1.431130e-02	0.4901544	-7.474242	-7.392106	-7.475333	-7.441226
USDCHF	fGARCH.TGARCH	7.900000e-06	559	1.431120e-02	1.2621200	-7.434674	-7.338882	-7.436128	-7.396169
USDCHF	fGARCH.NGARCH	4.064080e-02	559	1.416590e-02	6835.2391021	-23.859181	-23.763390	-23.860636	-23.820676
USDCHF	fGARCH.NAGARCH	8.620427e+287	559	-3.084232e+285	1236.5953284	-4.688806	-4.593014	-4.690260	-4.650301
USDCHF	fGARCH.GJRGARCH	2.300000e-06	559	1.431130e-02	0.4587686	-7.519756	-7.423965	-7.521210	-7.481251
USDCHF	gjrGARCH	2.300000e-06	559	1.431130e-02	0.4555439	-7.546330	-7.450539	-7.547784	-7.507825
USDCHF	iGARCH	3.700000e-06	559	1.431130e-02	0.5429386	-7.452233	-7.383753	-7.453014	-7.424706
USDCHF	csGARCH	3.700000e-06	559	1.431130e-02	0.4952953	-7.457041	-7.347594	-7.458911	-7.413047
USD/EUR
USDCAD	sGARCH	2.000000e-07	559	1.431130e-02	0.1828809	-7.978945	-7.898882	-7.979974	-7.946763
USDCAD	fGARCH.GARCH	3.000000e-07	559	1.431130e-02	0.1827221	-7.979083	-7.899020	-7.980112	-7.946901
USDCAD	fGARCH.TGARCH	8.000000e-07	559	1.431130e-02	0.4607513	-7.778762	-7.685046	-7.780146	-7.741092
USDCAD	fGARCH.NGARCH	7.000000e-07	559	1.431130e-02	3643.7047477	-13.987922	-13.894206	-13.989306	-13.950251
USDCAD	fGARCH.NAGARCH	2.000000e-07	559	1.431130e-02	0.1822239	-7.986122	-7.892406	-7.987507	-7.948452
USDCAD	fGARCH.GJRGARCH	2.000000e-07	559	1.431130e-02	0.1864332	-7.985711	-7.891995	-7.987095	-7.948040
USDCAD	gjrGARCH	2.000000e-07	559	1.431130e-02	0.1846478	-7.992367	-7.898651	-7.993751	-7.954697
USDCAD	iGARCH	2.000000e-07	559	1.431130e-02	0.1856758	-7.976740	-7.910331	-7.977467	-7.950046
USDCAD	csGARCH	2.000000e-07	559	1.431130e-02	0.1795049	-7.963757	-7.856388	-7.965549	-7.920598
USD/GBP
USDCNY	sGARCH	7.200000e-06	559	1.431120e-02	0.1978232	-6.862343	-6.774548	-6.863560	-6.827053
USDCNY	fGARCH.GARCH	7.100000e-06	559	1.431120e-02	0.1976357	-6.861473	-6.773677	-6.862690	-6.826183
USDCNY	fGARCH.TGARCH	5.366621e+04	559	-1.919936e+02	9.3556676	-6.380259	-6.278821	-6.381861	-6.339486
USDCNY	fGARCH.NGARCH	9.000000e-06	559	1.431120e-02	3052.2188213	-12.142771	-12.041334	-12.144374	-12.101998
USDCNY	fGARCH.NAGARCH	6.500000e-06	559	1.431120e-02	0.1907778	-6.897824	-6.796386	-6.899426	-6.857051
USDCNY	fGARCH.GJRGARCH	7.200000e-06	559	1.431120e-02	0.1869098	-6.894584	-6.793146	-6.896186	-6.853811
USDCNY	gjrGARCH	7.900000e-06	559	1.431120e-02	0.1766534	-6.910032	-6.808594	-6.911634	-6.869259
USDCNY	iGARCH	8.300000e-06	559	1.431120e-02	0.2034711	-6.851271	-6.777118	-6.852157	-6.821465
USDCNY	csGARCH	1.060000e-05	559	1.431120e-02	0.2116209	-6.884467	-6.769387	-6.886507	-6.838210
USD/JPY
USDJPY	sGARCH	9.769800e-03	559	1.427630e-02	0.1736917	1.721961	1.809420	1.720719	1.757115
USDJPY	fGARCH.GARCH	9.273200e-03	559	1.427810e-02	0.1737364	1.721989	1.809449	1.720747	1.757143
USDJPY	fGARCH.TGARCH	4.865454e+176	559	-1.740771e+174	333.4709800	2.502594	2.603697	2.500970	2.543232
USDJPY	fGARCH.NGARCH	1.185840e-02	559	1.426880e-02	9849.5117039	-17.953102	-17.852000	-17.954728	-17.912465
USDJPY	fGARCH.NAGARCH	4.822900e-03	559	1.429400e-02	0.1846586	1.709179	1.810281	1.707554	1.749817
USDJPY	fGARCH.GJRGARCH	7.071700e-03	559	1.428600e-02	0.1801842	1.718061	1.819164	1.716436	1.758699
USDJPY	gjrGARCH	4.906300e-03	559	1.429370e-02	0.1887046	1.705786	1.806888	1.704161	1.746424
USDJPY	iGARCH	9.597700e-03	559	1.427690e-02	0.1755607	1.719560	1.793377	1.718648	1.749230
USDJPY	csGARCH	8.935700e-03	559	1.427930e-02	0.1705228	1.729581	1.844326	1.727521	1.775703

6.2.2.1A : Table summary

Open Price Summary : Selected Models

Model	MSE	n	AIC.MSE	MSE.AIC	Akaike	Bayes	Shibata	Hannan.Quinn
sGARCH	1.397500e-03	3913	2.043800e-03	11.75295	-6.443206	-6.359295	-6.444338	-6.409477
fGARCH.GARCH	1.326600e-03	3913	2.043800e-03	11.75262	-6.442789	-6.358878	-6.443921	-6.409061
fGARCH.TGARCH	6.950648e+175	3913	-3.552593e+172	62.60034	-6.134026	-6.036466	-6.135528	-6.094811
fGARCH.NGARCH	6.447629e+69	3913	-3.295491e+66	5558.30794	-16.946047	-16.848488	-16.947550	-16.906833
fGARCH.NAGARCH	1.231490e+287	3913	-6.294350e+283	201.58772	-5.956724	-5.859164	-5.958226	-5.917509
fGARCH.GJRGARCH	1.011800e-03	3913	2.043900e-03	11.77688	-6.459395	-6.361835	-6.460897	-6.420180
gjrGARCH	7.026000e-04	3913	2.044100e-03	11.78104	-6.473291	-6.375731	-6.474793	-6.434076
iGARCH	1.373100e-03	3913	2.043800e-03	11.74837	-6.438736	-6.368474	-6.439552	-6.410494
csGARCH	1.278900e-03	3913	2.043800e-03	11.73289	-6.431737	-6.320529	-6.433662	-6.387036

6.2.2.1B : Table summary

Open Price Summary : Selected Models

Model	n
fGARCH.TGARCH	3
fGARCH.NGARCH	4
fGARCH.NAGARCH	4

6.2.2.1C : Table summary

Hi-Lo Price Summary : Selected Models

.id	Model	Date	Price	Price.T1	Akaike	Bayes	Shibata	Hannan.Quinn	diff	se
USDAUD	fGARCH.TGARCH	2013-06-03	1.026	-7.365624e+01	24.94125	25.06416	24.93897	24.99066	7.178971e+01	1
USDAUD	fGARCH.NGARCH	2014-04-14	1.062	1.419924e+09	-416.14914	-416.01257	-416.15194	-416.09424	1.337028e+09	1
USDAUD	fGARCH.NAGARCH	2015-02-09	1.288	9.042209e+09	101.92162	102.05819	101.91883	101.97652	7.020349e+09	1
USDAUD	fGARCH.NAGARCH	2015-02-10	1.283	-9.623617e+31	153.81460	153.95080	153.81183	153.86934	7.500870e+31	1
USDGBP	fGARCH.NGARCH	2015-04-21	0.670	-1.002521e+06	-574.98397	-574.84777	-574.98674	-574.92923	1.496300e+06	1
USDGBP	fGARCH.NGARCH	2015-06-08	0.652	5.022905e+36	-490.21025	-490.08768	-490.21251	-490.16099	7.703841e+36	1
USDCHF	fGARCH.NGARCH	2013-12-12	0.887	-3.879205e+00	-432.53948	-432.40291	-432.54228	-432.48459	4.373400e+00	1
USDCHF	fGARCH.NAGARCH	2013-12-16	0.890	2.195181e+145	732.21537	732.35232	732.21256	732.27043	2.466495e+145	1
USDCHF	fGARCH.NAGARCH	2015-01-09	1.018	-1.228938e+24	226.37592	226.53936	226.37196	226.44161	1.207208e+24	1
USDCNY	fGARCH.TGARCH	2013-10-09	6.111	5.483283e+03	60.01301	60.13593	60.01074	60.06242	8.972808e+02	1
USDJPY	fGARCH.TGARCH	2013-03-31	94.262	-5.215159e+89	433.75044	433.91433	433.74645	433.81632	5.532621e+87	1

6.2.2.1D : Table summary

## selected models' filtered closing price.
op <- united.fx3 %>% 
  separate(Type, c('Cur', 'Type')) %>% 
  dplyr::filter(Type == 'Op') %>% dplyr::select(-Cur, -Type)

acc <- op %>% 
  ddply(.(.id, Model), summarise, 
        MSE = mean((Price.T1 - Price)^2), 
        n = length(Price), 
        AIC.MSE = (-2*MSE)/n+2*4/n, 
        MSE.AIC = mean((Akaike - mean(Akaike))^2),
        Akaike = mean(Akaike), 
        Bayes = mean(Bayes), 
        Shibata = mean(Shibata), 
        Hannan.Quinn = mean(Hannan.Quinn)) %>% 
  tbl_df %>% mutate(MSE = round(MSE, 7))

Open Price Summary : Selected Models

.id	Model	MSE	n	AIC.MSE	MSE.AIC	Akaike	Bayes	Shibata	Hannan.Quinn
USD/AUD
USDAUD	sGARCH	0.0000010	491	0.0162933	1.552965e-01	-7.255999	-7.175113	-7.257040	-7.223486
USDAUD	fGARCH.GARCH	0.0000010	491	0.0162933	1.550478e-01	-7.255768	-7.174883	-7.256809	-7.223255
USDAUD	fGARCH.TGARCH	0.0000028	491	0.0162933	4.659861e-01	-7.075776	-6.981237	-7.077175	-7.037775
USDAUD	fGARCH.NGARCH	0.0000042	491	0.0162933	4.823863e+03	-16.020749	-15.926210	-16.022148	-15.982748
USDAUD	fGARCH.NAGARCH	0.0000009	491	0.0162933	1.624586e-01	-7.266697	-7.172158	-7.268097	-7.228696
USDAUD	fGARCH.GJRGARCH	0.0000010	491	0.0162933	1.577197e-01	-7.259961	-7.165422	-7.261361	-7.221960
USDAUD	gjrGARCH	0.0000009	491	0.0162933	1.603771e-01	-7.267731	-7.173192	-7.269131	-7.229730
USDAUD	iGARCH	0.0000010	491	0.0162933	1.543457e-01	-7.260642	-7.193410	-7.261378	-7.233617
USDAUD	csGARCH	0.0000013	491	0.0162933	1.583888e-01	-7.238290	-7.130098	-7.240102	-7.194801
USD/CAD
USDEUR	sGARCH	0.0000004	491	0.0162933	2.930375e-01	-8.196676	-8.113510	-8.197774	-8.163246
USDEUR	fGARCH.GARCH	0.0000003	491	0.0162933	2.930072e-01	-8.196584	-8.113418	-8.197682	-8.163154
USDEUR	fGARCH.TGARCH	0.0000006	491	0.0162933	5.259412e-01	-8.065962	-7.969142	-8.067427	-8.027044
USDEUR	fGARCH.NGARCH	0.0000010	491	0.0162933	4.602062e+03	-14.911766	-14.814946	-14.913232	-14.872848
USDEUR	fGARCH.NAGARCH	0.0000003	491	0.0162933	2.996033e-01	-8.204053	-8.107233	-8.205519	-8.165135
USDEUR	fGARCH.GJRGARCH	0.0000003	491	0.0162933	3.030600e-01	-8.207974	-8.111154	-8.209439	-8.169056
USDEUR	gjrGARCH	0.0000003	491	0.0162933	3.096157e-01	-8.224027	-8.127207	-8.225492	-8.185109
USDEUR	iGARCH	0.0000004	491	0.0162933	2.976361e-01	-8.195299	-8.125786	-8.196083	-8.167357
USDEUR	csGARCH	0.0000005	491	0.0162933	2.899635e-01	-8.174967	-8.064494	-8.176853	-8.130561
USD/CHF
USDGBP	sGARCH	0.0000001	491	0.0162933	9.204250e-02	-8.931378	-8.847453	-8.932528	-8.897645
USDGBP	fGARCH.GARCH	0.0000001	491	0.0162933	9.183250e-02	-8.931460	-8.847535	-8.932610	-8.897727
USDGBP	fGARCH.TGARCH	0.0000002	491	0.0162933	5.389813e-01	-8.624512	-8.526948	-8.626031	-8.585296
USDGBP	fGARCH.NGARCH	0.0000002	491	0.0162933	5.363799e+03	-18.033020	-17.935456	-18.034539	-17.993804
USDGBP	fGARCH.NAGARCH	0.0000001	491	0.0162933	3.027577e+01	-8.694542	-8.596978	-8.696062	-8.655327
USDGBP	fGARCH.GJRGARCH	0.0000002	491	0.0162933	9.765950e-02	-8.943473	-8.845909	-8.944993	-8.904258
USDGBP	gjrGARCH	0.0000001	491	0.0162933	1.015423e-01	-8.956995	-8.859431	-8.958514	-8.917779
USDGBP	iGARCH	0.0000001	491	0.0162933	9.220240e-02	-8.931753	-8.861466	-8.932587	-8.903502
USDGBP	csGARCH	0.0000001	491	0.0162933	9.088370e-02	-8.912202	-8.800999	-8.914143	-8.867505
USD/CNY
USDCHF	sGARCH	0.0000041	491	0.0162933	4.518895e-01	-7.433157	-7.351521	-7.434229	-7.400342
USDCHF	fGARCH.GARCH	0.0000040	491	0.0162933	4.530726e-01	-7.430680	-7.349044	-7.431752	-7.397865
USDCHF	fGARCH.TGARCH	0.0000090	491	0.0162932	1.352953e+00	-7.372595	-7.277303	-7.374029	-7.334291
USDCHF	fGARCH.NGARCH	0.0000029	491	0.0162933	6.374749e+03	-22.404203	-22.308911	-22.405637	-22.365899
USDCHF	fGARCH.NAGARCH	0.0000020	491	0.0162933	8.397673e+01	-6.713228	-6.617935	-6.714662	-6.674924
USDCHF	fGARCH.GJRGARCH	0.0000025	491	0.0162933	4.278410e-01	-7.476790	-7.381498	-7.478224	-7.438486
USDCHF	gjrGARCH	0.0000025	491	0.0162933	4.304914e-01	-7.499835	-7.404543	-7.501269	-7.461531
USDCHF	iGARCH	0.0000040	491	0.0162933	5.064959e-01	-7.407406	-7.339426	-7.408170	-7.380080
USDCHF	csGARCH	0.0000040	491	0.0162933	4.585189e-01	-7.413811	-7.304862	-7.415659	-7.370017
USD/EUR
USDCAD	sGARCH	0.0000002	491	0.0162933	1.883629e-01	-7.956061	-7.876171	-7.957084	-7.923948
USDCAD	fGARCH.GARCH	0.0000002	491	0.0162933	1.883037e-01	-7.956364	-7.876474	-7.957387	-7.924251
USDCAD	fGARCH.TGARCH	0.0000009	491	0.0162933	4.792764e-01	-7.743756	-7.650213	-7.745134	-7.706155
USDCAD	fGARCH.NGARCH	0.0000005	491	0.0162933	2.747227e+03	-12.624617	-12.531073	-12.625994	-12.587016
USDCAD	fGARCH.NAGARCH	0.0000002	491	0.0162933	1.881104e-01	-7.963479	-7.869936	-7.964857	-7.925878
USDCAD	fGARCH.GJRGARCH	0.0000002	491	0.0162933	1.927649e-01	-7.963615	-7.870072	-7.964993	-7.926014
USDCAD	gjrGARCH	0.0000002	491	0.0162933	1.903911e-01	-7.970021	-7.876477	-7.971398	-7.932420
USDCAD	iGARCH	0.0000002	491	0.0162933	1.918450e-01	-7.954097	-7.887860	-7.954819	-7.927472
USDCAD	csGARCH	0.0000002	491	0.0162933	1.852977e-01	-7.941470	-7.834273	-7.943255	-7.898381
USD/GBP
USDCNY	sGARCH	0.0000074	491	0.0162932	1.773845e-01	-6.814375	-6.726459	-6.815597	-6.779037
USDCNY	fGARCH.GARCH	0.0000073	491	0.0162932	1.771088e-01	-6.813752	-6.725835	-6.814973	-6.778413
USDCNY	fGARCH.TGARCH	0.0000168	491	0.0162932	1.462199e+00	-6.463322	-6.361764	-6.464929	-6.422501
USDCNY	fGARCH.NGARCH	0.0000088	491	0.0162932	3.471099e+03	-12.822717	-12.721159	-12.824323	-12.781895
USDCNY	fGARCH.NAGARCH	0.0000070	491	0.0162933	1.714372e-01	-6.852013	-6.750455	-6.853620	-6.811192
USDCNY	fGARCH.GJRGARCH	0.0000077	491	0.0162932	1.680038e-01	-6.849872	-6.748314	-6.851479	-6.809051
USDCNY	gjrGARCH	0.0000084	491	0.0162932	1.583541e-01	-6.865933	-6.764375	-6.867540	-6.825112
USDCNY	iGARCH	0.0000087	491	0.0162932	1.816203e-01	-6.802680	-6.728405	-6.803569	-6.772825
USDCNY	csGARCH	0.0000113	491	0.0162932	1.895557e-01	-6.836793	-6.721593	-6.838838	-6.790489
USD/JPY
USDJPY	sGARCH	0.0103458	491	0.0162511	1.689252e-01	1.761495	1.848057	1.760279	1.796288
USDJPY	fGARCH.GARCH	0.0097996	491	0.0162534	1.689307e-01	1.761563	1.848125	1.760347	1.796356
USDJPY	fGARCH.TGARCH	0.0234038	491	0.0161979	1.800080e-01	1.766814	1.867018	1.765219	1.807091
USDJPY	fGARCH.NGARCH	0.0125690	491	0.0162421	1.088562e+04	-19.851067	-19.750864	-19.852663	-19.810791
USDJPY	fGARCH.NAGARCH	0.0049535	491	0.0162731	1.799802e-01	1.749415	1.849619	1.747819	1.789692
USDJPY	fGARCH.GJRGARCH	0.0071923	491	0.0162640	1.751105e-01	1.758221	1.858425	1.756625	1.798498
USDJPY	gjrGARCH	0.0051468	491	0.0162723	1.833403e-01	1.746705	1.846909	1.745109	1.786982
USDJPY	iGARCH	0.0102148	491	0.0162517	1.704412e-01	1.759555	1.832476	1.758666	1.788865
USDJPY	csGARCH	0.0094206	491	0.0162549	1.655455e-01	1.769141	1.882987	1.767114	1.814901

6.2.2.2A : Table summary

Open Price Summary : Selected Models

Model	MSE	n	AIC.MSE	MSE.AIC	Akaike	Bayes	Shibata	Hannan.Quinn
sGARCH	0.0014799	3437	0.0023268	11.73799	-6.403736	-6.320310	-6.404853	-6.370202
fGARCH.GARCH	0.0014018	3437	0.0023268	11.73749	-6.403292	-6.319866	-6.404409	-6.369758
fGARCH.TGARCH	0.0033477	3437	0.0023257	11.77506	-6.225587	-6.128513	-6.227072	-6.186567
fGARCH.NGARCH	0.0017981	3437	0.0023266	5478.27908	-16.666877	-16.569803	-16.668362	-16.627857
fGARCH.NAGARCH	0.0007091	3437	0.0023272	27.65430	-6.277800	-6.180725	-6.279285	-6.238780
fGARCH.GJRGARCH	0.0010292	3437	0.0023270	11.76573	-6.420495	-6.323421	-6.421981	-6.381475
gjrGARCH	0.0007370	3437	0.0023272	11.77211	-6.433977	-6.336902	-6.435462	-6.394957
iGARCH	0.0014613	3437	0.0023268	11.73410	-6.398903	-6.329125	-6.399706	-6.370855
csGARCH	0.0013483	3437	0.0023268	11.71882	-6.392627	-6.281905	-6.394534	-6.348122

6.2.2.2B : Table summary

Open Price Summary : Selected Models

Model	n

6.2.2.2C : Table summary

Hi-Lo Price Summary : Selected Models

.id	Model	Date	Price	Price.T1	Akaike	Bayes	Shibata	Hannan.Quinn	diff	se

6.2.2.2D : Table summary

6.3 High Price

6.3.1 All Models

## filtered bias highest price.
hp <- fx %>% separate(Type, c('Cur', 'Type')) %>% 
  dplyr::filter(Type == 'Hi') %>% 
  dplyr::select(-Cur, -Type)

ntmID <- hp %>% dplyr::filter(se == 1) %>% .$Date %>% unlist %>% sort

acc <- hp %>% dplyr::filter(!Date %in% ntmID & Date %in% ntimeID2) %>% 
  ddply(.(.id, Model), summarise, 
        MSE = mean((Price.T1 - Price)^2), 
        n = length(Price), 
        AIC.MSE = (-2*MSE)/n+2*4/n, 
        MSE.AIC = mean((Akaike - mean(Akaike))^2),
        Akaike = mean(Akaike), 
        Bayes = mean(Bayes), 
        Shibata = mean(Shibata), 
        Hannan.Quinn = mean(Hannan.Quinn)) %>% 
  tbl_df %>% mutate(MSE = round(MSE, 7))

High Price Summary : All Models

.id	Model	MSE	n	AIC.MSE	MSE.AIC	Akaike	Bayes	Shibata	Hannan.Quinn
USD/AUD
USDAUD	sGARCH	0.0000003	539	0.0148423	1.505831e-01	-7.431208	-7.353373	-7.432176	-7.399921
USDAUD	fGARCH.GARCH	0.0000003	539	0.0148423	1.504512e-01	-7.431376	-7.353541	-7.432344	-7.400089
USDAUD	fGARCH.TGARCH	0.0000037	539	0.0148423	7.170720e-01	-7.130776	-7.039288	-7.132091	-7.094002
USDAUD	fGARCH.AVGARCH	0.0000000	52	0.1538462	7.201320e-02	-7.670617	-7.571365	-7.672139	-7.630722
USDAUD	fGARCH.NGARCH	0.0000006	539	0.0148423	1.023081e+03	-7.261812	-7.170324	-7.263126	-7.225037
USDAUD	fGARCH.NAGARCH	0.0000002	539	0.0148423	1.564071e-01	-7.444181	-7.352693	-7.445496	-7.407406
USDAUD	fGARCH.APARCH	0.0000037	346	0.0231214	3.969971e+03	-13.961849	-13.856617	-13.963565	-13.919548
USDAUD	fGARCH.GJRGARCH	0.0000002	539	0.0148423	1.542758e-01	-7.431425	-7.339937	-7.432740	-7.394651
USDAUD	fGARCH.ALLGARCH	0.0000002	264	0.0303030	4.082340e-02	-7.666726	-7.545968	-7.668972	-7.618186
USDAUD	eGARCH	0.0000003	489	0.0163599	1.302487e-01	-7.471389	-7.379065	-7.472729	-7.434278
USDAUD	gjrGARCH	0.0000002	539	0.0148423	1.567967e-01	-7.438546	-7.347058	-7.439861	-7.401771
USDAUD	apARCH	0.0000004	83	0.0963855	4.227900e-03	-7.869490	-7.763521	-7.871247	-7.826894
USDAUD	iGARCH	0.0000003	539	0.0148423	1.506351e-01	-7.433660	-7.369477	-7.434335	-7.407861
USDAUD	csGARCH	0.0000003	539	0.0148423	1.498658e-01	-7.416993	-7.311852	-7.418708	-7.374731
USD/CAD
USDEUR	sGARCH	0.0000008	539	0.0148423	2.780160e-01	-8.495465	-8.412517	-8.496557	-8.462123
USDEUR	fGARCH.GARCH	0.0000008	539	0.0148423	2.764101e-01	-8.496004	-8.413057	-8.497097	-8.462663
USDEUR	fGARCH.TGARCH	0.0000018	539	0.0148423	3.577326e-01	-8.351673	-8.255073	-8.353132	-8.312843
USDEUR	fGARCH.AVGARCH	0.0000003	27	0.2962963	3.179274e-01	-7.954440	-7.834094	-7.956648	-7.906065
USDEUR	fGARCH.NGARCH	0.0000012	539	0.0148423	7.278426e+03	-21.227611	-21.131011	-21.229070	-21.188781
USDEUR	fGARCH.NAGARCH	0.0000007	539	0.0148423	2.779905e-01	-8.495233	-8.398633	-8.496692	-8.456403
USDEUR	fGARCH.APARCH	0.0000042	122	0.0655737	8.178180e+03	-22.553823	-22.436457	-22.555949	-22.506647
USDEUR	fGARCH.GJRGARCH	0.0000007	539	0.0148423	2.742681e-01	-8.495361	-8.398762	-8.496821	-8.456532
USDEUR	fGARCH.ALLGARCH	0.0000007	373	0.0214477	6.337447e+03	-19.669264	-19.546370	-19.671589	-19.619864
USDEUR	eGARCH	0.0000006	491	0.0162933	6.799606e+00	-8.488138	-8.391442	-8.489604	-8.449270
USDEUR	gjrGARCH	0.0000007	539	0.0148423	2.623649e-01	-8.518057	-8.421457	-8.519516	-8.479227
USDEUR	apARCH	0.0000002	83	0.0963855	1.323816e-01	-8.181167	-8.061208	-8.183378	-8.132947
USDEUR	iGARCH	0.0000008	539	0.0148423	2.707332e-01	-8.494502	-8.425208	-8.495282	-8.466648
USDEUR	csGARCH	0.0000007	539	0.0148423	2.315713e-01	-8.497019	-8.386766	-8.498897	-8.452701
USD/CHF
USDGBP	sGARCH	0.0000001	539	0.0148423	1.293068e-01	-9.103594	-9.019713	-9.104738	-9.069879
USDGBP	fGARCH.GARCH	0.0000001	539	0.0148423	1.292046e-01	-9.103646	-9.019764	-9.104789	-9.069930
USDGBP	fGARCH.TGARCH	0.0000004	539	0.0148423	7.317778e-01	-8.782749	-8.685228	-8.784262	-8.743551
USDGBP	fGARCH.AVGARCH	0.0000000	34	0.2352941	1.576003e+02	-6.569828	-6.468899	-6.571394	-6.529263
USDGBP	fGARCH.NGARCH	0.0000002	539	0.0148423	1.166757e+03	-9.744419	-9.646898	-9.745932	-9.705221
USDGBP	fGARCH.NAGARCH	0.0000001	539	0.0148423	1.488994e+02	-8.403167	-8.305646	-8.404680	-8.363969
USDGBP	fGARCH.APARCH	0.0000002	347	0.0230548	3.062370e+03	-15.512899	-15.406758	-15.514658	-15.470235
USDGBP	fGARCH.GJRGARCH	0.0000001	539	0.0148423	1.305382e-01	-9.114034	-9.016513	-9.115547	-9.074836
USDGBP	fGARCH.ALLGARCH	0.0000001	375	0.0213333	1.125753e+03	-11.483487	-11.362179	-11.485762	-11.434727
USDGBP	eGARCH	0.0000001	488	0.0163934	6.775820e+00	-9.042341	-8.945157	-9.043848	-9.003278
USDGBP	gjrGARCH	0.0000001	539	0.0148423	1.092035e-01	-9.130449	-9.032928	-9.131962	-9.091251
USDGBP	apARCH	0.0000003	83	0.0963855	2.023198e-01	-8.959825	-8.853828	-8.961584	-8.917222
USDGBP	iGARCH	0.0000001	539	0.0148423	1.299649e-01	-9.103112	-9.032870	-9.103939	-9.074879
USDGBP	csGARCH	0.0000001	539	0.0148423	7.847350e-02	-9.102936	-8.991774	-9.104870	-9.058255
USD/CNY
USDCHF	sGARCH	0.0000031	539	0.0148423	4.455625e-01	-7.668662	-7.586317	-7.669740	-7.635562
USDCHF	fGARCH.GARCH	0.0000031	539	0.0148423	4.453478e-01	-7.668428	-7.586084	-7.669506	-7.635328
USDCHF	fGARCH.TGARCH	0.0000004	539	0.0148423	2.867757e-01	-7.708878	-7.612878	-7.710320	-7.670289
USDCHF	fGARCH.AVGARCH	0.0000003	16	0.5000000	2.317470e-02	-7.934905	-7.820994	-7.936898	-7.889110
USDCHF	fGARCH.NGARCH	0.0000023	539	0.0148423	1.513801e+03	-10.121845	-10.025846	-10.123288	-10.083257
USDCHF	fGARCH.NAGARCH	0.0000015	539	0.0148423	1.466591e+02	-6.759087	-6.663087	-6.760529	-6.720498
USDCHF	fGARCH.APARCH	0.0000003	345	0.0231884	1.689155e+03	-11.847221	-11.735193	-11.849166	-11.802188
USDCHF	fGARCH.GJRGARCH	0.0000019	539	0.0148423	4.159060e-01	-7.693727	-7.597727	-7.695169	-7.655138
USDCHF	fGARCH.ALLGARCH	0.0000004	372	0.0215054	7.463068e+03	-19.254769	-19.129700	-19.257169	-19.204494
USDCHF	eGARCH	0.0000004	491	0.0162933	1.490083e+00	-7.745519	-7.650598	-7.746932	-7.707364
USDCHF	gjrGARCH	0.0000019	539	0.0148423	4.261263e-01	-7.718911	-7.622911	-7.720353	-7.680322
USDCHF	apARCH	0.0000001	82	0.0975610	2.752000e-03	-7.996560	-7.887000	-7.998403	-7.952518
USDCHF	iGARCH	0.0000031	539	0.0148423	4.878432e-01	-7.645388	-7.576699	-7.646155	-7.617777
USDCHF	csGARCH	0.0000031	539	0.0148423	4.498704e-01	-7.645041	-7.535386	-7.646901	-7.600964
USD/EUR
USDCAD	sGARCH	0.0000010	539	0.0148423	1.539558e-01	-8.165550	-8.075817	-8.166827	-8.129481
USDCAD	fGARCH.GARCH	0.0000010	539	0.0148423	1.540620e-01	-8.165630	-8.075897	-8.166908	-8.129561
USDCAD	fGARCH.TGARCH	0.0000020	539	0.0148423	9.117732e-01	-7.923351	-7.819966	-7.925022	-7.881794
USDCAD	fGARCH.AVGARCH	0.0000000	40	0.2000000	2.232913e+02	-5.811174	-5.710815	-5.812732	-5.770834
USDCAD	fGARCH.NGARCH	0.0000258	539	0.0148422	1.438110e+04	-41.600698	-41.497313	-41.602368	-41.559141
USDCAD	fGARCH.NAGARCH	0.0000008	539	0.0148423	1.528308e-01	-8.172854	-8.069468	-8.174524	-8.131297
USDCAD	fGARCH.APARCH	0.0000009	344	0.0232558	2.965907e+03	-13.243581	-13.134163	-13.245415	-13.199598
USDCAD	fGARCH.GJRGARCH	0.0000008	539	0.0148423	1.493709e-01	-8.164933	-8.061548	-8.166603	-8.123376
USDCAD	fGARCH.ALLGARCH	0.0000009	373	0.0214477	3.396954e+03	-14.946877	-14.822111	-14.949250	-14.896725
USDCAD	eGARCH	0.0000009	485	0.0164948	9.351387e-01	-8.159834	-8.057130	-8.161483	-8.118551
USDCAD	gjrGARCH	0.0000007	539	0.0148423	1.467107e-01	-8.167786	-8.064400	-8.169456	-8.126229
USDCAD	apARCH	0.0000000	82	0.0975610	4.302500e-03	-8.398745	-8.298480	-8.400295	-8.358442
USDCAD	iGARCH	0.0000010	539	0.0148423	1.544022e-01	-8.166904	-8.090825	-8.167842	-8.136323
USDCAD	csGARCH	0.0000010	539	0.0148423	1.527841e-01	-8.149170	-8.032132	-8.151286	-8.102126
USD/GBP
USDCNY	sGARCH	0.0000611	539	0.0148421	4.555229e-01	-6.244619	-6.149066	-6.246060	-6.206211
USDCNY	fGARCH.GARCH	0.0000609	539	0.0148421	4.570853e-01	-6.243905	-6.148352	-6.245347	-6.205498
USDCNY	fGARCH.TGARCH	0.0000385	539	0.0148422	2.554016e+00	-5.879803	-5.770607	-5.881659	-5.835911
USDCNY	fGARCH.AVGARCH	0.0000002	12	0.6666666	3.333200e-03	-7.004461	-6.888806	-7.006489	-6.957979
USDCNY	fGARCH.NGARCH	0.0000640	539	0.0148421	6.341758e+02	-7.341120	-7.231923	-7.342976	-7.297228
USDCNY	fGARCH.NAGARCH	0.0000385	539	0.0148422	4.173584e-01	-6.275785	-6.166589	-6.277641	-6.231894
USDCNY	fGARCH.APARCH	0.0012390	344	0.0232486	1.149087e+04	-25.696324	-25.572945	-25.698652	-25.646731
USDCNY	fGARCH.GJRGARCH	0.0000418	539	0.0148421	4.438478e-01	-6.255569	-6.146373	-6.257425	-6.211677
USDCNY	fGARCH.ALLGARCH	0.0000624	373	0.0214474	3.573186e+03	-12.290016	-12.152501	-12.292888	-12.234741
USDCNY	eGARCH	0.0000434	488	0.0163933	4.375166e-01	-6.154482	-6.046495	-6.156301	-6.111077
USDCNY	gjrGARCH	0.0000353	539	0.0148422	4.638331e-01	-6.270742	-6.161546	-6.272598	-6.226851
USDCNY	apARCH	0.0000185	83	0.0963851	4.801230e-02	-6.842821	-6.729597	-6.844768	-6.797314
USDCNY	iGARCH	0.0000598	539	0.0148421	4.467546e-01	-6.230797	-6.148886	-6.231877	-6.197873
USDCNY	csGARCH	0.0000605	539	0.0148421	4.653298e-01	-6.236084	-6.113245	-6.238406	-6.186709
USD/JPY
USDJPY	sGARCH	0.0126236	539	0.0147955	1.347097e-01	1.397277	1.491381	1.395855	1.435102
USDJPY	fGARCH.GARCH	0.0130348	539	0.0147939	1.344858e-01	1.397500	1.491604	1.396077	1.435325
USDJPY	fGARCH.TGARCH	0.0092688	539	0.0148079	1.778116e-01	1.425259	1.533006	1.423428	1.468568
USDJPY	fGARCH.AVGARCH	0.0352913	40	0.1982354	1.330442e-01	1.016510	1.145209	1.013927	1.068237
USDJPY	fGARCH.NGARCH	0.2130925	539	0.0140516	3.191562e+03	-4.211216	-4.103469	-4.213047	-4.167907
USDJPY	fGARCH.NAGARCH	0.0098863	539	0.0148056	1.400137e-01	1.385825	1.493572	1.383994	1.429134
USDJPY	fGARCH.APARCH	322.7699425	125	-5.1003191	1.093747e+04	-16.939683	-16.811521	-16.942238	-16.888171
USDJPY	fGARCH.GJRGARCH	0.0108609	539	0.0148020	1.365876e-01	1.393265	1.501012	1.391434	1.436574
USDJPY	fGARCH.ALLGARCH	0.2995051	193	0.0383471	1.082361e+02	1.996757	2.138744	1.993668	2.053828
USDJPY	eGARCH	0.0491749	489	0.0161588	1.039042e+00	1.490306	1.597507	1.488492	1.533395
USDJPY	gjrGARCH	0.0110967	539	0.0148011	1.463540e-01	1.386481	1.494228	1.384650	1.429790
USDJPY	apARCH	0.2014515	82	0.0926475	1.068989e+05	-79.906640	-79.779577	-79.909144	-79.855570
USDJPY	iGARCH	0.0123905	539	0.0147963	1.357671e-01	1.395353	1.475815	1.394287	1.427695
USDJPY	csGARCH	0.0123930	539	0.0147963	1.320258e-01	1.401980	1.523369	1.399688	1.450772

6.3.1.1 : Table summary

High Price Summary : All Models

Model	MSE	n	AIC.MSE	MSE.AIC	Akaike	Bayes	Shibata	Hannan.Quinn
sGARCH	0.0018129	3773	0.0021194	11.42014	-6.530260	-6.443632	-6.531463	-6.495439
fGARCH.GARCH	0.0018716	3773	0.0021193	11.42096	-6.530213	-6.443584	-6.531416	-6.495392
fGARCH.TGARCH	0.0013308	3773	0.0021196	11.60970	-6.335996	-6.235719	-6.337580	-6.295689
fGARCH.AVGARCH	0.0063876	221	0.0361413	75.00683	-5.610021	-5.500452	-5.611894	-5.565980
fGARCH.NGARCH	0.0304552	3773	0.0021042	4317.12836	-14.501246	-14.400969	-14.502830	-14.460939
fGARCH.NAGARCH	0.0014183	3773	0.0021196	52.86355	-6.309212	-6.208935	-6.310795	-6.268905
fGARCH.APARCH	20.4494026	1973	-0.0166745	5273.35842	-16.505535	-16.392858	-16.507505	-16.460243
fGARCH.GJRGARCH	0.0015581	3773	0.0021195	11.41965	-6.537398	-6.437121	-6.538981	-6.497091
fGARCH.ALLGARCH	0.0248939	2323	0.0034224	3558.97613	-13.174223	-13.047245	-13.176702	-13.123182
eGARCH	0.0070356	3421	0.0023344	13.89889	-6.509513	-6.409663	-6.511085	-6.469378
gjrGARCH	0.0015908	3773	0.0021195	11.44031	-6.551144	-6.450867	-6.552728	-6.510837
apARCH	0.0285824	578	0.0137419	15794.75814	-18.236304	-18.124587	-18.238242	-18.191399
iGARCH	0.0017793	3773	0.0021194	11.41386	-6.525573	-6.452593	-6.526449	-6.496238
csGARCH	0.0017798	3773	0.0021194	11.40042	-6.520752	-6.406827	-6.522769	-6.474959

6.3.1.2 : Table summary

High Price Summary : All Models

Model	n
fGARCH.GARCH	2
fGARCH.NGARCH	13
fGARCH.APARCH	6
fGARCH.ALLGARCH	2
eGARCH	5
apARCH	5

6.3.1.3 : Table summary

Hi-Lo Price Summary : Selected Models

.id	Model	Date	Price	Price.T1	Akaike	Bayes	Shibata	Hannan.Quinn	diff	se
USDAUD	apARCH	2013-05-16	1.030	5.216021e+74	363.18829	363.37949	363.18291	363.2651	5.064098e+74	1
USDEUR	fGARCH.GARCH	2015-02-05	0.884	2.683682e+92	412.26245	412.38502	412.26019	412.3117	3.035839e+92	1
USDEUR	fGARCH.NGARCH	2016-04-28	0.880	4.510825e-01	-594.67151	-594.53532	-594.67429	-594.6168	5.125938e-01	1
USDGBP	fGARCH.NGARCH	2016-07-20	0.759	7.366569e+74	-405.81049	-405.70183	-405.81227	-405.7668	9.705624e+74	1
USDCHF	fGARCH.GARCH	2014-05-25	0.897	-3.484066e+62	366.06788	366.27330	366.06169	366.1505	3.884132e+62	1
USDCHF	fGARCH.NGARCH	2015-10-30	0.991	-1.889325e+01	-584.26763	-584.15837	-584.26944	-584.2237	1.906483e+01	1
USDCAD	fGARCH.NGARCH	2015-02-05	1.258	-2.752758e+42	-487.60238	-487.42533	-487.60700	-487.5312	2.188202e+42	1
USDCAD	fGARCH.NGARCH	2015-03-29	1.270	-6.542943e+22	-529.24031	-529.13105	-529.24211	-529.1964	5.151924e+22	1
USDCAD	fGARCH.NGARCH	2015-07-21	1.305	4.139802e+61	-435.14267	-435.00647	-435.14544	-435.0879	3.172262e+61	1
USDCAD	fGARCH.NGARCH	2016-05-02	1.270	2.847428e+37	-493.89133	-493.74110	-493.89469	-493.8309	2.242069e+37	1
USDCAD	eGARCH	2015-08-26	1.330	-3.733849e+102	106.42168	106.55787	106.41890	106.4764	2.807405e+102	1
USDCNY	fGARCH.APARCH	2013-10-29	6.134	2.876649e+25	-526.99014	-526.82626	-526.99413	-526.9243	4.689679e+24	1
USDCNY	fGARCH.APARCH	2013-11-07	6.144	-8.647337e+68	-406.98318	-406.81929	-406.98716	-406.9173	1.407444e+68	1
USDCNY	fGARCH.APARCH	2014-06-19	6.221	-7.210200e+39	-479.34500	-479.18112	-479.34899	-479.2791	1.159010e+39	1
USDJPY	fGARCH.NGARCH	2013-05-20	102.872	1.639729e+20	126.89546	127.03166	126.89269	126.9502	1.593951e+18	1
USDJPY	fGARCH.NGARCH	2013-06-16	95.106	-2.728130e+05	179.13197	179.26854	179.12918	179.1869	2.868516e+03	1
USDJPY	fGARCH.NGARCH	2013-06-17	95.753	3.511368e+02	10.57076	10.70695	10.56798	10.6255	3.667111e+00	1
USDJPY	fGARCH.NGARCH	2013-06-19	98.239	4.076553e+124	740.36101	740.49721	740.35824	740.4158	4.149628e+122	1
USDJPY	fGARCH.NGARCH	2013-07-01	100.438	4.397652e+23	-244.81945	-244.68326	-244.82222	-244.7647	4.378474e+21	1
USDJPY	fGARCH.NGARCH	2013-07-22	100.170	-7.099425e+16	107.52083	107.65702	107.51805	107.5756	7.087376e+14	1
USDJPY	fGARCH.APARCH	2013-03-29	94.255	1.067074e+03	-571.14158	-570.93672	-571.14772	-571.0592	1.132114e+01	1
USDJPY	fGARCH.APARCH	2013-05-13	102.261	1.875536e+63	-401.56417	-401.44159	-401.56643	-401.5149	1.834068e+61	1
USDJPY	fGARCH.APARCH	2013-06-12	95.930	-1.338837e+49	118.94181	119.09162	118.93847	119.0020	1.395639e+47	1
USDJPY	fGARCH.ALLGARCH	2013-12-03	103.369	3.656304e+138	-201.51651	-201.35263	-201.52050	-201.4506	3.537137e+136	1
USDJPY	fGARCH.ALLGARCH	2013-12-12	103.077	-3.572408e+44	285.95110	286.12865	285.94645	286.0225	3.465767e+42	1
USDJPY	eGARCH	2013-04-07	99.016	-1.249428e+80	167.04585	167.19608	167.04249	167.1062	1.261845e+78	1
USDJPY	eGARCH	2013-05-13	102.261	1.483098e+63	161.81392	161.92288	161.81213	161.8577	1.450307e+61	1
USDJPY	eGARCH	2013-06-16	95.106	2.867306e+54	123.66867	123.80524	123.66588	123.7236	3.014853e+52	1
USDJPY	eGARCH	2013-11-18	100.333	-1.192013e+13	283.35474	283.49169	283.35193	283.4098	1.188057e+11	1
USDJPY	apARCH	2013-01-29	90.990	-1.175138e+50	-1305.50500	-1305.34157	-1305.50896	-1305.4393	1.291503e+48	1
USDJPY	apARCH	2013-04-09	99.694	-7.412985e+02	-1357.52847	-1357.39228	-1357.53125	-1357.4737	7.435739e+00	1
USDJPY	apARCH	2013-05-09	101.949	-3.960522e+122	494.60505	494.72762	494.60279	494.6543	3.884807e+120	1
USDJPY	apARCH	2013-05-14	102.760	6.892843e+01	-1352.81576	-1352.65233	-1352.81972	-1352.7501	6.707710e-01	1

6.3.1.4 : Table summary

6.3.2 Selected Models

## selected models' filtered highest price.
hp <- united.fx2 %>% 
  separate(Type, c('Cur', 'Type')) %>% 
  dplyr::filter(Type == 'Hi') %>% dplyr::select(-Cur, -Type)

acc <- hp %>% 
  ddply(.(.id, Model), summarise, 
        MSE = mean((Price.T1 - Price)^2), 
        n = length(Price), 
        AIC.MSE = (-2*MSE)/n+2*4/n, 
        MSE.AIC = mean((Akaike - mean(Akaike))^2),
        Akaike = mean(Akaike), 
        Bayes = mean(Bayes), 
        Shibata = mean(Shibata), 
        Hannan.Quinn = mean(Hannan.Quinn)) %>% 
  tbl_df %>% mutate(MSE = round(MSE, 7))

High Price Summary : Selected Models

.id	Model	MSE	n	AIC.MSE	MSE.AIC	Akaike	Bayes	Shibata	Hannan.Quinn
USD/AUD
USDAUD	sGARCH	3.000000e-07	559	1.431130e-02	1.521648e-01	-7.437208	-7.359273	-7.438181	-7.405881
USDAUD	fGARCH.GARCH	3.000000e-07	559	1.431130e-02	1.520092e-01	-7.437344	-7.359409	-7.438317	-7.406017
USDAUD	fGARCH.TGARCH	3.500000e-06	559	1.431130e-02	7.058772e-01	-7.144229	-7.052640	-7.145549	-7.107414
USDAUD	fGARCH.NGARCH	3.000000e-06	559	1.431130e-02	1.593938e+03	-8.316497	-8.224908	-8.317817	-8.279682
USDAUD	fGARCH.NAGARCH	3.000000e-07	559	1.431130e-02	1.580276e-01	-7.450223	-7.358635	-7.451544	-7.413408
USDAUD	fGARCH.GJRGARCH	2.000000e-07	559	1.431130e-02	1.561037e-01	-7.437738	-7.346149	-7.439058	-7.400923
USDAUD	gjrGARCH	2.000000e-07	559	1.431130e-02	1.584622e-01	-7.444678	-7.353089	-7.445998	-7.407863
USDAUD	iGARCH	3.000000e-07	559	1.431130e-02	1.523136e-01	-7.439802	-7.375520	-7.440482	-7.413963
USDAUD	csGARCH	3.000000e-07	559	1.431130e-02	1.514441e-01	-7.422979	-7.317737	-7.424699	-7.380676
USD/CAD
USDEUR	sGARCH	8.000000e-07	559	1.431130e-02	2.720759e-01	-8.490468	-8.407383	-8.491564	-8.457071
USDEUR	fGARCH.GARCH	8.000000e-07	559	1.431130e-02	2.705361e-01	-8.490991	-8.407906	-8.492087	-8.457594
USDEUR	fGARCH.TGARCH	1.800000e-06	559	1.431130e-02	3.522086e-01	-8.344873	-8.248135	-8.346336	-8.305988
USDEUR	fGARCH.NGARCH	1.200000e-06	559	1.431130e-02	7.036238e+03	-20.638619	-20.541881	-20.640082	-20.599734
USDEUR	fGARCH.NAGARCH	7.000000e-07	559	1.431130e-02	2.721233e-01	-8.490133	-8.393395	-8.491597	-8.451248
USDEUR	fGARCH.GJRGARCH	7.000000e-07	559	1.431130e-02	2.684809e-01	-8.490216	-8.393478	-8.491679	-8.451331
USDEUR	gjrGARCH	7.000000e-07	559	1.431130e-02	2.573258e-01	-8.512878	-8.416141	-8.514342	-8.473994
USDEUR	iGARCH	8.000000e-07	559	1.431130e-02	2.649865e-01	-8.489482	-8.420051	-8.490265	-8.461574
USDEUR	csGARCH	7.000000e-07	559	1.431130e-02	2.273320e-01	-8.491418	-8.381027	-8.493301	-8.447045
USD/CHF
USDGBP	sGARCH	1.000000e-07	559	1.431130e-02	1.255523e-01	-9.101342	-9.017778	-9.102477	-9.067754
USDGBP	fGARCH.GARCH	1.000000e-07	559	1.431130e-02	1.254537e-01	-9.101389	-9.017825	-9.102524	-9.067801
USDGBP	fGARCH.TGARCH	4.000000e-07	559	1.431130e-02	7.100763e-01	-8.786098	-8.688894	-8.787601	-8.747027
USDGBP	fGARCH.NGARCH	2.000000e-07	559	1.431130e-02	1.125841e+03	-9.681669	-9.584464	-9.683171	-9.642598
USDGBP	fGARCH.NAGARCH	1.000000e-07	559	1.431130e-02	1.435870e+02	-8.426095	-8.328891	-8.427597	-8.387024
USDGBP	fGARCH.GJRGARCH	1.000000e-07	559	1.431130e-02	1.267718e-01	-9.111770	-9.014566	-9.113273	-9.072699
USDGBP	gjrGARCH	1.000000e-07	559	1.431130e-02	1.063133e-01	-9.127723	-9.030519	-9.129226	-9.088652
USDGBP	iGARCH	1.000000e-07	559	1.431130e-02	1.262008e-01	-9.100764	-9.030840	-9.101584	-9.072659
USDGBP	csGARCH	1.000000e-07	559	1.431130e-02	7.665450e-02	-9.099947	-8.989103	-9.101870	-9.055394
USD/CNY
USDCHF	sGARCH	3.100000e-06	559	1.431130e-02	4.377709e-01	-7.669915	-7.587337	-7.670999	-7.636721
USDCHF	fGARCH.GARCH	3.100000e-06	559	1.431130e-02	4.375650e-01	-7.669689	-7.587111	-7.670773	-7.636495
USDCHF	fGARCH.TGARCH	5.000000e-07	559	1.431130e-02	2.843040e-01	-7.707818	-7.611585	-7.709267	-7.669136
USDCHF	fGARCH.NGARCH	7.073077e-01	559	1.178070e-02	2.655649e+03	-12.118128	-12.021895	-12.119578	-12.079446
USDCHF	fGARCH.NAGARCH	1.500000e-06	559	1.431130e-02	1.414517e+02	-6.794313	-6.698080	-6.795762	-6.755630
USDCHF	fGARCH.GJRGARCH	2.000000e-06	559	1.431130e-02	4.085573e-01	-7.694735	-7.598502	-7.696185	-7.656053
USDCHF	gjrGARCH	1.900000e-06	559	1.431130e-02	4.185573e-01	-7.719767	-7.623534	-7.721216	-7.681084
USDCHF	iGARCH	3.100000e-06	559	1.431130e-02	4.793057e-01	-7.647093	-7.578172	-7.647865	-7.619389
USDCHF	csGARCH	3.100000e-06	559	1.431130e-02	4.419797e-01	-7.646381	-7.536492	-7.648248	-7.602209
USD/EUR
USDCAD	sGARCH	9.000000e-07	559	1.431130e-02	1.544139e-01	-8.170387	-8.080613	-8.171666	-8.134301
USDCAD	fGARCH.GARCH	9.000000e-07	559	1.431130e-02	1.545209e-01	-8.170531	-8.080757	-8.171810	-8.134445
USDCAD	fGARCH.TGARCH	2.000000e-06	559	1.431130e-02	9.016971e-01	-7.931385	-7.827958	-7.933057	-7.889811
USDCAD	fGARCH.NGARCH	3.065824e+120	559	-1.096896e+118	1.460436e+04	-42.106546	-42.003118	-42.108218	-42.064972
USDCAD	fGARCH.NAGARCH	7.000000e-07	559	1.431130e-02	1.531831e-01	-8.177455	-8.074028	-8.179127	-8.135881
USDCAD	fGARCH.GJRGARCH	8.000000e-07	559	1.431130e-02	1.498210e-01	-8.169686	-8.066259	-8.171359	-8.128113
USDCAD	gjrGARCH	7.000000e-07	559	1.431130e-02	1.471574e-01	-8.172520	-8.069093	-8.174192	-8.130946
USDCAD	iGARCH	9.000000e-07	559	1.431130e-02	1.547462e-01	-8.171812	-8.095691	-8.172751	-8.141214
USDCAD	csGARCH	1.000000e-06	559	1.431130e-02	1.532442e-01	-8.153903	-8.036823	-8.156021	-8.106841
USD/GBP
USDCNY	sGARCH	6.300000e-05	559	1.431100e-02	4.477761e-01	-6.249283	-6.153511	-6.250731	-6.210787
USDCNY	fGARCH.GARCH	6.280000e-05	559	1.431100e-02	4.492890e-01	-6.248594	-6.152823	-6.250043	-6.210099
USDCNY	fGARCH.TGARCH	3.970000e-05	559	1.431110e-02	2.481502e+00	-5.892319	-5.782905	-5.894183	-5.848340
USDCNY	fGARCH.NGARCH	6.540000e-05	559	1.431100e-02	6.115255e+02	-7.306839	-7.197425	-7.308702	-7.262860
USDCNY	fGARCH.NAGARCH	3.950000e-05	559	1.431110e-02	4.102266e-01	-6.279606	-6.170192	-6.281470	-6.235627
USDCNY	fGARCH.GJRGARCH	4.260000e-05	559	1.431110e-02	4.361674e-01	-6.260008	-6.150595	-6.261872	-6.216030
USDCNY	gjrGARCH	3.630000e-05	559	1.431110e-02	4.557971e-01	-6.274817	-6.165403	-6.276680	-6.230838
USDCNY	iGARCH	6.260000e-05	559	1.431100e-02	4.394265e-01	-6.235814	-6.153685	-6.236899	-6.202802
USDCNY	csGARCH	6.190000e-05	559	1.431100e-02	4.574758e-01	-6.240600	-6.117543	-6.242931	-6.191137
USD/JPY
USDJPY	sGARCH	1.377350e-02	559	1.426200e-02	1.333411e-01	1.400651	1.495488	1.399205	1.438771
USDJPY	fGARCH.GARCH	1.457990e-02	559	1.425910e-02	1.331475e-01	1.400950	1.495788	1.399504	1.439070
USDJPY	fGARCH.TGARCH	1.004660e-02	559	1.427530e-02	1.775850e-01	1.428467	1.536947	1.426610	1.472071
USDJPY	fGARCH.NGARCH	2.972860e+246	559	-1.063635e+244	4.457274e+03	-2.654210	-2.545729	-2.656067	-2.610606
USDJPY	fGARCH.NAGARCH	1.162970e-02	559	1.426970e-02	1.387974e-01	1.389546	1.498027	1.387689	1.433150
USDJPY	fGARCH.GJRGARCH	1.193290e-02	559	1.426860e-02	1.353829e-01	1.396830	1.505310	1.394973	1.440433
USDJPY	gjrGARCH	1.278950e-02	559	1.426550e-02	1.449849e-01	1.390041	1.498521	1.388184	1.433644
USDJPY	iGARCH	1.454770e-02	559	1.425920e-02	1.344519e-01	1.398596	1.479791	1.397509	1.431232
USDJPY	csGARCH	1.292400e-02	559	1.426500e-02	1.309096e-01	1.405506	1.527629	1.403186	1.454594

6.3.2.1A : Table summary

High Price Summary : Selected Models

Model	MSE	n	AIC.MSE	MSE.AIC	Akaike	Bayes	Shibata	Hannan.Quinn
sGARCH	1.977400e-03	3913	2.043500e-03	11.42366	-6.531136	-6.444344	-6.532345	-6.496249
fGARCH.GARCH	2.092600e-03	3913	2.043400e-03	11.42467	-6.531084	-6.444292	-6.532293	-6.496198
fGARCH.TGARCH	1.442100e-03	3913	2.043700e-03	11.60227	-6.339751	-6.239310	-6.341341	-6.299378
fGARCH.NGARCH	4.246942e+245	3913	-2.170684e+242	4734.79519	-14.688929	-14.588489	-14.690519	-14.648557
fGARCH.NAGARCH	1.667500e-03	3913	2.043600e-03	51.38677	-6.318326	-6.217885	-6.319915	-6.277953
fGARCH.GJRGARCH	1.711300e-03	3913	2.043600e-03	11.42364	-6.538189	-6.437748	-6.539779	-6.497816
gjrGARCH	1.832800e-03	3913	2.043500e-03	11.44392	-6.551763	-6.451322	-6.553353	-6.511390
iGARCH	2.087900e-03	3913	2.043400e-03	11.41716	-6.526596	-6.453453	-6.527477	-6.497196
csGARCH	1.855900e-03	3913	2.043500e-03	11.40387	-6.521389	-6.407299	-6.523412	-6.475530

6.3.2.1B : Table summary

High Price Summary : Selected Models

Model	n
fGARCH.NGARCH	7

6.3.2.1C : Table summary

Hi-Lo Price Summary : Selected Models

.id	Model	Date	Price	Price.T1	Akaike	Bayes	Shibata	Hannan.Quinn	diff	se
USDCHF	fGARCH.NGARCH	2015-10-30	0.991	-1.889325e+01	-584.2676	-584.1584	-584.2694	-584.2237	1.906483e+01	1
USDCAD	fGARCH.NGARCH	2015-03-29	1.270	-6.542943e+22	-529.2403	-529.1310	-529.2421	-529.1964	5.151924e+22	1
USDCAD	fGARCH.NGARCH	2015-07-21	1.305	4.139802e+61	-435.1427	-435.0065	-435.1454	-435.0879	3.172262e+61	1
USDJPY	fGARCH.NGARCH	2013-05-20	102.872	1.639729e+20	126.8955	127.0317	126.8927	126.9502	1.593951e+18	1
USDJPY	fGARCH.NGARCH	2013-06-16	95.106	-2.728130e+05	179.1320	179.2685	179.1292	179.1869	2.868516e+03	1
USDJPY	fGARCH.NGARCH	2013-06-19	98.239	4.076553e+124	740.3610	740.4972	740.3582	740.4158	4.149628e+122	1
USDJPY	fGARCH.NGARCH	2013-07-22	100.170	-7.099425e+16	107.5208	107.6570	107.5181	107.5756	7.087376e+14	1

6.3.2.1D : Table summary

## selected models' filtered highest price.
hp <- united.fx3 %>% 
  separate(Type, c('Cur', 'Type')) %>% 
  dplyr::filter(Type == 'Hi') %>% dplyr::select(-Cur, -Type)

acc <- hp %>% 
  ddply(.(.id, Model), summarise, 
        MSE = mean((Price.T1 - Price)^2), 
        n = length(Price), 
        AIC.MSE = (-2*MSE)/n+2*4/n, 
        MSE.AIC = mean((Akaike - mean(Akaike))^2),
        Akaike = mean(Akaike), 
        Bayes = mean(Bayes), 
        Shibata = mean(Shibata), 
        Hannan.Quinn = mean(Hannan.Quinn)) %>% 
  tbl_df %>% mutate(MSE = round(MSE, 7))

High Price Summary : Selected Models

.id	Model	MSE	n	AIC.MSE	MSE.AIC	Akaike	Bayes	Shibata	Hannan.Quinn
USD/AUD
USDAUD	sGARCH	0.0000003	491	0.0162933	1.598610e-01	-7.415756	-7.338455	-7.416709	-7.384684
USDAUD	fGARCH.GARCH	0.0000004	491	0.0162933	1.597193e-01	-7.415992	-7.338691	-7.416946	-7.384920
USDAUD	fGARCH.TGARCH	0.0000040	491	0.0162933	7.653141e-01	-7.094573	-7.003618	-7.095871	-7.058013
USDAUD	fGARCH.NGARCH	0.0000034	491	0.0162933	1.807330e+03	-8.536410	-8.445456	-8.537708	-8.499850
USDAUD	fGARCH.NAGARCH	0.0000003	491	0.0162933	1.661490e-01	-7.428772	-7.337817	-7.430070	-7.392212
USDAUD	fGARCH.GJRGARCH	0.0000002	491	0.0162933	1.641685e-01	-7.416436	-7.325481	-7.417733	-7.379875
USDAUD	gjrGARCH	0.0000002	491	0.0162933	1.667364e-01	-7.423330	-7.332376	-7.424628	-7.386770
USDAUD	iGARCH	0.0000003	491	0.0162933	1.600531e-01	-7.418332	-7.354684	-7.418994	-7.392748
USDAUD	csGARCH	0.0000003	491	0.0162933	1.591417e-01	-7.401789	-7.297181	-7.403485	-7.359741
USD/CAD
USDEUR	sGARCH	0.0000008	491	0.0162933	2.632251e-01	-8.438008	-8.355206	-8.439095	-8.404725
USDEUR	fGARCH.GARCH	0.0000008	491	0.0162933	2.615960e-01	-8.438672	-8.355869	-8.439759	-8.405388
USDEUR	fGARCH.TGARCH	0.0000020	491	0.0162933	3.447276e-01	-8.286664	-8.190208	-8.288117	-8.247892
USDEUR	fGARCH.NGARCH	0.0000011	491	0.0162933	7.056029e+03	-20.701974	-20.605518	-20.703427	-20.663202
USDEUR	fGARCH.NAGARCH	0.0000007	491	0.0162933	2.623139e-01	-8.437107	-8.340651	-8.438560	-8.398335
USDEUR	fGARCH.GJRGARCH	0.0000007	491	0.0162933	2.585683e-01	-8.437428	-8.340973	-8.438882	-8.398657
USDEUR	gjrGARCH	0.0000007	491	0.0162933	2.475362e-01	-8.461622	-8.365166	-8.463075	-8.422850
USDEUR	iGARCH	0.0000007	491	0.0162933	2.556639e-01	-8.437206	-8.368057	-8.437981	-8.409411
USDEUR	csGARCH	0.0000007	491	0.0162933	2.161844e-01	-8.441896	-8.331787	-8.443768	-8.397636
USD/CHF
USDGBP	sGARCH	0.0000001	491	0.0162933	1.227914e-01	-9.063485	-8.980465	-9.064600	-9.030116
USDGBP	fGARCH.GARCH	0.0000001	491	0.0162933	1.226449e-01	-9.063506	-8.980487	-9.064622	-9.030137
USDGBP	fGARCH.TGARCH	0.0000004	491	0.0162933	6.843266e-01	-8.746484	-8.649826	-8.747966	-8.707633
USDGBP	fGARCH.NGARCH	0.0000003	491	0.0162933	1.280771e+03	-9.775258	-9.678600	-9.776740	-9.736407
USDGBP	fGARCH.NAGARCH	0.0000001	491	0.0162933	3.602124e+01	-8.805719	-8.709061	-8.807201	-8.766868
USDGBP	fGARCH.GJRGARCH	0.0000001	491	0.0162933	1.243757e-01	-9.074318	-8.977660	-9.075800	-9.035467
USDGBP	gjrGARCH	0.0000001	491	0.0162933	1.018125e-01	-9.091547	-8.994889	-9.093029	-9.052696
USDGBP	iGARCH	0.0000001	491	0.0162933	1.235977e-01	-9.062939	-8.993558	-9.063742	-9.035052
USDGBP	csGARCH	0.0000001	491	0.0162933	6.907600e-02	-9.065048	-8.954751	-9.066948	-9.020715
USD/CNY
USDCHF	sGARCH	0.0000033	491	0.0162933	4.130057e-01	-7.636158	-7.552628	-7.637268	-7.602582
USDCHF	fGARCH.GARCH	0.0000033	491	0.0162933	4.128855e-01	-7.635978	-7.552448	-7.637087	-7.602402
USDCHF	fGARCH.TGARCH	0.0000005	491	0.0162933	2.797040e-01	-7.677410	-7.580223	-7.678888	-7.638344
USDCHF	fGARCH.NGARCH	0.0000032	491	0.0162933	2.348763e+03	-11.684824	-11.587638	-11.686302	-11.645758
USDCHF	fGARCH.NAGARCH	0.0000016	491	0.0162933	1.607448e+02	-6.618881	-6.521695	-6.620359	-6.579815
USDCHF	fGARCH.GJRGARCH	0.0000021	491	0.0162933	3.886764e-01	-7.660111	-7.562924	-7.661589	-7.621045
USDCHF	gjrGARCH	0.0000021	491	0.0162933	4.064955e-01	-7.680454	-7.583267	-7.681932	-7.641388
USDCHF	iGARCH	0.0000034	491	0.0162933	4.555835e-01	-7.612347	-7.542473	-7.613140	-7.584260
USDCHF	csGARCH	0.0000034	491	0.0162933	4.178346e-01	-7.612469	-7.501627	-7.614369	-7.567914
USD/EUR
USDCAD	sGARCH	0.0000009	491	0.0162933	1.590320e-01	-8.148008	-8.058618	-8.149278	-8.112077
USDCAD	fGARCH.GARCH	0.0000009	491	0.0162933	1.591533e-01	-8.148092	-8.058703	-8.149362	-8.112161
USDCAD	fGARCH.TGARCH	0.0000020	491	0.0162933	9.623340e-01	-7.885341	-7.782298	-7.887002	-7.843922
USDCAD	fGARCH.NGARCH	0.0000282	491	0.0162932	1.514453e+04	-43.242439	-43.139396	-43.244100	-43.201020
USDCAD	fGARCH.NAGARCH	0.0000007	491	0.0162933	1.571476e-01	-8.154143	-8.051100	-8.155804	-8.112724
USDCAD	fGARCH.GJRGARCH	0.0000007	491	0.0162933	1.542251e-01	-8.147451	-8.044408	-8.149112	-8.106032
USDCAD	gjrGARCH	0.0000007	491	0.0162933	1.513320e-01	-8.150441	-8.047398	-8.152102	-8.109022
USDCAD	iGARCH	0.0000009	491	0.0162933	1.598610e-01	-8.149335	-8.073598	-8.150266	-8.118892
USDCAD	csGARCH	0.0000008	491	0.0162933	1.577256e-01	-8.131076	-8.014380	-8.133182	-8.084169
USD/GBP
USDCNY	sGARCH	0.0000700	491	0.0162930	4.599824e-01	-6.275939	-6.178884	-6.277425	-6.236928
USDCNY	fGARCH.GARCH	0.0000698	491	0.0162930	4.617461e-01	-6.275154	-6.178099	-6.276640	-6.236143
USDCNY	fGARCH.TGARCH	0.0000422	491	0.0162931	2.704794e+00	-5.922961	-5.812265	-5.924868	-5.878467
USDCNY	fGARCH.NGARCH	0.0000724	491	0.0162930	6.959325e+02	-7.478213	-7.367517	-7.480119	-7.433719
USDCNY	fGARCH.NAGARCH	0.0000445	491	0.0162931	4.165837e-01	-6.307816	-6.197120	-6.309722	-6.263321
USDCNY	fGARCH.GJRGARCH	0.0000475	491	0.0162931	4.474065e-01	-6.285745	-6.175049	-6.287651	-6.241251
USDCNY	gjrGARCH	0.0000406	491	0.0162931	4.670423e-01	-6.302518	-6.191822	-6.304424	-6.258024
USDCNY	iGARCH	0.0000695	491	0.0162930	4.511389e-01	-6.262173	-6.178760	-6.263291	-6.228645
USDCNY	csGARCH	0.0000688	491	0.0162930	4.711008e-01	-6.266174	-6.141836	-6.268552	-6.216196
USD/JPY
USDJPY	sGARCH	0.0143627	491	0.0162348	1.253537e-01	1.439006	1.534387	1.437546	1.477344
USDJPY	fGARCH.GARCH	0.0148237	491	0.0162329	1.252929e-01	1.439044	1.534425	1.437584	1.477382
USDJPY	fGARCH.TGARCH	0.0106403	491	0.0162499	1.737724e-01	1.469370	1.578392	1.467496	1.513191
USDJPY	fGARCH.NGARCH	0.2225781	491	0.0153866	2.425858e+03	-3.112727	-3.003704	-3.114600	-3.068905
USDJPY	fGARCH.NAGARCH	0.0117384	491	0.0162455	1.297163e-01	1.428333	1.537356	1.426460	1.472155
USDJPY	fGARCH.GJRGARCH	0.0117611	491	0.0162454	1.266761e-01	1.435448	1.544471	1.433574	1.479269
USDJPY	gjrGARCH	0.0129197	491	0.0162407	1.362814e-01	1.429257	1.538279	1.427383	1.473078
USDJPY	iGARCH	0.0151310	491	0.0162316	1.263277e-01	1.437196	1.518935	1.436097	1.470051
USDJPY	csGARCH	0.0140804	491	0.0162359	1.232585e-01	1.443423	1.566087	1.441084	1.492728

6.3.2.2A : Table summary

High Price Summary : Selected Models

Model	MSE	n	AIC.MSE	MSE.AIC	Akaike	Bayes	Shibata	Hannan.Quinn
sGARCH	0.0020626	3437	0.0023264	11.42197	-6.505478	-6.418553	-6.506690	-6.470538
fGARCH.GARCH	0.0021284	3437	0.0023264	11.42250	-6.505479	-6.418553	-6.506690	-6.470538
fGARCH.TGARCH	0.0015273	3437	0.0023267	11.62771	-6.306295	-6.205721	-6.307888	-6.265868
fGARCH.NGARCH	0.0318124	3437	0.0023091	4552.46853	-14.933121	-14.832547	-14.934714	-14.892694
fGARCH.NAGARCH	0.0016838	3437	0.0023266	39.03963	-6.332015	-6.231441	-6.333608	-6.291589
fGARCH.GJRGARCH	0.0016875	3437	0.0023266	11.42298	-6.512292	-6.411718	-6.513885	-6.471865
gjrGARCH	0.0018520	3437	0.0023265	11.44553	-6.525808	-6.425234	-6.527401	-6.485382
iGARCH	0.0021723	3437	0.0023263	11.41575	-6.500733	-6.427456	-6.501617	-6.471279
csGARCH	0.0020221	3437	0.0023264	11.40408	-6.496433	-6.382211	-6.498460	-6.450520

6.3.2.2B : Table summary

High Price Summary : Selected Models

Model	n

6.3.2.2C : Table summary

Hi-Lo Price Summary : Selected Models

.id	Model	Date	Price	Price.T1	Akaike	Bayes	Shibata	Hannan.Quinn	diff	se

6.3.2.2D : Table summary

6.4 Low Price

6.4.1 All Models

## filtered bias lowest price.
lp <- fx %>% separate(Type, c('Cur', 'Type')) %>% 
  dplyr::filter(Type == 'Lo') %>% 
  dplyr::select(-Cur, -Type)

ntmID <- lp %>% dplyr::filter(se == 1) %>% .$Date %>% unlist %>% sort

acc <- lp %>% dplyr::filter(!Date %in% ntmID & Date %in% ntimeID2) %>% 
  ddply(.(.id, Model), summarise, 
        MSE = mean((Price.T1 - Price)^2), 
        n = length(Price), 
        AIC.MSE = (-2*MSE)/n+2*4/n, 
        MSE.AIC = mean((Akaike - mean(Akaike))^2),
        Akaike = mean(Akaike), 
        Bayes = mean(Bayes), 
        Shibata = mean(Shibata), 
        Hannan.Quinn = mean(Hannan.Quinn)) %>% 
  tbl_df %>% mutate(MSE = round(MSE, 7))

Low Price Summary : All Models

.id	Model	MSE	n	AIC.MSE	MSE.AIC	Akaike	Bayes	Shibata	Hannan.Quinn
USD/AUD
USDAUD	sGARCH	0.0000003	484	0.0165289	1.730755e-01	-7.4383433	-7.360172	-7.4393090	-7.406921
USDAUD	fGARCH.GARCH	0.0000003	484	0.0165289	1.731705e-01	-7.4382819	-7.360111	-7.4392476	-7.406860
USDAUD	fGARCH.TGARCH	0.0000025	484	0.0165289	9.072887e-01	-7.1406291	-7.048804	-7.1419430	-7.103719
USDAUD	fGARCH.AVGARCH	0.0000000	50	0.1600000	1.954909e+02	-5.7686745	-5.667345	-5.7702560	-5.727944
USDAUD	fGARCH.NGARCH	0.0000063	484	0.0165289	1.536145e+04	-41.3097652	-41.217940	-41.3110791	-41.272855
USDAUD	fGARCH.NAGARCH	0.0000006	484	0.0165289	1.983395e-01	-7.4372049	-7.345380	-7.4385188	-7.400295
USDAUD	fGARCH.APARCH	0.0000036	298	0.0268456	7.560565e+03	-21.6075988	-21.500617	-21.6093582	-21.564595
USDAUD	fGARCH.GJRGARCH	0.0000013	484	0.0165289	1.963006e-01	-7.4314950	-7.339670	-7.4328089	-7.394585
USDAUD	fGARCH.ALLGARCH	0.0000006	206	0.0388349	9.768837e+03	-24.8361133	-24.712957	-24.8384397	-24.786609
USDAUD	eGARCH	0.0000005	434	0.0184332	8.253949e+00	-7.3815591	-7.289007	-7.3828934	-7.344356
USDAUD	gjrGARCH	0.0000014	484	0.0165289	1.971001e-01	-7.4364778	-7.344653	-7.4377917	-7.399567
USDAUD	apARCH	0.0000001	84	0.0952381	3.247800e-03	-7.9394345	-7.832113	-7.9412253	-7.896294
USDAUD	iGARCH	0.0000013	484	0.0165289	1.919050e-01	-7.4354985	-7.370981	-7.4361698	-7.409565
USDAUD	csGARCH	0.0000007	484	0.0165289	1.928439e-01	-7.4172217	-7.311743	-7.4189369	-7.374823
USD/CAD
USDEUR	sGARCH	0.0000002	484	0.0165289	2.705705e-01	-8.3913103	-8.310778	-8.3923554	-8.358939
USDEUR	fGARCH.GARCH	0.0000002	484	0.0165289	2.709654e-01	-8.3911319	-8.310600	-8.3921771	-8.358761
USDEUR	fGARCH.TGARCH	0.0000007	484	0.0165289	5.295668e-01	-8.1889377	-8.094752	-8.1903399	-8.151079
USDEUR	fGARCH.AVGARCH	0.0000000	26	0.3076923	4.485169e-01	-7.8175320	-7.716716	-7.8190856	-7.777008
USDEUR	fGARCH.NGARCH	0.0000070	484	0.0165289	1.472004e+04	-33.2154490	-33.121263	-33.2168512	-33.177590
USDEUR	fGARCH.NAGARCH	0.0000002	484	0.0165289	1.403078e+02	-7.8634613	-7.769275	-7.8648635	-7.825602
USDEUR	fGARCH.APARCH	0.0000005	111	0.0720721	2.270741e+03	-12.7415295	-12.633311	-12.7433663	-12.698030
USDEUR	fGARCH.GJRGARCH	0.0000002	484	0.0165289	2.712809e-01	-8.3965097	-8.302324	-8.3979119	-8.358650
USDEUR	fGARCH.ALLGARCH	0.0000002	318	0.0251572	1.579104e+03	-11.6895383	-11.568473	-11.6918051	-11.640873
USDEUR	eGARCH	0.0000002	437	0.0183066	2.043052e+00	-8.4469405	-8.352189	-8.4483613	-8.408854
USDEUR	gjrGARCH	0.0000002	484	0.0165289	2.757950e-01	-8.4133068	-8.319121	-8.4147090	-8.375448
USDEUR	apARCH	0.0000000	84	0.0952381	3.677000e-04	-8.3212266	-8.219444	-8.3228304	-8.280313
USDEUR	iGARCH	0.0000002	484	0.0165289	2.667864e-01	-8.3884119	-8.321533	-8.3891538	-8.361529
USDEUR	csGARCH	0.0000002	484	0.0165289	2.649661e-01	-8.3703968	-8.262557	-8.3722089	-8.327049
USD/CHF
USDGBP	sGARCH	0.0000000	484	0.0165289	7.227940e-02	-9.1042104	-9.027899	-9.1051427	-9.073537
USDGBP	fGARCH.GARCH	0.0000002	484	0.0165289	7.404510e-02	-9.1013984	-9.025087	-9.1023307	-9.070725
USDGBP	fGARCH.TGARCH	0.0000001	484	0.0165289	2.451551e-01	-8.8779545	-8.788004	-8.8792269	-8.841800
USDGBP	fGARCH.AVGARCH	0.0000001	31	0.2580645	1.239286e-01	-9.0826534	-8.972345	-9.0845693	-9.038317
USDGBP	fGARCH.NGARCH	0.0000025	484	0.0165289	1.461007e+03	-11.6465816	-11.556632	-11.6478539	-11.610427
USDGBP	fGARCH.NAGARCH	0.0000000	484	0.0165289	2.255544e+01	-8.8913858	-8.801436	-8.8926582	-8.855231
USDGBP	fGARCH.APARCH	0.0000001	299	0.0267559	2.220126e+00	-8.7816630	-8.676649	-8.7833832	-8.739452
USDGBP	fGARCH.GJRGARCH	0.0000000	484	0.0165289	7.541920e-02	-9.1159234	-9.025973	-9.1171958	-9.079768
USDGBP	fGARCH.ALLGARCH	0.0000002	320	0.0250000	1.061215e+03	-10.9792420	-10.859385	-10.9814594	-10.931065
USDGBP	eGARCH	0.0000000	433	0.0184758	1.224720e-01	-9.1343153	-9.044346	-9.1355914	-9.098152
USDGBP	gjrGARCH	0.0000000	484	0.0165289	7.823570e-02	-9.1268217	-9.036872	-9.1280940	-9.090667
USDGBP	apARCH	0.0000000	84	0.0952381	3.404000e-03	-9.2689163	-9.163348	-9.2706556	-9.226486
USDGBP	iGARCH	0.0000001	484	0.0165289	7.544850e-02	-9.1002350	-9.037563	-9.1008811	-9.075044
USDGBP	csGARCH	0.0000001	484	0.0165289	7.229800e-02	-9.0834450	-8.979856	-9.0851104	-9.041808
USD/CNY
USDCHF	sGARCH	0.0000091	484	0.0165289	3.506709e-01	-7.6889621	-7.608953	-7.6899757	-7.656801
USDCHF	fGARCH.GARCH	0.0000091	484	0.0165289	3.504722e-01	-7.6887624	-7.608753	-7.6897759	-7.656601
USDCHF	fGARCH.TGARCH	0.0000001	484	0.0165289	2.414152e-01	-7.6368083	-7.543142	-7.6381772	-7.599158
USDCHF	fGARCH.AVGARCH	0.0000002	16	0.5000000	9.931160e-02	-7.8876405	-7.784873	-7.8892785	-7.846326
USDCHF	fGARCH.NGARCH	0.0000074	484	0.0165289	8.804070e+02	-9.0330070	-8.939341	-9.0343759	-8.995357
USDCHF	fGARCH.NAGARCH	0.0000051	484	0.0165289	3.469194e-01	-7.7143800	-7.620714	-7.7157489	-7.676730
USDCHF	fGARCH.APARCH	0.0000090	297	0.0269360	6.662720e+03	-22.4945125	-22.393077	-22.4961088	-22.453737
USDCHF	fGARCH.GJRGARCH	0.0000053	484	0.0165289	3.012133e-01	-7.7207938	-7.627128	-7.7221627	-7.683143
USDCHF	fGARCH.ALLGARCH	0.0000001	316	0.0253165	1.350816e+03	-10.7719037	-10.655873	-10.7739720	-10.725262
USDCHF	eGARCH	0.0000283	436	0.0183485	2.833244e-01	-7.7924611	-7.700235	-7.7937901	-7.755390
USDCHF	gjrGARCH	0.0000070	484	0.0165289	3.066543e-01	-7.7396940	-7.646028	-7.7410629	-7.702044
USDCHF	apARCH	0.0000000	83	0.0963855	2.285500e-03	-8.0165499	-7.917035	-8.0180745	-7.976546
USDCHF	iGARCH	0.0003129	484	0.0165276	7.642181e-01	-7.4440042	-7.377651	-7.4447161	-7.417333
USDCHF	csGARCH	0.0000875	484	0.0165286	5.105184e-01	-7.5841278	-7.476805	-7.5859051	-7.540988
USD/EUR
USDCAD	sGARCH	0.0000002	484	0.0165289	2.077697e-01	-8.0582208	-7.984343	-8.0590801	-8.028525
USDCAD	fGARCH.GARCH	0.0000002	484	0.0165289	2.079155e-01	-8.0581520	-7.984275	-8.0590112	-8.028456
USDCAD	fGARCH.TGARCH	0.0000010	484	0.0165289	6.322389e-01	-7.8138439	-7.726313	-7.8150346	-7.778660
USDCAD	fGARCH.AVGARCH	0.0000000	37	0.2162162	9.743570e-02	-8.2867029	-8.185956	-8.2882652	-8.246206
USDCAD	fGARCH.NGARCH	0.0000023	484	0.0165289	5.295652e+03	-15.5249309	-15.437400	-15.5261215	-15.489747
USDCAD	fGARCH.NAGARCH	0.0000001	484	0.0165289	2.080171e-01	-8.0675837	-7.980053	-8.0687744	-8.032400
USDCAD	fGARCH.APARCH	0.0000001	296	0.0270270	2.861713e+03	-17.2853411	-17.185857	-17.2868613	-17.245351
USDCAD	fGARCH.GJRGARCH	0.0000001	484	0.0165289	2.080528e-01	-8.0593477	-7.971817	-8.0605383	-8.024164
USDCAD	fGARCH.ALLGARCH	0.0000001	318	0.0251572	1.808394e+03	-12.3980833	-12.284660	-12.4000441	-12.352490
USDCAD	eGARCH	0.0000002	430	0.0186047	2.842401e+00	-8.0268562	-7.939005	-8.0280555	-7.991543
USDCAD	gjrGARCH	0.0000001	484	0.0165289	2.086037e-01	-8.0661110	-7.978580	-8.0673016	-8.030927
USDCAD	apARCH	0.0000000	83	0.0963855	2.258300e-03	-8.4910086	-8.388823	-8.4926252	-8.449933
USDCAD	iGARCH	0.0000004	484	0.0165289	2.081975e-01	-8.0579848	-7.997761	-8.0585667	-8.033777
USDCAD	csGARCH	0.0000002	484	0.0165289	2.065812e-01	-8.0417961	-7.940611	-8.0433714	-8.001124
USD/GBP
USDCNY	sGARCH	0.0021474	484	0.0165201	2.445869e+00	-6.5114601	-6.425234	-6.5126378	-6.476801
USDCNY	fGARCH.GARCH	0.0011683	484	0.0165241	2.460450e+00	-6.5091994	-6.422973	-6.5103771	-6.474541
USDCNY	fGARCH.TGARCH	0.0040343	484	0.0165123	2.528636e+00	-6.3996831	-6.299815	-6.4012396	-6.359541
USDCNY	fGARCH.AVGARCH	0.0000002	12	0.6666666	1.992000e-03	-7.0562794	-6.947421	-7.0580670	-7.012529
USDCNY	fGARCH.NGARCH	0.5753579	484	0.0141514	1.398668e+03	-8.9481452	-8.848277	-8.9497016	-8.908003
USDCNY	fGARCH.NAGARCH	0.0007122	484	0.0165260	2.610237e+00	-6.5062671	-6.406399	-6.5078235	-6.466125
USDCNY	fGARCH.APARCH	0.0012013	296	0.0270189	3.337535e+03	-12.7074535	-12.589522	-12.7096017	-12.660051
USDCNY	fGARCH.GJRGARCH	0.0017122	484	0.0165219	2.920414e+00	-6.4593603	-6.359492	-6.4609167	-6.419218
USDCNY	fGARCH.ALLGARCH	0.0025675	318	0.0251411	2.534200e+03	-11.7028813	-11.572608	-11.7054805	-11.650517
USDCNY	eGARCH	0.0024656	434	0.0184218	5.316365e+00	-6.0500151	-5.949655	-6.0515908	-6.009675
USDCNY	gjrGARCH	0.0017572	484	0.0165217	2.457657e+00	-6.5323248	-6.432456	-6.5338813	-6.492183
USDCNY	apARCH	0.0000031	84	0.0952380	4.716700e-03	-7.0178693	-6.903224	-7.0198740	-6.971791
USDCNY	iGARCH	0.0022341	484	0.0165197	2.925274e+00	-6.3895497	-6.316965	-6.3904017	-6.360374
USDCNY	csGARCH	0.0024519	484	0.0165188	2.990677e+00	-6.4271865	-6.313676	-6.4291743	-6.381561
USD/JPY
USDJPY	sGARCH	0.0122722	484	0.0164782	1.823328e-01	1.5729333	1.658843	1.5717395	1.607464
USDJPY	fGARCH.GARCH	0.0116044	484	0.0164810	1.817694e-01	1.5734009	1.659310	1.5722071	1.607932
USDJPY	fGARCH.TGARCH	0.0123503	484	0.0164779	2.594695e-01	1.6019844	1.701536	1.6004134	1.641999
USDJPY	fGARCH.AVGARCH	0.0615865	37	0.2128872	5.636226e-01	0.9338363	1.073338	0.9308645	0.989905
USDJPY	fGARCH.NGARCH	0.0175687	484	0.0164563	6.448609e+03	-11.3130595	-11.213508	-11.3146305	-11.273045
USDJPY	fGARCH.NAGARCH	0.0086354	484	0.0164932	1.916717e-01	1.5486556	1.648207	1.5470846	1.588670
USDJPY	fGARCH.APARCH	0.5084782	114	0.0612548	1.537085e+04	-27.8940585	-27.762847	-27.8967039	-27.841321
USDJPY	fGARCH.GJRGARCH	0.0121299	484	0.0164788	1.872344e-01	1.5677913	1.667342	1.5662203	1.607806
USDJPY	fGARCH.ALLGARCH	0.0155203	198	0.0402473	5.756555e+03	-8.9606092	-8.826272	-8.9633621	-8.906613
USDJPY	eGARCH	0.0141837	434	0.0183678	2.495819e-01	1.5702403	1.671443	1.5686170	1.610918
USDJPY	gjrGARCH	0.0098692	484	0.0164881	1.900683e-01	1.5632008	1.662752	1.5616298	1.603215
USDJPY	apARCH	0.8428061	83	0.0760770	1.624791e+05	-128.2723537	-128.136965	-128.2751615	-128.217938
USDJPY	iGARCH	0.0110787	484	0.0164831	1.853079e-01	1.5714299	1.643698	1.5705601	1.600478
USDJPY	csGARCH	0.0255159	484	0.0164235	1.743396e-01	1.5830015	1.696195	1.5810007	1.628499

6.4.1.1 : Table summary

Low Price Summary : All Models

Model	MSE	n	AIC.MSE	MSE.AIC	Akaike	Bayes	Shibata	Hannan.Quinn
sGARCH	0.0020613	3388	0.0023601	11.99343	-6.517082	-6.436934	-6.518109	-6.484866
fGARCH.GARCH	0.0018261	3388	0.0023602	11.99455	-6.516218	-6.436070	-6.517245	-6.484002
fGARCH.TGARCH	0.0023413	3388	0.0023599	11.82519	-6.350839	-6.257042	-6.352221	-6.313137
fGARCH.AVGARCH	0.0109029	209	0.0381732	58.57421	-6.010457	-5.900663	-6.012343	-5.966325
fGARCH.NGARCH	0.0847074	3388	0.0023113	6655.81231	-18.712991	-18.619194	-18.714373	-18.675289
fGARCH.NAGARCH	0.0013362	3388	0.0023605	34.79162	-6.418804	-6.325007	-6.420186	-6.381102
fGARCH.APARCH	0.0340888	1711	0.0046358	4750.64019	-17.076418	-16.968452	-17.078232	-17.033019
fGARCH.GJRGARCH	0.0019785	3388	0.0023601	12.06833	-6.516520	-6.422723	-6.517902	-6.478818
fGARCH.ALLGARCH	0.0019508	1994	0.0040101	2927.59154	-12.632447	-12.510590	-12.634733	-12.583465
eGARCH	0.0023827	3038	0.0026317	14.27553	-6.465883	-6.371743	-6.467277	-6.428043
gjrGARCH	0.0016621	3388	0.0023603	12.02126	-6.535934	-6.442137	-6.537316	-6.498231
apARCH	0.1195781	585	0.0132664	24809.02700	-25.214903	-25.105431	-25.216772	-25.170901
iGARCH	0.0019468	3388	0.0023601	12.04127	-6.463465	-6.396965	-6.464190	-6.436735
csGARCH	0.0040081	3388	0.0023589	12.04502	-6.477310	-6.369865	-6.479101	-6.434122

6.4.1.2 : Table summary

Low Price Summary : All Models

Model	n
sGARCH	2
fGARCH.GARCH	2
fGARCH.TGARCH	2
fGARCH.NGARCH	43
fGARCH.NAGARCH	9
fGARCH.APARCH	9
fGARCH.GJRGARCH	4
fGARCH.ALLGARCH	54
eGARCH	5
gjrGARCH	3
apARCH	3
iGARCH	9
csGARCH	4

6.4.1.3 : Table summary

Hi-Lo Price Summary : Selected Models

.id	Model	Date	Price	Price.T1	Akaike	Bayes	Shibata	Hannan.Quinn	diff	se
USDAUD	fGARCH.NGARCH	2013-06-27	1.077	2.542027e+00	-590.320340	-590.197426	-590.322615	-590.270933	2.360285e+00	1
USDAUD	fGARCH.NGARCH	2017-03-26	1.307	1.111220e-02	-586.980288	-586.857373	-586.982562	-586.930880	8.502100e-03	1
USDEUR	fGARCH.NGARCH	2014-10-14	0.779	-2.018651e+51	-468.909622	-468.759806	-468.912961	-468.849407	2.591336e+51	1
USDEUR	fGARCH.NGARCH	2015-03-02	0.890	-4.015994e+07	83.346290	83.510176	83.342305	83.412167	4.512353e+07	1
USDEUR	fGARCH.NGARCH	2015-06-04	0.887	-1.394863e+18	-545.380537	-545.244340	-545.383310	-545.325796	1.572562e+18	1
USDEUR	fGARCH.NGARCH	2015-06-24	0.891	1.892803e+10	77.586765	77.722962	77.583992	77.641506	2.124358e+10	1
USDGBP	fGARCH.TGARCH	2014-06-19	0.586	-3.465523e+73	364.832355	365.037213	364.826216	364.914701	5.913861e+73	1
USDGBP	fGARCH.NGARCH	2014-06-19	0.586	4.316118e-01	-160.018385	-159.813528	-160.024525	-159.936039	7.365389e-01	1
USDGBP	csGARCH	2014-12-05	0.637	9.285102e+149	758.957433	759.107249	758.954093	759.017647	1.457630e+150	1
USDCHF	sGARCH	2015-01-16	0.850	1.189676e+00	-6.687989	-6.606271	-6.689007	-6.655145	1.399619e+00	1
USDCHF	fGARCH.GARCH	2015-01-16	0.850	1.189676e+00	-6.687989	-6.606271	-6.689007	-6.655145	1.399619e+00	1
USDCHF	fGARCH.TGARCH	2015-01-16	0.850	1.182560e+00	-6.882116	-6.786779	-6.883495	-6.843798	1.391247e+00	1
USDCHF	fGARCH.NGARCH	2015-01-16	0.850	1.182556e+00	-6.811955	-6.716617	-6.813334	-6.773637	1.391243e+00	1
USDCHF	fGARCH.NGARCH	2015-09-07	0.970	-8.823318e+01	-587.029347	-586.920390	-587.031140	-586.985555	9.096204e+01	1
USDCHF	fGARCH.NAGARCH	2015-01-16	0.850	1.188451e+00	-6.758750	-6.663413	-6.760129	-6.720432	1.398178e+00	1
USDCHF	fGARCH.GJRGARCH	2015-01-16	0.850	1.189203e+00	-6.775060	-6.679723	-6.776439	-6.736742	1.399062e+00	1
USDCHF	fGARCH.ALLGARCH	2015-01-16	0.850	1.184971e+00	-6.882670	-6.760093	-6.884927	-6.833404	1.394083e+00	1
USDCHF	eGARCH	2015-01-16	0.850	1.179679e+00	-6.756294	-6.660957	-6.757673	-6.717976	1.387858e+00	1
USDCHF	eGARCH	2015-01-21	0.851	5.746862e-01	-6.615293	-6.519955	-6.616671	-6.576975	6.753070e-01	1
USDCHF	gjrGARCH	2015-01-16	0.850	1.187461e+00	-6.834457	-6.739119	-6.835835	-6.796138	1.397013e+00	1
USDCHF	gjrGARCH	2015-01-19	0.857	5.503465e-01	-6.799206	-6.703606	-6.800595	-6.760778	6.421780e-01	1
USDCHF	iGARCH	2015-01-16	0.850	1.189656e+00	-6.696311	-6.628212	-6.697021	-6.668940	1.399595e+00	1
USDCHF	iGARCH	2015-01-19	0.857	5.467194e-01	-6.659730	-6.591444	-6.660445	-6.632281	6.379457e-01	1
USDCHF	iGARCH	2015-01-20	0.869	1.169574e+00	-6.632037	-6.563939	-6.632748	-6.604667	1.345885e+00	1
USDCHF	iGARCH	2015-01-21	0.851	5.536845e-01	-6.599117	-6.531019	-6.599827	-6.571747	6.506281e-01	1
USDCHF	iGARCH	2015-01-22	0.853	1.132264e+00	-6.569994	-6.501896	-6.570705	-6.542624	1.327390e+00	1
USDCHF	iGARCH	2015-01-26	0.876	1.153558e+00	-6.519110	-6.450824	-6.519825	-6.491661	1.316847e+00	1
USDCHF	iGARCH	2015-01-27	0.894	6.896106e-01	-6.470927	-6.402829	-6.471637	-6.443557	7.713765e-01	1
USDCHF	iGARCH	2015-02-02	0.920	7.319616e-01	-6.350835	-6.255235	-6.352225	-6.312407	7.956105e-01	1
USDCHF	csGARCH	2015-01-16	0.850	1.193636e+00	-6.688153	-6.579196	-6.689945	-6.644361	1.404278e+00	1
USDCHF	csGARCH	2015-01-22	0.853	1.141360e+00	-6.534724	-6.425767	-6.536516	-6.490932	1.338054e+00	1
USDCHF	csGARCH	2015-01-23	0.868	6.200740e-01	-6.493151	-6.384194	-6.494943	-6.449359	7.143710e-01	1
USDCNY	sGARCH	2014-07-10	2.201	2.987751e+00	-4.665480	-4.583537	-4.666505	-4.632541	1.357452e+00	1
USDCNY	fGARCH.GARCH	2014-07-10	2.201	2.987874e+00	-4.665479	-4.583536	-4.666505	-4.632541	1.357508e+00	1
USDCNY	fGARCH.NGARCH	2014-07-17	6.192	-5.016306e+02	-585.712986	-585.631043	-585.714011	-585.680047	8.101269e+01	1
USDCNY	fGARCH.NGARCH	2014-07-20	6.195	1.194381e+01	-589.430373	-589.348203	-589.431406	-589.397340	1.927975e+00	1
USDCNY	fGARCH.NGARCH	2014-07-22	6.189	1.945038e+01	-591.466725	-591.384782	-591.467750	-591.433786	3.142734e+00	1
USDCNY	fGARCH.NGARCH	2014-07-23	6.182	-3.637318e+01	-588.553531	-588.471588	-588.554557	-588.520593	5.883724e+00	1
USDCNY	fGARCH.NGARCH	2014-07-27	6.176	4.872521e+01	-587.187420	-587.105250	-587.188453	-587.154387	7.889444e+00	1
USDCNY	fGARCH.NGARCH	2014-07-31	6.163	2.769268e+01	-590.455881	-590.373938	-590.456907	-590.422943	4.493377e+00	1
USDCNY	fGARCH.NGARCH	2014-08-03	6.168	3.201427e+01	-587.733648	-587.651478	-587.734681	-587.700615	5.190381e+00	1
USDCNY	fGARCH.NGARCH	2014-08-05	6.153	1.853196e+01	-589.664961	-589.583018	-589.665987	-589.632023	3.011858e+00	1
USDCNY	fGARCH.NGARCH	2014-08-06	6.147	2.635122e+01	-591.728569	-591.646626	-591.729595	-591.695631	4.286842e+00	1
USDCNY	fGARCH.NGARCH	2014-08-10	6.144	5.336958e+01	-588.785684	-588.703514	-588.786717	-588.752651	8.686456e+00	1
USDCNY	fGARCH.NGARCH	2014-08-12	6.144	4.740305e+01	-587.300349	-587.218406	-587.301374	-587.267410	7.715340e+00	1
USDCNY	fGARCH.NGARCH	2014-08-13	6.142	8.825968e+00	-589.224653	-589.142710	-589.225679	-589.191715	1.436986e+00	1
USDCNY	fGARCH.NGARCH	2014-08-14	6.136	4.872331e+01	-586.351874	-586.269931	-586.352899	-586.318935	7.940565e+00	1
USDCNY	fGARCH.NGARCH	2014-08-19	6.130	-1.240483e+01	-590.789977	-590.708034	-590.791003	-590.757039	2.023627e+00	1
USDCNY	fGARCH.NGARCH	2014-08-20	6.130	9.161532e+00	-592.227353	-592.145410	-592.228379	-592.194415	1.494540e+00	1
USDCNY	fGARCH.NGARCH	2014-08-21	6.141	-1.525661e+01	-590.144127	-590.062184	-590.145153	-590.111189	2.484385e+00	1
USDCNY	fGARCH.NGARCH	2014-08-24	6.140	-3.247607e+01	-589.174302	-589.092132	-589.175335	-589.141269	5.289262e+00	1
USDCNY	fGARCH.NGARCH	2014-08-25	6.142	6.174800e+01	-572.956479	-572.874536	-572.957505	-572.923541	1.005340e+01	1
USDCNY	fGARCH.NGARCH	2014-08-26	6.133	9.738678e+01	-587.251542	-587.169599	-587.252568	-587.218604	1.587914e+01	1
USDCNY	fGARCH.NGARCH	2014-08-31	6.129	2.545583e+02	-584.923023	-584.840853	-584.924056	-584.889989	4.153341e+01	1
USDCNY	fGARCH.NGARCH	2014-09-01	6.132	1.596999e+02	-584.161053	-584.079110	-584.162079	-584.128115	2.604369e+01	1
USDCNY	fGARCH.NGARCH	2014-09-02	6.131	-1.989882e+01	-589.399865	-589.317922	-589.400891	-589.366927	3.245608e+00	1
USDCNY	fGARCH.NGARCH	2014-09-04	6.128	-2.866168e+01	-585.515480	-585.433537	-585.516505	-585.482541	4.677168e+00	1
USDCNY	fGARCH.NGARCH	2014-09-08	6.122	-2.517129e+01	-587.872377	-587.790434	-587.873402	-587.839438	4.111612e+00	1
USDCNY	fGARCH.NGARCH	2014-09-11	6.120	1.708482e+01	-588.380157	-588.298214	-588.381183	-588.347219	2.791637e+00	1
USDCNY	fGARCH.NGARCH	2014-09-14	6.125	-7.626137e+01	-589.072288	-588.990119	-589.073322	-589.039255	1.245084e+01	1
USDCNY	fGARCH.NGARCH	2014-09-16	6.129	-1.759094e+02	-585.597533	-585.515590	-585.598558	-585.564594	2.870116e+01	1
USDCNY	fGARCH.NGARCH	2014-09-21	6.128	-2.039517e+01	-588.488512	-588.406343	-588.489546	-588.455479	3.328194e+00	1
USDCNY	fGARCH.NGARCH	2014-09-23	6.124	1.512941e+01	-590.152856	-590.070913	-590.153882	-590.119918	2.470511e+00	1
USDCNY	fGARCH.NGARCH	2014-10-01	6.128	-1.146657e+02	-584.091459	-584.009516	-584.092485	-584.058521	1.871177e+01	1
USDCNY	fGARCH.NGARCH	2014-10-06	6.129	-2.283202e+01	-579.908511	-579.826568	-579.909537	-579.875573	3.725243e+00	1
USDCNY	fGARCH.NGARCH	2014-10-07	6.125	5.146397e+01	-565.845084	-565.763141	-565.846110	-565.812146	8.402281e+00	1
USDCNY	fGARCH.NGARCH	2014-10-09	6.120	6.182692e+01	-583.758544	-583.676826	-583.759562	-583.725700	1.010244e+01	1
USDCNY	fGARCH.NGARCH	2014-11-26	6.123	6.187566e+01	-583.601907	-583.520189	-583.602924	-583.569062	1.010545e+01	1
USDCNY	fGARCH.NAGARCH	2014-07-10	2.201	2.977219e+00	-4.669064	-4.573464	-4.670453	-4.630636	1.352666e+00	1
USDCNY	fGARCH.NAGARCH	2014-07-24	6.182	-3.603032e+02	14.561667	14.643610	14.560642	14.594606	5.828262e+01	1
USDCNY	fGARCH.NAGARCH	2014-07-29	6.162	-3.579216e+02	14.548624	14.630567	14.547598	14.581562	5.808530e+01	1
USDCNY	fGARCH.NAGARCH	2014-07-31	6.163	-3.531901e+02	14.522470	14.604413	14.521444	14.555409	5.730814e+01	1
USDCNY	fGARCH.NAGARCH	2014-08-04	6.161	-3.492923e+02	14.548440	14.630382	14.547414	14.581378	5.669409e+01	1
USDCNY	fGARCH.NAGARCH	2014-08-26	6.133	4.865151e+00	104.667516	104.749459	104.666490	104.700454	7.932742e-01	1
USDCNY	fGARCH.NAGARCH	2014-09-04	6.128	4.796821e+02	172.167572	172.249515	172.166546	172.200510	7.827710e+01	1
USDCNY	fGARCH.NAGARCH	2014-10-19	6.113	-3.344848e+02	98.972743	99.054686	98.971717	99.005682	5.471696e+01	1
USDCNY	fGARCH.APARCH	2014-07-15	6.194	2.096796e+01	-591.356584	-591.260983	-591.357973	-591.318155	3.385206e+00	1
USDCNY	fGARCH.APARCH	2014-07-24	6.182	2.156616e+01	103.442134	103.537734	103.440745	103.480562	3.488541e+00	1
USDCNY	fGARCH.APARCH	2014-08-18	6.127	4.686359e+01	-590.025600	-589.930000	-590.026990	-589.987172	7.648701e+00	1
USDCNY	fGARCH.APARCH	2014-08-20	6.130	-1.738365e+02	-587.118563	-587.022963	-587.119952	-587.080135	2.835831e+01	1
USDCNY	fGARCH.APARCH	2014-09-22	6.128	2.649730e+02	-583.798821	-583.703221	-583.800210	-583.760393	4.323972e+01	1
USDCNY	fGARCH.APARCH	2014-11-20	6.109	-1.204425e+02	-584.497904	-584.402566	-584.499282	-584.459586	1.971558e+01	1
USDCNY	fGARCH.APARCH	2014-11-26	6.123	1.763058e+02	-584.737735	-584.642398	-584.739114	-584.699417	2.879403e+01	1
USDCNY	fGARCH.APARCH	2014-12-19	6.205	1.811908e+02	-585.237794	-585.142457	-585.239173	-585.199476	2.920077e+01	1
USDCNY	fGARCH.GJRGARCH	2014-07-10	2.201	2.979918e+00	-4.677596	-4.581996	-4.678985	-4.639168	1.353893e+00	1
USDCNY	fGARCH.GJRGARCH	2014-09-01	6.132	1.263740e+01	98.054293	98.136236	98.053267	98.087231	2.060893e+00	1
USDCNY	fGARCH.GJRGARCH	2014-11-12	6.114	-3.508494e+01	94.016565	94.098283	94.015548	94.049410	5.738460e+00	1
USDCNY	fGARCH.ALLGARCH	2014-07-10	2.201	2.966190e+00	-4.732654	-4.609740	-4.734928	-4.683247	1.347655e+00	1
USDCNY	fGARCH.ALLGARCH	2014-07-16	6.191	-3.928444e+01	-582.734556	-582.625298	-582.736361	-582.690638	6.345410e+00	1
USDCNY	fGARCH.ALLGARCH	2014-07-17	6.192	1.616838e+02	-583.779418	-583.670160	-583.781223	-583.735500	2.611173e+01	1
USDCNY	fGARCH.ALLGARCH	2014-07-20	6.195	3.493327e+01	-587.564830	-587.455270	-587.566649	-587.520785	5.638946e+00	1
USDCNY	fGARCH.ALLGARCH	2014-07-21	6.193	2.379018e+02	-582.588057	-582.478800	-582.589863	-582.544139	3.841462e+01	1
USDCNY	fGARCH.ALLGARCH	2014-07-27	6.176	6.750841e+01	-588.539587	-588.430027	-588.541406	-588.495542	1.093077e+01	1
USDCNY	fGARCH.ALLGARCH	2014-07-31	6.163	-1.535570e+01	-587.168301	-587.059044	-587.170107	-587.124384	2.491595e+00	1
USDCNY	fGARCH.ALLGARCH	2014-08-03	6.168	-1.336380e+01	-588.926648	-588.817089	-588.928467	-588.882604	2.166635e+00	1
USDCNY	fGARCH.ALLGARCH	2014-08-05	6.153	6.028594e+02	19.084869	19.194126	19.083063	19.128787	9.797812e+01	1
USDCNY	fGARCH.ALLGARCH	2014-08-06	6.147	2.980786e+01	-588.051008	-587.941750	-588.052813	-588.007090	4.849171e+00	1
USDCNY	fGARCH.ALLGARCH	2014-08-07	6.146	-7.094383e+01	-586.949487	-586.840229	-586.951292	-586.905569	1.154309e+01	1
USDCNY	fGARCH.ALLGARCH	2014-08-11	6.144	2.489838e+01	-587.776345	-587.667088	-587.778151	-587.732427	4.052471e+00	1
USDCNY	fGARCH.ALLGARCH	2014-08-12	6.144	6.297337e+01	-587.294543	-587.185286	-587.296349	-587.250625	1.024957e+01	1
USDCNY	fGARCH.ALLGARCH	2014-08-13	6.142	-2.219940e+01	-590.296221	-590.186964	-590.298027	-590.252303	3.614361e+00	1
USDCNY	fGARCH.ALLGARCH	2014-08-14	6.136	-1.404711e+02	-587.700902	-587.591645	-587.702708	-587.656984	2.289295e+01	1
USDCNY	fGARCH.ALLGARCH	2014-08-17	6.133	5.944981e+02	109.501754	109.611314	109.499935	109.545799	9.693430e+01	1
USDCNY	fGARCH.ALLGARCH	2014-08-19	6.130	-5.155929e+01	-585.152751	-585.043494	-585.154557	-585.108833	8.410978e+00	1
USDCNY	fGARCH.ALLGARCH	2014-08-20	6.130	-1.929233e+02	-586.176906	-586.067649	-586.178711	-586.132988	3.147199e+01	1
USDCNY	fGARCH.ALLGARCH	2014-08-24	6.140	1.671067e+01	-588.414218	-588.304658	-588.416037	-588.370173	2.721608e+00	1
USDCNY	fGARCH.ALLGARCH	2014-08-25	6.142	2.016595e+01	-590.032967	-589.923710	-590.034773	-589.989049	3.283287e+00	1
USDCNY	fGARCH.ALLGARCH	2014-08-26	6.133	-9.193458e+00	-592.028938	-591.919680	-592.030743	-591.985020	1.499015e+00	1
USDCNY	fGARCH.ALLGARCH	2014-08-27	6.132	9.527845e+01	-586.491601	-586.382343	-586.493406	-586.447683	1.553791e+01	1
USDCNY	fGARCH.ALLGARCH	2014-09-03	6.125	-3.275840e+02	13.412488	13.521745	13.410682	13.456406	5.348311e+01	1
USDCNY	fGARCH.ALLGARCH	2014-09-10	6.119	3.412713e+01	-588.214319	-588.105062	-588.216125	-588.170401	5.577240e+00	1
USDCNY	fGARCH.ALLGARCH	2014-09-11	6.120	1.713551e+02	-585.306314	-585.197057	-585.308120	-585.262397	2.799920e+01	1
USDCNY	fGARCH.ALLGARCH	2014-09-14	6.125	-1.143873e+01	-591.115129	-591.005570	-591.116949	-591.071085	1.867548e+00	1
USDCNY	fGARCH.ALLGARCH	2014-09-15	6.132	6.270890e+01	-587.125551	-587.016294	-587.127357	-587.081633	1.022650e+01	1
USDCNY	fGARCH.ALLGARCH	2014-09-17	6.129	1.185828e+01	-590.965879	-590.856622	-590.967685	-590.921961	1.934781e+00	1
USDCNY	fGARCH.ALLGARCH	2014-09-18	6.127	5.849842e+01	-586.243193	-586.133936	-586.244999	-586.199275	9.547645e+00	1
USDCNY	fGARCH.ALLGARCH	2014-09-22	6.128	-7.554483e+01	-585.523762	-585.414505	-585.525568	-585.479844	1.232781e+01	1
USDCNY	fGARCH.ALLGARCH	2014-09-23	6.124	6.743292e+01	-586.611629	-586.502371	-586.613434	-586.567711	1.101125e+01	1
USDCNY	fGARCH.ALLGARCH	2014-09-24	6.125	-1.361419e+02	-583.665628	-583.556371	-583.667434	-583.621710	2.222725e+01	1
USDCNY	fGARCH.ALLGARCH	2014-09-28	6.117	-1.470848e+00	-589.397050	-589.287490	-589.398869	-589.353005	2.404524e-01	1
USDCNY	fGARCH.ALLGARCH	2014-10-02	6.128	-1.655563e+01	-586.788690	-586.679433	-586.790496	-586.744772	2.701636e+00	1
USDCNY	fGARCH.ALLGARCH	2014-10-05	6.129	1.461850e+01	-590.597425	-590.487865	-590.599244	-590.553380	2.385136e+00	1
USDCNY	fGARCH.ALLGARCH	2014-10-07	6.125	-2.893222e+00	-592.477892	-592.368634	-592.479697	-592.433974	4.723629e-01	1
USDCNY	fGARCH.ALLGARCH	2014-10-13	6.113	6.047961e+01	-587.057935	-586.948978	-587.059727	-587.014143	9.893606e+00	1
USDCNY	fGARCH.ALLGARCH	2014-10-15	6.112	-2.322660e+02	-584.723325	-584.614368	-584.725117	-584.679533	3.800164e+01	1
USDCNY	fGARCH.ALLGARCH	2014-10-28	6.103	5.800710e+01	-589.031088	-588.922131	-589.032880	-588.987295	9.504686e+00	1
USDCNY	fGARCH.ALLGARCH	2014-11-04	6.105	-1.520227e+02	-585.103628	-584.994670	-585.105420	-585.059835	2.490134e+01	1
USDCNY	fGARCH.ALLGARCH	2014-11-07	6.102	3.102281e+01	-590.154705	-590.045748	-590.156497	-590.110913	5.084040e+00	1
USDCNY	fGARCH.ALLGARCH	2014-11-10	6.105	-1.387418e+02	-584.273462	-584.164205	-584.275268	-584.229544	2.272592e+01	1
USDCNY	fGARCH.ALLGARCH	2014-11-20	6.109	-4.671149e+01	-588.176614	-588.067656	-588.178406	-588.132821	7.646340e+00	1
USDCNY	fGARCH.ALLGARCH	2014-11-25	6.126	-3.509017e+01	-588.097661	-587.988704	-588.099453	-588.053869	5.728072e+00	1
USDCNY	fGARCH.ALLGARCH	2014-11-27	6.125	-4.766673e+01	-589.227416	-589.118459	-589.229208	-589.183624	7.782323e+00	1
USDCNY	fGARCH.ALLGARCH	2014-12-02	6.137	-3.559250e+01	-586.845104	-586.736147	-586.846896	-586.801311	5.799658e+00	1
USDCNY	fGARCH.ALLGARCH	2014-12-05	6.140	-1.335011e+00	-590.219456	-590.110499	-590.221248	-590.175664	2.174285e-01	1
USDCNY	fGARCH.ALLGARCH	2014-12-18	6.187	2.127975e+01	-591.310725	-591.201768	-591.312518	-591.266933	3.439430e+00	1
USDCNY	fGARCH.ALLGARCH	2014-12-19	6.205	1.828485e+01	-589.889033	-589.780075	-589.890825	-589.845240	2.946793e+00	1
USDCNY	eGARCH	2014-07-10	2.201	2.758887e+00	-4.752441	-4.656841	-4.753830	-4.714013	1.253470e+00	1
USDCNY	gjrGARCH	2014-07-10	2.201	2.894085e+00	-4.702450	-4.606850	-4.703839	-4.664022	1.314895e+00	1
USDCNY	iGARCH	2014-07-10	2.201	2.988228e+00	-4.673441	-4.605156	-4.674157	-4.645993	1.357668e+00	1
USDJPY	fGARCH.APARCH	2013-02-07	93.093	-3.970675e+14	-210.537651	-210.401828	-210.540404	-210.483067	4.265278e+12	1
USDJPY	fGARCH.ALLGARCH	2013-04-08	98.639	2.419383e+10	-45.341071	-45.164015	-45.345691	-45.269908	2.452765e+08	1
USDJPY	fGARCH.ALLGARCH	2013-04-14	97.623	1.365824e+02	9.689241	9.866784	9.684586	9.760608	1.399080e+00	1
USDJPY	fGARCH.ALLGARCH	2013-05-15	101.850	1.719010e+30	-497.287445	-497.124010	-497.291401	-497.221757	1.687786e+28	1
USDJPY	fGARCH.ALLGARCH	2013-06-19	96.211	-8.650911e+03	78.994799	79.117376	78.992542	79.044066	8.991603e+01	1
USDJPY	eGARCH	2013-03-19	94.770	2.936350e+60	155.742660	155.919716	155.738040	155.813823	3.098396e+58	1
USDJPY	eGARCH	2013-04-14	97.623	-5.344121e+15	115.987973	116.138202	115.984609	116.048361	5.474244e+13	1
USDJPY	apARCH	2013-03-15	95.160	-1.758223e+61	315.688639	315.824835	315.685866	315.743379	1.847649e+59	1
USDJPY	apARCH	2013-04-04	95.817	6.156224e+02	8.903971	9.094646	8.898637	8.980607	6.424981e+00	1
USDJPY	apARCH	2013-04-17	97.640	-4.147166e+22	-1334.100214	-1333.950398	-1334.103553	-1334.039999	4.247405e+20	1

6.4.2.4 : Table summary

6.4.2 Selected Models

## selected models' filtered lowest price.
lp <- united.fx2 %>% 
  separate(Type, c('Cur', 'Type')) %>% 
  dplyr::filter(Type == 'Lo') %>% dplyr::select(-Cur, -Type)

acc <- lp %>% 
  ddply(.(.id, Model), summarise, 
        MSE = mean((Price.T1 - Price)^2), 
        n = length(Price), 
        AIC.MSE = (-2*MSE)/n+2*4/n, 
        MSE.AIC = mean((Akaike - mean(Akaike))^2),
        Akaike = mean(Akaike), 
        Bayes = mean(Bayes), 
        Shibata = mean(Shibata), 
        Hannan.Quinn = mean(Hannan.Quinn)) %>% 
  tbl_df %>% mutate(MSE = round(MSE, 7))

Low Price Summary : Selected Models

.id	Model	MSE	n	AIC.MSE	MSE.AIC	Akaike	Bayes	Shibata	Hannan.Quinn
USD/AUD
USDAUD	sGARCH	3.000000e-07	559	1.431130e-02	1.635410e-01	-7.474533	-7.395006	-7.475542	-7.442566
USDAUD	fGARCH.GARCH	3.000000e-07	559	1.431130e-02	1.636406e-01	-7.474507	-7.394980	-7.475517	-7.442540
USDAUD	fGARCH.TGARCH	2.400000e-06	559	1.431130e-02	8.492932e-01	-7.196383	-7.103202	-7.197746	-7.158928
USDAUD	fGARCH.NGARCH	3.845000e-03	559	1.429750e-02	1.452705e+04	-38.783691	-38.690511	-38.785054	-38.746236
USDAUD	fGARCH.NAGARCH	6.000000e-07	559	1.431130e-02	1.863712e-01	-7.474842	-7.381661	-7.476204	-7.437387
USDAUD	fGARCH.GJRGARCH	1.200000e-06	559	1.431130e-02	1.843323e-01	-7.468833	-7.375653	-7.470196	-7.431378
USDAUD	gjrGARCH	1.200000e-06	559	1.431130e-02	1.851478e-01	-7.473855	-7.380674	-7.475218	-7.436400
USDAUD	iGARCH	1.200000e-06	559	1.431130e-02	1.800006e-01	-7.472048	-7.406174	-7.472758	-7.445569
USDAUD	csGARCH	6.000000e-07	559	1.431130e-02	1.809284e-01	-7.453969	-7.347135	-7.455738	-7.411026
USD/CAD
USDEUR	sGARCH	2.000000e-07	559	1.431130e-02	3.130009e-01	-8.483968	-8.402594	-8.485037	-8.451259
USDEUR	fGARCH.GARCH	2.000000e-07	559	1.431130e-02	3.132199e-01	-8.483714	-8.402340	-8.484783	-8.451005
USDEUR	fGARCH.TGARCH	7.000000e-07	559	1.431130e-02	5.616512e-01	-8.289653	-8.194626	-8.291083	-8.251456
USDEUR	fGARCH.NGARCH	3.480575e+33	559	-1.245286e+31	1.389143e+04	-31.662079	-31.567052	-31.663509	-31.623882
USDEUR	fGARCH.NAGARCH	2.000000e-07	559	1.431130e-02	1.216795e+02	-8.027114	-7.932086	-8.028543	-7.988917
USDEUR	fGARCH.GJRGARCH	2.000000e-07	559	1.431130e-02	3.127732e-01	-8.488332	-8.393304	-8.489761	-8.450135
USDEUR	gjrGARCH	2.000000e-07	559	1.431130e-02	3.145620e-01	-8.503633	-8.408605	-8.505062	-8.465435
USDEUR	iGARCH	2.000000e-07	559	1.431130e-02	3.095536e-01	-8.481167	-8.413446	-8.481930	-8.453946
USDEUR	csGARCH	2.000000e-07	559	1.431130e-02	3.063827e-01	-8.462086	-8.353405	-8.463929	-8.418401
USD/CHF
USDGBP	sGARCH	0.000000e+00	559	1.431130e-02	8.946890e-02	-9.161118	-9.082595	-9.162118	-9.129556
USDGBP	fGARCH.GARCH	2.000000e-07	559	1.431130e-02	9.100420e-02	-9.158372	-9.079849	-9.159371	-9.126810
USDGBP	fGARCH.TGARCH	2.148452e+144	559	-7.686770e+141	2.497319e+02	-8.248833	-8.156670	-8.250181	-8.211788
USDGBP	fGARCH.NGARCH	4.480000e-05	559	1.431110e-02	1.304970e+03	-11.631014	-11.538851	-11.632362	-11.593970
USDGBP	fGARCH.NAGARCH	0.000000e+00	559	1.431130e-02	1.958370e+01	-8.978418	-8.886255	-8.979766	-8.941373
USDGBP	fGARCH.GJRGARCH	0.000000e+00	559	1.431130e-02	9.174750e-02	-9.172810	-9.080647	-9.174158	-9.135766
USDGBP	gjrGARCH	0.000000e+00	559	1.431130e-02	9.343310e-02	-9.182518	-9.090355	-9.183865	-9.145473
USDGBP	iGARCH	1.000000e-07	559	1.431130e-02	9.246110e-02	-9.157658	-9.092774	-9.158362	-9.131578
USDGBP	csGARCH	1.000000e-07	559	1.431130e-02	8.889350e-02	-9.139872	-9.034069	-9.141621	-9.097345
USD/CNY
USDCHF	sGARCH	2.144000e-04	559	1.431050e-02	3.752016e-01	-7.774831	-7.694935	-7.775843	-7.742716
USDCHF	fGARCH.GARCH	2.144000e-04	559	1.431050e-02	3.749116e-01	-7.774567	-7.694670	-7.775579	-7.742451
USDCHF	fGARCH.TGARCH	1.983000e-04	559	1.431060e-02	2.708022e-01	-7.708955	-7.615403	-7.710322	-7.671351
USDCHF	fGARCH.NGARCH	1.423492e+01	559	-3.661870e-02	1.359109e+03	-9.977072	-9.883520	-9.978439	-9.939467
USDCHF	fGARCH.NAGARCH	2.094000e-04	559	1.431050e-02	3.677811e-01	-7.797744	-7.704192	-7.799111	-7.760140
USDCHF	fGARCH.GJRGARCH	2.105000e-04	559	1.431050e-02	3.267764e-01	-7.802842	-7.709290	-7.804209	-7.765237
USDCHF	gjrGARCH	2.099000e-04	559	1.431050e-02	3.288728e-01	-7.819683	-7.726131	-7.821050	-7.782079
USDCHF	iGARCH	1.074700e-03	559	1.430740e-02	7.945705e-01	-7.544803	-7.478562	-7.545514	-7.518176
USDCHF	csGARCH	5.459000e-04	559	1.430930e-02	5.454560e-01	-7.668232	-7.561024	-7.670007	-7.625138
USD/EUR
USDCAD	sGARCH	2.000000e-07	559	1.431130e-02	1.916711e-01	-8.088370	-8.013856	-8.089250	-8.058418
USDCAD	fGARCH.GARCH	2.000000e-07	559	1.431130e-02	1.918087e-01	-8.088324	-8.013809	-8.089204	-8.058372
USDCAD	fGARCH.TGARCH	9.000000e-07	559	1.431130e-02	5.853322e-01	-7.839604	-7.751436	-7.840818	-7.804164
USDCAD	fGARCH.NGARCH	2.000000e-06	559	1.431130e-02	4.591249e+03	-14.552735	-14.464567	-14.553949	-14.517295
USDCAD	fGARCH.NAGARCH	1.000000e-07	559	1.431130e-02	1.924688e-01	-8.099150	-8.010982	-8.100364	-8.063710
USDCAD	fGARCH.GJRGARCH	1.000000e-07	559	1.431130e-02	1.918669e-01	-8.089459	-8.001291	-8.090673	-8.054019
USDCAD	gjrGARCH	1.000000e-07	559	1.431130e-02	1.920297e-01	-8.095753	-8.007585	-8.096967	-8.060313
USDCAD	iGARCH	4.000000e-07	559	1.431130e-02	1.919475e-01	-8.088169	-8.027308	-8.088769	-8.063705
USDCAD	csGARCH	2.000000e-07	559	1.431130e-02	1.907060e-01	-8.072317	-7.970495	-8.073917	-8.031388
USD/GBP
USDCNY	sGARCH	2.262900e-03	559	1.430320e-02	3.480297e+00	-6.119973	-6.035698	-6.121100	-6.086099
USDCNY	fGARCH.GARCH	1.389700e-03	559	1.430630e-02	3.485897e+00	-6.119032	-6.034756	-6.120159	-6.085157
USDCNY	fGARCH.TGARCH	3.759400e-03	559	1.429780e-02	3.134419e+00	-6.069236	-5.971318	-6.070735	-6.029878
USDCNY	fGARCH.NGARCH	7.743124e+02	559	-2.756037e+00	2.084163e+04	-44.814337	-44.716419	-44.815836	-44.774979
USDCNY	fGARCH.NAGARCH	1.306003e+03	559	-4.658330e+00	1.045896e+02	-5.276130	-5.178212	-5.277628	-5.236771
USDCNY	fGARCH.GJRGARCH	7.771340e-02	559	1.403320e-02	2.347145e+01	-5.865308	-5.767390	-5.866807	-5.825950
USDCNY	gjrGARCH	2.022800e-03	559	1.430400e-02	3.419189e+00	-6.150783	-6.052865	-6.152281	-6.111424
USDCNY	iGARCH	2.897400e-03	559	1.430090e-02	3.806027e+00	-6.006029	-5.935396	-6.006838	-5.977638
USDCNY	csGARCH	2.429700e-03	559	1.430260e-02	3.951922e+00	-6.038950	-5.927390	-6.040872	-5.994108
USD/JPY
USDJPY	sGARCH	1.185130e-02	559	1.426890e-02	1.932612e-01	1.505986	1.592135	1.504786	1.540614
USDJPY	fGARCH.GARCH	1.135080e-02	559	1.427070e-02	1.928677e-01	1.506372	1.592520	1.505171	1.540999
USDJPY	fGARCH.TGARCH	1.251800e-02	559	1.426650e-02	2.640584e-01	1.532982	1.632773	1.531404	1.573093
USDJPY	fGARCH.NGARCH	1.698360e-02	559	1.425050e-02	6.624668e+03	-11.603252	-11.503462	-11.604831	-11.563142
USDJPY	fGARCH.NAGARCH	8.457900e-03	559	1.428100e-02	2.019745e-01	1.480656	1.580447	1.479078	1.520767
USDJPY	fGARCH.GJRGARCH	1.166140e-02	559	1.426950e-02	1.977772e-01	1.500435	1.600226	1.498857	1.540546
USDJPY	gjrGARCH	9.850400e-03	559	1.427600e-02	2.015961e-01	1.494715	1.594506	1.493136	1.534826
USDJPY	iGARCH	1.079900e-02	559	1.427260e-02	1.960169e-01	1.504274	1.576780	1.503399	1.533418
USDJPY	csGARCH	2.392930e-02	559	1.422570e-02	1.855740e-01	1.516742	1.630175	1.514733	1.562337

6.4.2.1A : Table summary

Low Price Summary : Selected Models

Model	MSE	n	AIC.MSE	MSE.AIC	Akaike	Bayes	Shibata	Hannan.Quinn
sGARCH	2.047000e-03	3913	2.043400e-03	12.16584	-6.513830	-6.433221	-6.514872	-6.481428
fGARCH.GARCH	1.850800e-03	3913	2.043500e-03	12.16547	-6.513163	-6.432555	-6.514206	-6.480762
fGARCH.TGARCH	3.069217e+143	3913	-1.568728e+140	47.10154	-6.259955	-6.165698	-6.261354	-6.222067
fGARCH.NGARCH	4.972251e+32	3913	-2.541401e+29	9205.66142	-23.289169	-23.194912	-23.290569	-23.251282
fGARCH.NAGARCH	1.865731e+02	3913	-9.331620e-02	46.48641	-6.310392	-6.216134	-6.311791	-6.272504
fGARCH.GJRGARCH	1.279810e-02	3913	2.037900e-03	15.06350	-6.483879	-6.389621	-6.485278	-6.445991
gjrGARCH	1.726400e-03	3913	2.043600e-03	12.17306	-6.533073	-6.438816	-6.534472	-6.495186
iGARCH	2.110400e-03	3913	2.043400e-03	12.20295	-6.463657	-6.396697	-6.464396	-6.436742
csGARCH	3.843700e-03	3913	2.042500e-03	12.21308	-6.474098	-6.366192	-6.475907	-6.430724

6.4.2.1B : Table summary

Low Price Summary : Selected Models

Model	n
sGARCH	1
fGARCH.GARCH	1
fGARCH.TGARCH	2
fGARCH.NGARCH	38
fGARCH.NAGARCH	7
fGARCH.GJRGARCH	2
gjrGARCH	1
iGARCH	6
csGARCH	3

6.4.2.1C : Table summary

Hi-Lo Price Summary : Selected Models

.id	Model	Date	Price	Price.T1	Akaike	Bayes	Shibata	Hannan.Quinn	diff	se
USDAUD	fGARCH.NGARCH	2013-06-27	1.077	2.542027e+00	-590.320340	-590.197426	-590.322615	-590.270933	2.360285e+00	1
USDEUR	fGARCH.NGARCH	2015-03-02	0.890	-4.015994e+07	83.346290	83.510176	83.342305	83.412167	4.512353e+07	1
USDEUR	fGARCH.NGARCH	2015-06-04	0.887	-1.394863e+18	-545.380537	-545.244340	-545.383310	-545.325796	1.572562e+18	1
USDEUR	fGARCH.NGARCH	2015-06-24	0.891	1.892803e+10	77.586765	77.722962	77.583992	77.641506	2.124358e+10	1
USDGBP	fGARCH.TGARCH	2014-06-19	0.586	-3.465523e+73	364.832355	365.037213	364.826216	364.914701	5.913861e+73	1
USDGBP	fGARCH.NGARCH	2014-06-19	0.586	4.316118e-01	-160.018385	-159.813528	-160.024525	-159.936039	7.365389e-01	1
USDCHF	sGARCH	2015-01-16	0.850	1.189676e+00	-6.687989	-6.606271	-6.689007	-6.655145	1.399619e+00	1
USDCHF	fGARCH.GARCH	2015-01-16	0.850	1.189676e+00	-6.687989	-6.606271	-6.689007	-6.655145	1.399619e+00	1
USDCHF	fGARCH.TGARCH	2015-01-16	0.850	1.182560e+00	-6.882116	-6.786779	-6.883495	-6.843798	1.391247e+00	1
USDCHF	fGARCH.NGARCH	2015-01-16	0.850	1.182556e+00	-6.811955	-6.716617	-6.813334	-6.773637	1.391243e+00	1
USDCHF	fGARCH.NGARCH	2015-09-07	0.970	-8.823318e+01	-587.029347	-586.920390	-587.031140	-586.985555	9.096204e+01	1
USDCHF	fGARCH.NAGARCH	2015-01-16	0.850	1.188451e+00	-6.758750	-6.663413	-6.760129	-6.720432	1.398178e+00	1
USDCHF	fGARCH.GJRGARCH	2015-01-16	0.850	1.189203e+00	-6.775060	-6.679723	-6.776439	-6.736742	1.399062e+00	1
USDCHF	gjrGARCH	2015-01-16	0.850	1.187461e+00	-6.834457	-6.739119	-6.835835	-6.796138	1.397013e+00	1
USDCHF	iGARCH	2015-01-16	0.850	1.189656e+00	-6.696311	-6.628212	-6.697021	-6.668940	1.399595e+00	1
USDCHF	iGARCH	2015-01-20	0.869	1.169574e+00	-6.632037	-6.563939	-6.632748	-6.604667	1.345885e+00	1
USDCHF	iGARCH	2015-01-21	0.851	5.536845e-01	-6.599117	-6.531019	-6.599827	-6.571747	6.506281e-01	1
USDCHF	iGARCH	2015-01-22	0.853	1.132264e+00	-6.569994	-6.501896	-6.570705	-6.542624	1.327390e+00	1
USDCHF	iGARCH	2015-01-27	0.894	6.896106e-01	-6.470927	-6.402829	-6.471637	-6.443557	7.713765e-01	1
USDCHF	iGARCH	2015-02-02	0.920	7.319616e-01	-6.350835	-6.255235	-6.352225	-6.312407	7.956105e-01	1
USDCHF	csGARCH	2015-01-16	0.850	1.193636e+00	-6.688153	-6.579196	-6.689945	-6.644361	1.404278e+00	1
USDCHF	csGARCH	2015-01-22	0.853	1.141360e+00	-6.534724	-6.425767	-6.536516	-6.490932	1.338054e+00	1
USDCHF	csGARCH	2015-01-23	0.868	6.200740e-01	-6.493151	-6.384194	-6.494943	-6.449359	7.143710e-01	1
USDCNY	fGARCH.NGARCH	2014-07-17	6.192	-5.016306e+02	-585.712986	-585.631043	-585.714011	-585.680047	8.101269e+01	1
USDCNY	fGARCH.NGARCH	2014-07-20	6.195	1.194381e+01	-589.430373	-589.348203	-589.431406	-589.397340	1.927975e+00	1
USDCNY	fGARCH.NGARCH	2014-07-22	6.189	1.945038e+01	-591.466725	-591.384782	-591.467750	-591.433786	3.142734e+00	1
USDCNY	fGARCH.NGARCH	2014-07-23	6.182	-3.637318e+01	-588.553531	-588.471588	-588.554557	-588.520593	5.883724e+00	1
USDCNY	fGARCH.NGARCH	2014-07-27	6.176	4.872521e+01	-587.187420	-587.105250	-587.188453	-587.154387	7.889444e+00	1
USDCNY	fGARCH.NGARCH	2014-07-31	6.163	2.769268e+01	-590.455881	-590.373938	-590.456907	-590.422943	4.493377e+00	1
USDCNY	fGARCH.NGARCH	2014-08-03	6.168	3.201427e+01	-587.733648	-587.651478	-587.734681	-587.700615	5.190381e+00	1
USDCNY	fGARCH.NGARCH	2014-08-05	6.153	1.853196e+01	-589.664961	-589.583018	-589.665987	-589.632023	3.011858e+00	1
USDCNY	fGARCH.NGARCH	2014-08-06	6.147	2.635122e+01	-591.728569	-591.646626	-591.729595	-591.695631	4.286842e+00	1
USDCNY	fGARCH.NGARCH	2014-08-12	6.144	4.740305e+01	-587.300349	-587.218406	-587.301374	-587.267410	7.715340e+00	1
USDCNY	fGARCH.NGARCH	2014-08-13	6.142	8.825968e+00	-589.224653	-589.142710	-589.225679	-589.191715	1.436986e+00	1
USDCNY	fGARCH.NGARCH	2014-08-14	6.136	4.872331e+01	-586.351874	-586.269931	-586.352899	-586.318935	7.940565e+00	1
USDCNY	fGARCH.NGARCH	2014-08-19	6.130	-1.240483e+01	-590.789977	-590.708034	-590.791003	-590.757039	2.023627e+00	1
USDCNY	fGARCH.NGARCH	2014-08-20	6.130	9.161532e+00	-592.227353	-592.145410	-592.228379	-592.194415	1.494540e+00	1
USDCNY	fGARCH.NGARCH	2014-08-21	6.141	-1.525661e+01	-590.144127	-590.062184	-590.145153	-590.111189	2.484385e+00	1
USDCNY	fGARCH.NGARCH	2014-08-24	6.140	-3.247607e+01	-589.174302	-589.092132	-589.175335	-589.141269	5.289262e+00	1
USDCNY	fGARCH.NGARCH	2014-08-25	6.142	6.174800e+01	-572.956479	-572.874536	-572.957505	-572.923541	1.005340e+01	1
USDCNY	fGARCH.NGARCH	2014-08-26	6.133	9.738678e+01	-587.251542	-587.169599	-587.252568	-587.218604	1.587914e+01	1
USDCNY	fGARCH.NGARCH	2014-08-31	6.129	2.545583e+02	-584.923023	-584.840853	-584.924056	-584.889989	4.153341e+01	1
USDCNY	fGARCH.NGARCH	2014-09-01	6.132	1.596999e+02	-584.161053	-584.079110	-584.162079	-584.128115	2.604369e+01	1
USDCNY	fGARCH.NGARCH	2014-09-02	6.131	-1.989882e+01	-589.399865	-589.317922	-589.400891	-589.366927	3.245608e+00	1
USDCNY	fGARCH.NGARCH	2014-09-04	6.128	-2.866168e+01	-585.515480	-585.433537	-585.516505	-585.482541	4.677168e+00	1
USDCNY	fGARCH.NGARCH	2014-09-08	6.122	-2.517129e+01	-587.872377	-587.790434	-587.873402	-587.839438	4.111612e+00	1
USDCNY	fGARCH.NGARCH	2014-09-11	6.120	1.708482e+01	-588.380157	-588.298214	-588.381183	-588.347219	2.791637e+00	1
USDCNY	fGARCH.NGARCH	2014-09-14	6.125	-7.626137e+01	-589.072288	-588.990119	-589.073322	-589.039255	1.245084e+01	1
USDCNY	fGARCH.NGARCH	2014-09-16	6.129	-1.759094e+02	-585.597533	-585.515590	-585.598558	-585.564594	2.870116e+01	1
USDCNY	fGARCH.NGARCH	2014-10-01	6.128	-1.146657e+02	-584.091459	-584.009516	-584.092485	-584.058521	1.871177e+01	1
USDCNY	fGARCH.NGARCH	2014-10-06	6.129	-2.283202e+01	-579.908511	-579.826568	-579.909537	-579.875573	3.725243e+00	1
USDCNY	fGARCH.NGARCH	2014-10-07	6.125	5.146397e+01	-565.845084	-565.763141	-565.846110	-565.812146	8.402281e+00	1
USDCNY	fGARCH.NGARCH	2014-10-09	6.120	6.182692e+01	-583.758544	-583.676826	-583.759562	-583.725700	1.010244e+01	1
USDCNY	fGARCH.NGARCH	2014-11-26	6.123	6.187566e+01	-583.601907	-583.520189	-583.602924	-583.569062	1.010545e+01	1
USDCNY	fGARCH.NAGARCH	2014-07-24	6.182	-3.603032e+02	14.561667	14.643610	14.560642	14.594606	5.828262e+01	1
USDCNY	fGARCH.NAGARCH	2014-07-31	6.163	-3.531901e+02	14.522470	14.604413	14.521444	14.555409	5.730814e+01	1
USDCNY	fGARCH.NAGARCH	2014-08-04	6.161	-3.492923e+02	14.548440	14.630382	14.547414	14.581378	5.669409e+01	1
USDCNY	fGARCH.NAGARCH	2014-08-26	6.133	4.865151e+00	104.667516	104.749459	104.666490	104.700454	7.932742e-01	1
USDCNY	fGARCH.NAGARCH	2014-09-04	6.128	4.796821e+02	172.167572	172.249515	172.166546	172.200510	7.827710e+01	1
USDCNY	fGARCH.NAGARCH	2014-10-19	6.113	-3.344848e+02	98.972743	99.054686	98.971717	99.005682	5.471696e+01	1
USDCNY	fGARCH.GJRGARCH	2014-09-01	6.132	1.263740e+01	98.054293	98.136236	98.053267	98.087231	2.060893e+00	1

6.4.2.2C : Table summary

## selected models' filtered lowest price.
lp <- united.fx3 %>% 
  separate(Type, c('Cur', 'Type')) %>% 
  dplyr::filter(Type == 'Lo') %>% dplyr::select(-Cur, -Type)

acc <- lp %>% 
  ddply(.(.id, Model), summarise, 
        MSE = mean((Price.T1 - Price)^2), 
        n = length(Price), 
        AIC.MSE = (-2*MSE)/n+2*4/n, 
        MSE.AIC = mean((Akaike - mean(Akaike))^2),
        Akaike = mean(Akaike), 
        Bayes = mean(Bayes), 
        Shibata = mean(Shibata), 
        Hannan.Quinn = mean(Hannan.Quinn)) %>% 
  tbl_df %>% mutate(MSE = round(MSE, 7))

Low Price Summary : Selected Models

.id	Model	MSE	n	AIC.MSE	MSE.AIC	Akaike	Bayes	Shibata	Hannan.Quinn
USD/AUD
USDAUD	sGARCH	0.0000003	491	0.0162933	1.722268e-01	-7.454446	-7.376306	-7.455413	-7.423037
USDAUD	fGARCH.GARCH	0.0000003	491	0.0162933	1.723236e-01	-7.454391	-7.376252	-7.455359	-7.422982
USDAUD	fGARCH.TGARCH	0.0000024	491	0.0162933	8.201947e-01	-7.181306	-7.089512	-7.182621	-7.144408
USDAUD	fGARCH.NGARCH	0.0000023	491	0.0162933	1.446018e+04	-40.027862	-39.936069	-40.029178	-39.990965
USDAUD	fGARCH.NAGARCH	0.0000006	491	0.0162933	1.975007e-01	-7.453909	-7.362116	-7.455224	-7.417012
USDAUD	fGARCH.GJRGARCH	0.0000013	491	0.0162933	1.954784e-01	-7.448052	-7.356258	-7.449367	-7.411154
USDAUD	gjrGARCH	0.0000013	491	0.0162933	1.964635e-01	-7.453334	-7.361541	-7.454649	-7.416437
USDAUD	iGARCH	0.0000013	491	0.0162933	1.909102e-01	-7.451504	-7.387018	-7.452177	-7.425583
USDAUD	csGARCH	0.0000007	491	0.0162933	1.917685e-01	-7.433320	-7.327873	-7.435036	-7.390934
USD/CAD
USDEUR	sGARCH	0.0000002	491	0.0162933	2.885522e-01	-8.422893	-8.341787	-8.423955	-8.390292
USDEUR	fGARCH.GARCH	0.0000002	491	0.0162933	2.889996e-01	-8.422751	-8.341645	-8.423813	-8.390150
USDEUR	fGARCH.TGARCH	0.0000007	491	0.0162933	5.458800e-01	-8.219329	-8.124569	-8.220750	-8.181239
USDEUR	fGARCH.NGARCH	0.0000069	491	0.0162933	1.386109e+04	-31.692109	-31.597350	-31.693530	-31.654020
USDEUR	fGARCH.NAGARCH	0.0000002	491	0.0162933	1.383656e+02	-7.901946	-7.807187	-7.903367	-7.863856
USDEUR	fGARCH.GJRGARCH	0.0000002	491	0.0162933	2.891723e-01	-8.427903	-8.333143	-8.429324	-8.389813
USDEUR	gjrGARCH	0.0000002	491	0.0162933	2.928362e-01	-8.444487	-8.349728	-8.445908	-8.406398
USDEUR	iGARCH	0.0000002	491	0.0162933	2.848900e-01	-8.419966	-8.352513	-8.420722	-8.392853
USDEUR	csGARCH	0.0000002	491	0.0162933	2.830434e-01	-8.401744	-8.293331	-8.403577	-8.358166
USD/CHF
USDGBP	sGARCH	0.0000000	491	0.0162933	7.918720e-02	-9.124748	-9.047831	-9.125698	-9.093831
USDGBP	fGARCH.GARCH	0.0000000	491	0.0162933	7.909750e-02	-9.124591	-9.047674	-9.125541	-9.093674
USDGBP	fGARCH.TGARCH	0.0000001	491	0.0162933	2.573198e-01	-8.893814	-8.803258	-8.895106	-8.857415
USDGBP	fGARCH.NGARCH	0.0000001	491	0.0162933	7.431681e+02	-10.447655	-10.357100	-10.448948	-10.411257
USDGBP	fGARCH.NAGARCH	0.0000000	491	0.0162933	2.223452e+01	-8.922798	-8.832242	-8.924091	-8.886400
USDGBP	fGARCH.GJRGARCH	0.0000000	491	0.0162933	8.257130e-02	-9.137255	-9.046700	-9.138547	-9.100857
USDGBP	gjrGARCH	0.0000000	491	0.0162933	8.464210e-02	-9.146972	-9.056416	-9.148264	-9.110574
USDGBP	iGARCH	0.0000001	491	0.0162933	8.043700e-02	-9.123571	-9.060293	-9.124232	-9.098137
USDGBP	csGARCH	0.0000000	491	0.0162933	7.926350e-02	-9.104345	-9.000151	-9.106033	-9.062465
USD/CNY
USDCHF	sGARCH	0.0000086	491	0.0162932	3.649843e-01	-7.726845	-7.646838	-7.727861	-7.694685
USDCHF	fGARCH.GARCH	0.0000086	491	0.0162932	3.647996e-01	-7.726647	-7.646639	-7.727662	-7.694487
USDCHF	fGARCH.TGARCH	0.0000005	491	0.0162933	2.568613e-01	-7.662339	-7.568675	-7.663710	-7.624689
USDCHF	fGARCH.NGARCH	0.0000071	491	0.0162933	8.678039e+02	-9.050322	-8.956658	-9.051693	-9.012673
USDCHF	fGARCH.NAGARCH	0.0000049	491	0.0162933	3.610822e-01	-7.750900	-7.657236	-7.752271	-7.713251
USDCHF	fGARCH.GJRGARCH	0.0000051	491	0.0162933	3.152371e-01	-7.757147	-7.663483	-7.758517	-7.719497
USDCHF	gjrGARCH	0.0000067	491	0.0162933	3.192749e-01	-7.775321	-7.681658	-7.776692	-7.737672
USDCHF	iGARCH	0.0003072	491	0.0162920	7.840631e-01	-7.491929	-7.425577	-7.492642	-7.465258
USDCHF	csGARCH	0.0000860	491	0.0162929	5.089767e-01	-7.631578	-7.524258	-7.633357	-7.588439
USD/EUR
USDCAD	sGARCH	0.0000001	491	0.0162933	2.032738e-01	-8.071944	-7.998259	-8.072798	-8.042326
USDCAD	fGARCH.GARCH	0.0000001	491	0.0162933	2.034299e-01	-8.071875	-7.998190	-8.072729	-8.042256
USDCAD	fGARCH.TGARCH	0.0000010	491	0.0162933	6.279643e-01	-7.821265	-7.733927	-7.822450	-7.786159
USDCAD	fGARCH.NGARCH	0.0000023	491	0.0162933	5.199091e+03	-15.694333	-15.606994	-15.695518	-15.659226
USDCAD	fGARCH.NAGARCH	0.0000001	491	0.0162933	2.038450e-01	-8.081793	-7.994454	-8.082977	-8.046686
USDCAD	fGARCH.GJRGARCH	0.0000001	491	0.0162933	2.035175e-01	-8.072978	-7.985639	-8.074162	-8.037871
USDCAD	gjrGARCH	0.0000001	491	0.0162933	2.039111e-01	-8.079681	-7.992343	-8.080866	-8.044575
USDCAD	iGARCH	0.0000004	491	0.0162933	2.036891e-01	-8.071687	-8.011655	-8.072264	-8.047557
USDCAD	csGARCH	0.0000002	491	0.0162933	2.021647e-01	-8.055589	-7.954597	-8.057158	-8.014994
USD/GBP
USDCNY	sGARCH	0.0022528	491	0.0162841	2.837319e+00	-6.387828	-6.302360	-6.388986	-6.353474
USDCNY	fGARCH.GARCH	0.0012758	491	0.0162881	2.829914e+00	-6.388514	-6.303046	-6.389671	-6.354160
USDCNY	fGARCH.TGARCH	0.0040670	491	0.0162767	2.788954e+00	-6.300241	-6.201131	-6.301774	-6.260403
USDCNY	fGARCH.NGARCH	0.5682675	491	0.0139785	2.764060e+03	-11.206343	-11.107233	-11.207877	-11.166506
USDCNY	fGARCH.NAGARCH	0.0008103	491	0.0162900	3.755623e+00	-6.345910	-6.246801	-6.347444	-6.306073
USDCNY	fGARCH.GJRGARCH	0.0018437	491	0.0162858	3.465342e+00	-6.316938	-6.217828	-6.318471	-6.277101
USDCNY	gjrGARCH	0.0019677	491	0.0162853	2.780578e+00	-6.417910	-6.318800	-6.419443	-6.378073
USDCNY	iGARCH	0.0024755	491	0.0162832	3.290245e+00	-6.264464	-6.192638	-6.265299	-6.235594
USDCNY	csGARCH	0.0025062	491	0.0162831	3.393031e+00	-6.297882	-6.185130	-6.299844	-6.252562
USD/JPY
USDJPY	sGARCH	0.0132002	491	0.0162395	1.923823e-01	1.542755	1.629687	1.541530	1.577697
USDJPY	fGARCH.GARCH	0.0126304	491	0.0162418	1.919074e-01	1.543187	1.630120	1.541962	1.578130
USDJPY	fGARCH.TGARCH	0.0139181	491	0.0162366	2.705567e-01	1.571968	1.672542	1.570362	1.612393
USDJPY	fGARCH.NGARCH	0.0189553	491	0.0162161	6.671006e+03	-11.474251	-11.373677	-11.475857	-11.433825
USDJPY	fGARCH.NAGARCH	0.0093116	491	0.0162553	2.020801e-01	1.517982	1.618556	1.516376	1.558408
USDJPY	fGARCH.GJRGARCH	0.0127913	491	0.0162412	1.971678e-01	1.537435	1.638008	1.535829	1.577860
USDJPY	gjrGARCH	0.0108716	491	0.0162490	2.009046e-01	1.532255	1.632829	1.530649	1.572681
USDJPY	iGARCH	0.0120062	491	0.0162444	1.952260e-01	1.541357	1.614647	1.540460	1.570816
USDJPY	csGARCH	0.0269816	491	0.0161834	1.838755e-01	1.553839	1.668055	1.551800	1.599748

6.4.2.2A : Table summary

Low Price Summary : Selected Models

Model	MSE	n	AIC.MSE	MSE.AIC	Akaike	Bayes	Shibata	Hannan.Quinn
sGARCH	0.0022089	3437	0.0023263	12.04390	-6.520850	-6.440528	-6.521883	-6.488564
fGARCH.GARCH	0.0019879	3437	0.0023265	12.04350	-6.520797	-6.440475	-6.521830	-6.488511
fGARCH.TGARCH	0.0025700	3437	0.0023261	11.83866	-6.358046	-6.264076	-6.359436	-6.320274
fGARCH.NGARCH	0.0838916	3437	0.0022788	6495.49238	-18.513268	-18.419297	-18.514657	-18.475496
fGARCH.NAGARCH	0.0014468	3437	0.0023268	34.62847	-6.419896	-6.325926	-6.421285	-6.382124
fGARCH.GJRGARCH	0.0020917	3437	0.0023264	12.14366	-6.517548	-6.423578	-6.518937	-6.479776
gjrGARCH	0.0018354	3437	0.0023265	12.05843	-6.540779	-6.446808	-6.542168	-6.503006
iGARCH	0.0021130	3437	0.0023264	12.09578	-6.468823	-6.402150	-6.469554	-6.442024
csGARCH	0.0042250	3437	0.0023252	12.10222	-6.481517	-6.373898	-6.483315	-6.438259

6.4.2.2B : Table summary

Low Price Summary : Selected Models

Model	n

6.4.2.2C : Table summary

Hi-Lo Price Summary : Selected Models

.id	Model	Date	Price	Price.T1	Akaike	Bayes	Shibata	Hannan.Quinn	diff	se

6.4.2.2D : Table summary

6.5 Close Price

6.5.1 All Models

## filtered bias closing price.
cp <- fx %>% separate(Type, c('Cur', 'Type')) %>% 
  dplyr::filter(Type == 'Cl') %>% 
  dplyr::select(-Cur, -Type)

ntmID <- cp %>% dplyr::filter(se == 1) %>% .$Date %>% unlist %>% sort

acc <- cp %>% dplyr::filter(!Date %in% ntmID & Date %in% ntimeID2) %>% 
  ddply(.(.id, Model), summarise, 
        MSE = mean((Price.T1 - Price)^2), 
        n = length(Price), 
        AIC.MSE = (-2*MSE)/n+2*4/n, 
        MSE.AIC = mean((Akaike - mean(Akaike))^2),
        Akaike = mean(Akaike), 
        Bayes = mean(Bayes), 
        Shibata = mean(Shibata), 
        Hannan.Quinn = mean(Hannan.Quinn)) %>% 
  tbl_df %>% mutate(MSE = round(MSE, 7))

Close Price Summary : All Models

.id	Model	MSE	n	AIC.MSE	MSE.AIC	Akaike	Bayes	Shibata	Hannan.Quinn
USD/AUD
USDAUD	sGARCH	0.0000008	553	0.0144665	1.567179e-01	-7.286875	-7.205357	-7.287939	-7.254108
USDAUD	fGARCH.GARCH	0.0000008	553	0.0144665	1.566690e-01	-7.287138	-7.205620	-7.288203	-7.254371
USDAUD	fGARCH.TGARCH	0.0000031	553	0.0144665	4.730421e-01	-7.096140	-7.000968	-7.097565	-7.057885
USDAUD	fGARCH.AVGARCH	0.0000001	54	0.1481481	4.757932e+00	-7.310062	-7.196754	-7.312065	-7.264516
USDAUD	fGARCH.NGARCH	0.0000126	553	0.0144665	1.135465e+04	-26.069613	-25.974441	-26.071038	-26.031357
USDAUD	fGARCH.NAGARCH	0.0000007	553	0.0144665	1.074984e+02	-6.856085	-6.760913	-6.857510	-6.817830
USDAUD	fGARCH.APARCH	0.0000002	358	0.0223464	2.116513e-01	-7.294250	-7.187617	-7.296025	-7.251386
USDAUD	fGARCH.GJRGARCH	0.0000007	553	0.0144665	1.594684e-01	-7.291695	-7.196523	-7.293120	-7.253439
USDAUD	fGARCH.ALLGARCH	0.0000010	270	0.0296296	1.260653e+03	-9.685524	-9.557883	-9.688039	-9.634217
USDAUD	eGARCH	0.0000012	502	0.0159363	6.292965e+00	-7.241758	-7.146059	-7.243200	-7.203291
USDAUD	gjrGARCH	0.0000007	553	0.0144665	1.625273e-01	-7.299096	-7.203924	-7.300521	-7.260840
USDAUD	apARCH	0.0000004	91	0.0879121	3.435700e-03	-7.756226	-7.637790	-7.758416	-7.708618
USDAUD	iGARCH	0.0000008	553	0.0144665	1.560441e-01	-7.291631	-7.223766	-7.292388	-7.264352
USDAUD	csGARCH	0.0000011	553	0.0144665	1.594027e-01	-7.270102	-7.161276	-7.271941	-7.226358
USD/CAD
USDEUR	sGARCH	0.0000004	553	0.0144665	3.417287e-01	-8.263680	-8.180259	-8.264786	-8.230148
USDEUR	fGARCH.GARCH	0.0000004	553	0.0144665	3.413142e-01	-8.263324	-8.179902	-8.264429	-8.229791
USDEUR	fGARCH.TGARCH	0.0000014	553	0.0144665	5.919376e-01	-8.147051	-8.049976	-8.148524	-8.108030
USDEUR	fGARCH.AVGARCH	0.0000000	28	0.2857143	2.975550e-02	-8.033852	-7.933416	-8.035424	-7.993481
USDEUR	fGARCH.NGARCH	0.0000024	553	0.0144665	9.208649e+03	-23.364972	-23.267897	-23.366446	-23.325952
USDEUR	fGARCH.NAGARCH	0.0000003	553	0.0144665	3.498244e-01	-8.279410	-8.182334	-8.280883	-8.240389
USDEUR	fGARCH.APARCH	0.0000001	128	0.0625000	3.344379e-01	-8.186082	-8.078174	-8.187903	-8.142707
USDEUR	fGARCH.GJRGARCH	0.0000003	553	0.0144665	3.501579e-01	-8.279866	-8.182791	-8.281340	-8.240845
USDEUR	fGARCH.ALLGARCH	0.0000005	384	0.0208333	2.676551e+03	-13.096552	-12.970125	-13.099000	-13.045732
USDEUR	eGARCH	0.0000010	504	0.0158730	8.123404e-01	-8.336544	-8.238081	-8.338059	-8.296966
USDEUR	gjrGARCH	0.0000004	553	0.0144665	3.546392e-01	-8.291377	-8.194302	-8.292851	-8.252357
USDEUR	apARCH	0.0000000	91	0.0879121	4.361000e-04	-8.097933	-7.998424	-8.099460	-8.057934
USDEUR	iGARCH	0.0000011	553	0.0144665	3.456698e-01	-8.262433	-8.192664	-8.263223	-8.234388
USDEUR	csGARCH	0.0000011	553	0.0144665	3.364927e-01	-8.246527	-8.135798	-8.248421	-8.202018
USD/CHF
USDGBP	sGARCH	0.0000002	553	0.0144665	1.126069e-01	-8.979091	-8.899689	-8.980119	-8.947176
USDGBP	fGARCH.GARCH	0.0000002	553	0.0144665	1.122041e-01	-8.979613	-8.900211	-8.980641	-8.947698
USDGBP	fGARCH.TGARCH	0.0000002	553	0.0144665	3.222083e-01	-8.747429	-8.654388	-8.748809	-8.710031
USDGBP	fGARCH.AVGARCH	0.0000000	36	0.2222222	1.055895e-01	-8.932965	-8.835728	-8.934416	-8.893883
USDGBP	fGARCH.NGARCH	0.0000010	553	0.0144665	6.609267e+03	-19.283441	-19.190399	-19.284820	-19.246043
USDGBP	fGARCH.NAGARCH	0.0000000	553	0.0144665	9.012670e-01	-8.957831	-8.864790	-8.959211	-8.920433
USDGBP	fGARCH.APARCH	0.0000008	359	0.0222841	2.293561e+03	-13.935971	-13.828655	-13.937787	-13.892835
USDGBP	fGARCH.GJRGARCH	0.0000000	553	0.0144665	1.177579e-01	-8.996964	-8.903922	-8.998344	-8.959566
USDGBP	fGARCH.ALLGARCH	0.0000001	386	0.0207254	1.434259e+03	-11.428115	-11.306083	-11.430430	-11.379064
USDGBP	eGARCH	0.0000001	501	0.0159681	1.052970e+02	-8.525935	-8.432049	-8.527342	-8.488198
USDGBP	gjrGARCH	0.0000001	553	0.0144665	1.239441e-01	-9.010310	-8.917269	-9.011690	-8.972913
USDGBP	apARCH	0.0000001	91	0.0879121	5.975900e-03	-9.070118	-8.971632	-9.071609	-9.030534
USDGBP	iGARCH	0.0000001	553	0.0144665	1.115696e-01	-8.981865	-8.916104	-8.982595	-8.955433
USDGBP	csGARCH	0.0000001	553	0.0144665	1.111786e-01	-8.960961	-8.854279	-8.962745	-8.918080
USD/CNY
USDCHF	sGARCH	0.0000037	553	0.0144665	4.816688e-01	-7.473136	-7.390007	-7.474246	-7.439721
USDCHF	fGARCH.GARCH	0.0000038	553	0.0144665	4.822807e-01	-7.473833	-7.390704	-7.474943	-7.440418
USDCHF	fGARCH.TGARCH	0.0000015	553	0.0144665	4.099288e-01	-7.535677	-7.438892	-7.537154	-7.496773
USDCHF	fGARCH.AVGARCH	0.0000004	16	0.4999999	6.610170e-02	-7.644302	-7.533805	-7.646256	-7.599879
USDCHF	fGARCH.NGARCH	0.0000025	553	0.0144665	1.404618e+04	-32.013940	-31.917155	-32.015417	-31.975036
USDCHF	fGARCH.NAGARCH	0.0000018	553	0.0144665	5.104681e+01	-6.817336	-6.720551	-6.818813	-6.778431
USDCHF	fGARCH.APARCH	0.0000077	357	0.0224089	7.408595e+03	-20.790589	-20.676082	-20.792635	-20.744560
USDCHF	fGARCH.GJRGARCH	0.0000025	553	0.0144665	4.521690e-01	-7.525262	-7.428477	-7.526738	-7.486357
USDCHF	fGARCH.ALLGARCH	0.0000039	382	0.0209424	6.193374e+03	-18.652755	-18.524589	-18.655288	-18.601235
USDCHF	eGARCH	0.0000006	504	0.0158730	3.702664e-01	-7.629485	-7.532671	-7.630966	-7.590569
USDCHF	gjrGARCH	0.0000023	553	0.0144665	4.519408e-01	-7.546989	-7.450204	-7.548466	-7.508085
USDCHF	apARCH	0.0000000	90	0.0888889	1.756000e-03	-7.795836	-7.695101	-7.797412	-7.755342
USDCHF	iGARCH	0.0000038	553	0.0144665	5.365865e-01	-7.451428	-7.381955	-7.452224	-7.423502
USDCHF	csGARCH	0.0000037	553	0.0144665	4.889091e-01	-7.457156	-7.346715	-7.459053	-7.412762
USD/EUR
USDCAD	sGARCH	0.0000003	553	0.0144665	1.978004e-01	-7.989967	-7.909208	-7.991016	-7.957505
USDCAD	fGARCH.GARCH	0.0000002	553	0.0144665	1.979657e-01	-7.989644	-7.908886	-7.990693	-7.957182
USDCAD	fGARCH.TGARCH	0.0000011	553	0.0144665	6.055084e-01	-7.772578	-7.678166	-7.773985	-7.734628
USDCAD	fGARCH.AVGARCH	0.0000001	42	0.1904762	4.624600e-02	-8.215936	-8.105061	-8.217839	-8.171368
USDCAD	fGARCH.NGARCH	0.0000041	553	0.0144665	1.053751e+04	-26.885457	-26.791045	-26.886864	-26.847507
USDCAD	fGARCH.NAGARCH	0.0000002	553	0.0144665	1.971210e-01	-7.998770	-7.904358	-8.000177	-7.960820
USDCAD	fGARCH.APARCH	0.0000003	356	0.0224719	1.431639e+03	-10.407152	-10.300263	-10.408928	-10.364185
USDCAD	fGARCH.GJRGARCH	0.0000002	553	0.0144665	2.013034e-01	-7.997480	-7.903068	-7.998888	-7.959530
USDCAD	fGARCH.ALLGARCH	0.0000019	384	0.0208333	5.671003e+03	-17.540233	-17.419102	-17.542489	-17.491542
USDCAD	eGARCH	0.0000003	498	0.0160643	1.532768e-01	-8.033433	-7.940467	-8.034792	-7.996065
USDCAD	gjrGARCH	0.0000003	553	0.0144665	2.000689e-01	-8.004257	-7.909845	-8.005664	-7.966307
USDCAD	apARCH	0.0000001	90	0.0888889	3.178200e-03	-8.321156	-8.210370	-8.323060	-8.276623
USDCAD	iGARCH	0.0000003	553	0.0144665	2.004687e-01	-7.988559	-7.921453	-7.989304	-7.961585
USDCAD	csGARCH	0.0000003	553	0.0144665	1.954402e-01	-7.974476	-7.866411	-7.976294	-7.931038
USD/GBP
USDCNY	sGARCH	0.0000083	553	0.0144665	2.007894e-01	-6.942489	-6.853278	-6.943742	-6.906630
USDCNY	fGARCH.GARCH	0.0000080	553	0.0144665	2.004679e-01	-6.942925	-6.853714	-6.944178	-6.907067
USDCNY	fGARCH.TGARCH	0.0000094	553	0.0144665	7.885634e-01	-6.719408	-6.616554	-6.721051	-6.678066
USDCNY	fGARCH.AVGARCH	0.0000035	12	0.6666661	3.877637e-01	-6.447781	-6.312844	-6.450517	-6.393549
USDCNY	fGARCH.NGARCH	0.0000189	553	0.0144665	1.230313e+03	-9.088979	-8.986126	-9.090623	-9.047637
USDCNY	fGARCH.NAGARCH	0.0000080	553	0.0144665	2.145262e-01	-6.957386	-6.854533	-6.959030	-6.916044
USDCNY	fGARCH.APARCH	0.0000209	356	0.0224718	6.375401e+03	-17.165553	-17.042353	-17.167869	-17.116032
USDCNY	fGARCH.GJRGARCH	0.0000070	553	0.0144665	2.110097e-01	-6.968106	-6.865252	-6.969749	-6.926764
USDCNY	fGARCH.ALLGARCH	0.0000095	384	0.0208333	9.088425e+02	-8.580385	-8.445461	-8.583148	-8.526152
USDCNY	eGARCH	0.0000077	501	0.0159680	2.411853e-01	-6.969939	-6.866549	-6.971602	-6.928382
USDCNY	gjrGARCH	0.0000070	553	0.0144665	1.894521e-01	-6.997001	-6.894148	-6.998644	-6.955659
USDCNY	apARCH	0.0000386	91	0.0879112	1.961479e+04	-21.371607	-21.241391	-21.374175	-21.319270
USDCNY	iGARCH	0.0000090	553	0.0144665	2.121893e-01	-6.930118	-6.854550	-6.931034	-6.899744
USDCNY	csGARCH	0.0000067	553	0.0144665	2.182596e-01	-6.958826	-6.842330	-6.960912	-6.912000
USD/JPY
USDJPY	sGARCH	0.0094092	553	0.0144325	1.720671e-01	1.733870	1.820897	1.732643	1.768851
USDJPY	fGARCH.GARCH	0.0093819	553	0.0144326	1.719134e-01	1.734063	1.821090	1.732836	1.769043
USDJPY	fGARCH.TGARCH	0.0064246	553	0.0144433	1.860764e-01	1.738223	1.838892	1.736614	1.778687
USDJPY	fGARCH.AVGARCH	0.0285310	42	0.1891176	1.650240e-02	1.153284	1.290785	1.150376	1.208549
USDJPY	fGARCH.NGARCH	0.0287785	553	0.0143625	9.671653e+03	-17.541130	-17.440461	-17.542738	-17.500666
USDJPY	fGARCH.NAGARCH	0.0058205	553	0.0144455	1.830371e-01	1.721374	1.822043	1.719765	1.761838
USDJPY	fGARCH.APARCH	0.0654349	132	0.0596146	7.904110e+03	-12.857489	-12.733954	-12.859886	-12.807837
USDJPY	fGARCH.GJRGARCH	0.0065264	553	0.0144429	1.783273e-01	1.730190	1.830860	1.728582	1.770654
USDJPY	fGARCH.ALLGARCH	1.3908392	205	0.0254552	1.043499e+04	-17.705769	-17.582823	-17.708125	-17.656351
USDJPY	eGARCH	0.0143896	502	0.0158789	3.204675e-01	1.771894	1.873705	1.770249	1.812816
USDJPY	gjrGARCH	0.0055060	553	0.0144466	1.862176e-01	1.718959	1.819629	1.717351	1.759423
USDJPY	apARCH	0.0470226	90	0.0878439	5.974878e+04	-44.064156	-43.935970	-44.066738	-44.012635
USDJPY	iGARCH	0.0096980	553	0.0144315	1.742472e-01	1.730081	1.803465	1.729182	1.759577
USDJPY	csGARCH	0.0092224	553	0.0144332	1.692324e-01	1.739656	1.853968	1.737613	1.785603

6.5.1.1 : Table summary

Close Price Summary : All Models

Model	MSE	n	AIC.MSE	MSE.AIC	Akaike	Bayes	Shibata	Hannan.Quinn
sGARCH	0.0013461	3871	0.0020660	11.81224	-6.457338	-6.373843	-6.458458	-6.423777
fGARCH.GARCH	0.0013422	3871	0.0020660	11.81299	-6.457488	-6.373992	-6.458607	-6.423926
fGARCH.TGARCH	0.0009202	3871	0.0020662	11.69890	-6.325723	-6.228579	-6.327211	-6.286675
fGARCH.AVGARCH	0.0052103	230	0.0347373	13.80301	-6.250398	-6.136266	-6.252444	-6.204522
fGARCH.NGARCH	0.0041172	3871	0.0020645	8999.24883	-22.035362	-21.938218	-22.036849	-21.996314
fGARCH.NAGARCH	0.0008331	3871	0.0020662	34.23002	-6.306492	-6.209348	-6.307980	-6.267444
fGARCH.APARCH	0.0042268	2046	0.0039059	3585.39221	-13.488507	-13.376283	-13.490474	-13.443397
fGARCH.GJRGARCH	0.0009339	3871	0.0020662	11.84919	-6.475598	-6.378453	-6.477085	-6.436550
fGARCH.ALLGARCH	0.1190515	2395	0.0032409	3752.97241	-13.712222	-13.585874	-13.714682	-13.661435
eGARCH	0.0020584	3512	0.0022767	27.66288	-6.422789	-6.325208	-6.424290	-6.383565
gjrGARCH	0.0007881	3871	0.0020662	11.85352	-6.490010	-6.392866	-6.491498	-6.450963
apARCH	0.0066808	634	0.0125972	11455.88297	-15.188058	-15.075726	-15.190035	-15.142906
iGARCH	0.0013876	3871	0.0020659	11.80779	-6.453708	-6.383861	-6.454512	-6.425632
csGARCH	0.0013193	3871	0.0020660	11.79309	-6.446913	-6.336120	-6.448822	-6.402379

6.5.1.2 : Table summary

Close Price Summary : All Models

Model	n
fGARCH.GARCH	1
fGARCH.NGARCH	6
fGARCH.APARCH	1
fGARCH.ALLGARCH	1
eGARCH	2
apARCH	1
iGARCH	1

6.5.1.3 : Table summary

Hi-Lo Price Summary : Selected Models

.id	Model	Date	Price	Price.T1	Akaike	Bayes	Shibata	Hannan.Quinn	diff	se
USDAUD	fGARCH.NGARCH	2013-08-04	1.12290	9.147871e+10	192.68901	192.79857	192.68720	192.73306	8.146648e+10	1
USDAUD	iGARCH	2014-10-15	1.13730	2.310843e+145	738.69906	738.80802	738.69727	738.74286	2.031868e+145	1
USDEUR	fGARCH.GARCH	2017-06-18	0.89220	6.667688e+68	356.68044	356.81701	356.67764	356.73533	7.473311e+68	1
USDEUR	fGARCH.APARCH	2014-10-14	0.79120	5.384163e+80	-406.95173	-406.81554	-406.95451	-406.89699	6.805059e+80	1
USDGBP	fGARCH.NGARCH	2014-03-31	0.60001	-1.642110e+04	-444.66156	-444.52499	-444.66436	-444.60667	2.736805e+04	1
USDGBP	fGARCH.NGARCH	2014-05-01	0.59188	9.637298e-01	-516.05113	-515.91456	-516.05393	-515.99623	1.628252e+00	1
USDGBP	fGARCH.NGARCH	2015-04-16	0.67016	1.865748e+15	-556.64744	-556.51124	-556.65021	-556.59270	2.784033e+15	1
USDGBP	fGARCH.NGARCH	2016-07-19	0.76287	-6.365327e+09	114.89850	115.03432	114.89575	114.95308	8.343921e+09	1
USDCHF	eGARCH	2014-08-28	0.91504	-3.241158e+02	62.34954	62.47246	62.34727	62.39895	3.542094e+02	1
USDCAD	fGARCH.NGARCH	2015-02-09	1.25170	-7.979335e+22	142.67377	142.78303	142.67197	142.71769	6.374798e+22	1
USDCAD	eGARCH	2016-02-11	1.39230	-2.425122e+125	65.72627	65.86284	65.72348	65.78117	1.741810e+125	1
USDJPY	fGARCH.ALLGARCH	2013-05-15	102.25800	6.921087e+61	309.37842	309.55547	309.37380	309.44958	6.768259e+59	1
USDJPY	apARCH	2013-05-15	102.25800	-4.614626e+04	12.69839	12.86183	12.69444	12.76408	4.512728e+02	1

6.5.1.4 : Table summary

6.5.2 Selected Models

## selected models' filtered closing price.
cp <- united.fx2 %>% 
  separate(Type, c('Cur', 'Type')) %>% 
  dplyr::filter(Type == 'Cl') %>% dplyr::select(-Cur, -Type)

acc <- cp %>% 
  ddply(.(.id, Model), summarise, 
        MSE = mean((Price.T1 - Price)^2), 
        n = length(Price), 
        AIC.MSE = (-2*MSE)/n+2*4/n, 
        MSE.AIC = mean((Akaike - mean(Akaike))^2),
        Akaike = mean(Akaike), 
        Bayes = mean(Bayes), 
        Shibata = mean(Shibata), 
        Hannan.Quinn = mean(Hannan.Quinn)) %>% 
  tbl_df %>% mutate(MSE = round(MSE, 7))

Close Price Summary : Selected Models

.id	Model	MSE	n	AIC.MSE	MSE.AIC	Akaike	Bayes	Shibata	Hannan.Quinn
USD/AUD
USDAUD	sGARCH	8.000000e-07	559	1.431130e-02	1.559246e-01	-7.288436	-7.206816	-7.289503	-7.255628
USDAUD	fGARCH.GARCH	8.000000e-07	559	1.431130e-02	1.558753e-01	-7.288696	-7.207077	-7.289763	-7.255888
USDAUD	fGARCH.TGARCH	3.100000e-06	559	1.431130e-02	4.728300e-01	-7.096628	-7.001354	-7.098056	-7.058331
USDAUD	fGARCH.NGARCH	1.250000e-05	559	1.431120e-02	1.123648e+04	-25.869362	-25.774089	-25.870790	-25.831066
USDAUD	fGARCH.NAGARCH	7.000000e-07	559	1.431130e-02	1.063490e+02	-6.862443	-6.767169	-6.863871	-6.824147
USDAUD	fGARCH.GJRGARCH	7.000000e-07	559	1.431130e-02	1.586611e-01	-7.293262	-7.197989	-7.294690	-7.254965
USDAUD	gjrGARCH	7.000000e-07	559	1.431130e-02	1.617046e-01	-7.300716	-7.205443	-7.302145	-7.262420
USDAUD	iGARCH	9.552767e+287	559	-3.417806e+285	9.939089e+02	-5.958293	-5.890326	-5.959052	-5.930973
USDAUD	csGARCH	1.100000e-06	559	1.431130e-02	1.586346e-01	-7.271781	-7.162854	-7.273623	-7.227996
USD/CAD
USDEUR	sGARCH	4.000000e-07	559	1.431130e-02	3.413732e-01	-8.267597	-8.184167	-8.268702	-8.234061
USDEUR	fGARCH.GARCH	4.000000e-07	559	1.431130e-02	3.409632e-01	-8.267238	-8.183808	-8.268342	-8.233702
USDEUR	fGARCH.TGARCH	1.300000e-06	559	1.431130e-02	5.897902e-01	-8.152291	-8.055208	-8.153764	-8.113267
USDEUR	fGARCH.NGARCH	2.400000e-06	559	1.431130e-02	9.112117e+03	-23.206788	-23.109706	-23.208262	-23.167765
USDEUR	fGARCH.NAGARCH	3.000000e-07	559	1.431130e-02	3.493310e-01	-8.283230	-8.186147	-8.284703	-8.244206
USDEUR	fGARCH.GJRGARCH	3.000000e-07	559	1.431130e-02	3.496629e-01	-8.283745	-8.186662	-8.285219	-8.244722
USDEUR	gjrGARCH	4.000000e-07	559	1.431130e-02	3.540859e-01	-8.295254	-8.198171	-8.296727	-8.256230
USDEUR	iGARCH	1.100000e-06	559	1.431130e-02	3.453162e-01	-8.266395	-8.196619	-8.267186	-8.238348
USDEUR	csGARCH	1.100000e-06	559	1.431130e-02	3.362058e-01	-8.250495	-8.139759	-8.252390	-8.205984
USD/CHF
USDGBP	sGARCH	2.000000e-07	559	1.431130e-02	1.127189e-01	-8.981649	-8.902148	-8.982680	-8.949694
USDGBP	fGARCH.GARCH	2.000000e-07	559	1.431130e-02	1.123181e-01	-8.982166	-8.902665	-8.983196	-8.950210
USDGBP	fGARCH.TGARCH	2.000000e-07	559	1.431130e-02	3.222055e-01	-8.751631	-8.658490	-8.753013	-8.714193
USDGBP	fGARCH.NGARCH	6.227218e+27	559	-2.227985e+25	7.390982e+03	-20.793321	-20.700180	-20.794704	-20.755883
USDGBP	fGARCH.NAGARCH	0.000000e+00	559	1.431130e-02	8.933084e-01	-8.960998	-8.867857	-8.962381	-8.923561
USDGBP	fGARCH.GJRGARCH	0.000000e+00	559	1.431130e-02	1.179164e-01	-8.999605	-8.906464	-9.000987	-8.962167
USDGBP	gjrGARCH	1.000000e-07	559	1.431130e-02	1.241116e-01	-9.012987	-8.919847	-9.014370	-8.975550
USDGBP	iGARCH	1.000000e-07	559	1.431130e-02	1.116974e-01	-8.984394	-8.918532	-8.985125	-8.957921
USDGBP	csGARCH	1.000000e-07	559	1.431130e-02	1.113388e-01	-8.963484	-8.856703	-8.965272	-8.920564
USD/CNY
USDCHF	sGARCH	3.600000e-06	559	1.431130e-02	4.833457e-01	-7.474117	-7.391001	-7.475226	-7.440707
USDCHF	fGARCH.GARCH	3.800000e-06	559	1.431130e-02	4.839503e-01	-7.474806	-7.391691	-7.475915	-7.441396
USDCHF	fGARCH.TGARCH	1.500000e-06	559	1.431130e-02	4.096568e-01	-7.537571	-7.440799	-7.539047	-7.498672
USDCHF	fGARCH.NGARCH	2.500000e-06	559	1.431130e-02	1.390160e+04	-31.754870	-31.658099	-31.756346	-31.715971
USDCHF	fGARCH.NAGARCH	1.800000e-06	559	1.431130e-02	5.051191e+01	-6.827660	-6.730889	-6.829136	-6.788761
USDCHF	fGARCH.GJRGARCH	2.500000e-06	559	1.431130e-02	4.534221e-01	-7.526291	-7.429520	-7.527768	-7.487393
USDCHF	gjrGARCH	2.200000e-06	559	1.431130e-02	4.533756e-01	-7.547867	-7.451096	-7.549344	-7.508969
USDCHF	iGARCH	3.800000e-06	559	1.431130e-02	5.381170e-01	-7.452484	-7.383024	-7.453279	-7.424564
USDCHF	csGARCH	3.600000e-06	559	1.431130e-02	4.904606e-01	-7.458188	-7.347761	-7.460085	-7.413800
USD/EUR
USDCAD	sGARCH	3.000000e-07	559	1.431130e-02	1.966726e-01	-7.991148	-7.910425	-7.992195	-7.958700
USDCAD	fGARCH.GARCH	2.000000e-07	559	1.431130e-02	1.968368e-01	-7.990829	-7.910107	-7.991876	-7.958381
USDCAD	fGARCH.TGARCH	1.100000e-06	559	1.431130e-02	6.003772e-01	-7.775149	-7.680773	-7.776554	-7.737213
USDCAD	fGARCH.NGARCH	1.138994e+43	559	-4.075114e+40	1.047875e+04	-26.414670	-26.320295	-26.416076	-26.376735
USDCAD	fGARCH.NAGARCH	2.000000e-07	559	1.431130e-02	1.959558e-01	-8.000013	-7.905637	-8.001418	-7.962077
USDCAD	fGARCH.GJRGARCH	2.000000e-07	559	1.431130e-02	2.001156e-01	-7.998766	-7.904391	-8.000172	-7.960831
USDCAD	gjrGARCH	3.000000e-07	559	1.431130e-02	1.989161e-01	-8.005552	-7.911176	-8.006957	-7.967616
USDCAD	iGARCH	3.000000e-07	559	1.431130e-02	1.992656e-01	-7.989905	-7.922836	-7.990649	-7.962946
USDCAD	csGARCH	3.000000e-07	559	1.431130e-02	1.942810e-01	-7.975787	-7.867758	-7.977604	-7.932364
USD/GBP
USDCNY	sGARCH	8.300000e-06	559	1.431120e-02	2.005993e-01	-6.944040	-6.854835	-6.945293	-6.908184
USDCNY	fGARCH.GARCH	8.100000e-06	559	1.431120e-02	2.004410e-01	-6.944340	-6.855135	-6.945593	-6.908484
USDCNY	fGARCH.TGARCH	9.400000e-06	559	1.431120e-02	7.839599e-01	-6.722028	-6.619180	-6.723671	-6.680688
USDCNY	fGARCH.NGARCH	1.880000e-05	559	1.431120e-02	1.217151e+03	-9.067536	-8.964689	-9.069180	-9.026197
USDCNY	fGARCH.NAGARCH	8.100000e-06	559	1.431120e-02	2.141826e-01	-6.958927	-6.856080	-6.960570	-6.917587
USDCNY	fGARCH.GJRGARCH	7.000000e-06	559	1.431120e-02	2.106660e-01	-6.969452	-6.866604	-6.971095	-6.928112
USDCNY	gjrGARCH	6.900000e-06	559	1.431120e-02	1.894846e-01	-6.998676	-6.895829	-7.000319	-6.957336
USDCNY	iGARCH	8.900000e-06	559	1.431120e-02	2.121785e-01	-6.932317	-6.856755	-6.933233	-6.901945
USDCNY	csGARCH	6.800000e-06	559	1.431120e-02	2.179735e-01	-6.960187	-6.843697	-6.962273	-6.913364
USD/JPY
USDJPY	sGARCH	9.465900e-03	559	1.427740e-02	1.721053e-01	1.731319	1.818461	1.730089	1.766346
USDJPY	fGARCH.GARCH	9.324200e-03	559	1.427790e-02	1.719392e-01	1.731538	1.818680	1.730308	1.766564
USDJPY	fGARCH.TGARCH	6.421400e-03	559	1.428830e-02	1.861072e-01	1.735527	1.836312	1.733916	1.776037
USDJPY	fGARCH.NGARCH	2.850280e-02	559	1.420930e-02	9.571683e+03	-17.337027	-17.236243	-17.338639	-17.296517
USDJPY	fGARCH.NAGARCH	5.789800e-03	559	1.429060e-02	1.830579e-01	1.718799	1.819584	1.717188	1.759310
USDJPY	fGARCH.GJRGARCH	6.495300e-03	559	1.428800e-02	1.783422e-01	1.727660	1.828444	1.726048	1.768170
USDJPY	gjrGARCH	5.510200e-03	559	1.429160e-02	1.863184e-01	1.716339	1.817123	1.714727	1.756849
USDJPY	iGARCH	9.626200e-03	559	1.427680e-02	1.742753e-01	1.727553	1.801052	1.726651	1.757095
USDJPY	csGARCH	9.167800e-03	559	1.427850e-02	1.692019e-01	1.737118	1.851544	1.735071	1.783111

6.5.2.1A : Table summary

Close Price Summary : Selected Models

Model	MSE	n	AIC.MSE	MSE.AIC	Akaike	Bayes	Shibata	Hannan.Quinn
sGARCH	1.354200e-03	3913	2.043800e-03	11.81143	-6.459381	-6.375847	-6.460501	-6.425804
fGARCH.GARCH	1.334000e-03	3913	2.043800e-03	11.81223	-6.459505	-6.375972	-6.460625	-6.425928
fGARCH.TGARCH	9.197000e-04	3913	2.044000e-03	11.69868	-6.328538	-6.231356	-6.330027	-6.289475
fGARCH.NGARCH	1.627135e+42	3913	-8.316559e+38	9032.89397	-22.063368	-21.966186	-22.064857	-22.024305
fGARCH.NAGARCH	8.287000e-04	3913	2.044000e-03	33.99004	-6.310639	-6.213457	-6.312127	-6.271576
fGARCH.GJRGARCH	9.294000e-04	3913	2.044000e-03	11.84838	-6.477637	-6.380455	-6.479126	-6.438574
gjrGARCH	7.887000e-04	3913	2.044100e-03	11.85262	-6.492102	-6.394920	-6.493591	-6.453039
iGARCH	1.364681e+287	3913	-6.975114e+283	153.67088	-6.265177	-6.195292	-6.265982	-6.237086
csGARCH	1.311500e-03	3913	2.043800e-03	11.79235	-6.448972	-6.338141	-6.450882	-6.404423

6.5.2.1B : Table summary

Close Price Summary : Selected Models

Model	n
fGARCH.NGARCH	3
iGARCH	1

6.5.2.1C : Table summary

Hi-Lo Price Summary : Selected Models

.id	Model	Date	Price	Price.T1	Akaike	Bayes	Shibata	Hannan.Quinn	diff	se
USDAUD	iGARCH	2014-10-15	1.13730	2.310843e+145	738.6991	738.8080	738.6973	738.7429	2.031868e+145	1
USDGBP	fGARCH.NGARCH	2014-03-31	0.60001	-1.642110e+04	-444.6616	-444.5250	-444.6644	-444.6067	2.736805e+04	1
USDGBP	fGARCH.NGARCH	2015-04-16	0.67016	1.865748e+15	-556.6474	-556.5112	-556.6502	-556.5927	2.784033e+15	1
USDCAD	fGARCH.NGARCH	2015-02-09	1.25170	-7.979335e+22	142.6738	142.7830	142.6720	142.7177	6.374798e+22	1

6.5.2.1D : Table summary

## selected models' filtered closing price.
cp <- united.fx3 %>% 
  separate(Type, c('Cur', 'Type')) %>% 
  dplyr::filter(Type == 'Cl') %>% dplyr::select(-Cur, -Type)

acc <- cp %>% 
  ddply(.(.id, Model), summarise, 
        MSE = mean((Price.T1 - Price)^2), 
        n = length(Price), 
        AIC.MSE = (-2*MSE)/n+2*4/n, 
        MSE.AIC = mean((Akaike - mean(Akaike))^2),
        Akaike = mean(Akaike), 
        Bayes = mean(Bayes), 
        Shibata = mean(Shibata), 
        Hannan.Quinn = mean(Hannan.Quinn)) %>% 
  tbl_df %>% mutate(MSE = round(MSE, 7))

Close Price Summary : Selected Models

.id	Model	MSE	n	AIC.MSE	MSE.AIC	Akaike	Bayes	Shibata	Hannan.Quinn
USD/AUD
USDAUD	sGARCH	0.0000007	491	0.0162933	1.637223e-01	-7.267723	-7.186867	-7.268767	-7.235222
USDAUD	fGARCH.GARCH	0.0000007	491	0.0162933	1.636806e-01	-7.267993	-7.187136	-7.269036	-7.235492
USDAUD	fGARCH.TGARCH	0.0000033	491	0.0162933	5.066926e-01	-7.071543	-6.977034	-7.072945	-7.033554
USDAUD	fGARCH.NGARCH	0.0000140	491	0.0162932	1.206057e+04	-27.390783	-27.296274	-27.392185	-27.352794
USDAUD	fGARCH.NAGARCH	0.0000006	491	0.0162933	1.210123e+02	-6.780957	-6.686447	-6.782358	-6.742967
USDAUD	fGARCH.GJRGARCH	0.0000007	491	0.0162933	1.665672e-01	-7.272389	-7.177879	-7.273791	-7.234400
USDAUD	gjrGARCH	0.0000007	491	0.0162933	1.698828e-01	-7.279745	-7.185235	-7.281147	-7.241756
USDAUD	iGARCH	0.0000008	491	0.0162933	1.634940e-01	-7.273318	-7.206115	-7.274057	-7.246305
USDAUD	csGARCH	0.0000010	491	0.0162933	1.665662e-01	-7.250420	-7.142257	-7.252233	-7.206942
USD/CAD
USDEUR	sGARCH	0.0000004	491	0.0162933	3.076462e-01	-8.200212	-8.117323	-8.201301	-8.166894
USDEUR	fGARCH.GARCH	0.0000004	491	0.0162933	3.078625e-01	-8.200262	-8.117373	-8.201351	-8.166944
USDEUR	fGARCH.TGARCH	0.0000006	491	0.0162933	5.534120e-01	-8.084657	-7.988115	-8.086113	-8.045851
USDEUR	fGARCH.NGARCH	0.0000026	491	0.0162933	1.034092e+04	-25.213270	-25.116727	-25.214725	-25.174463
USDEUR	fGARCH.NAGARCH	0.0000003	491	0.0162933	3.189047e-01	-8.217590	-8.121048	-8.219046	-8.178784
USDEUR	fGARCH.GJRGARCH	0.0000003	491	0.0162933	3.195550e-01	-8.218246	-8.121703	-8.219701	-8.179440
USDEUR	gjrGARCH	0.0000003	491	0.0162933	3.266021e-01	-8.231193	-8.134651	-8.232648	-8.192387
USDEUR	iGARCH	0.0000004	491	0.0162933	3.122231e-01	-8.201838	-8.132603	-8.202614	-8.174008
USDEUR	csGARCH	0.0000004	491	0.0162933	3.035363e-01	-8.186240	-8.076044	-8.188114	-8.141945
USD/CHF
USDGBP	sGARCH	0.0000002	491	0.0162933	1.004156e-01	-8.940852	-8.862125	-8.941861	-8.909208
USDGBP	fGARCH.GARCH	0.0000002	491	0.0162933	1.000421e-01	-8.941460	-8.862734	-8.942469	-8.909817
USDGBP	fGARCH.TGARCH	0.0000001	491	0.0162933	2.945567e-01	-8.715839	-8.623474	-8.717197	-8.678713
USDGBP	fGARCH.NGARCH	0.0000011	491	0.0162933	6.755534e+03	-19.368150	-19.275785	-19.369509	-19.331025
USDGBP	fGARCH.NAGARCH	0.0000000	491	0.0162933	9.851031e-01	-8.914671	-8.822305	-8.916029	-8.877545
USDGBP	fGARCH.GJRGARCH	0.0000000	491	0.0162933	1.061723e-01	-8.958759	-8.866393	-8.960117	-8.921633
USDGBP	gjrGARCH	0.0000001	491	0.0162933	1.124518e-01	-8.971597	-8.879232	-8.972955	-8.934471
USDGBP	iGARCH	0.0000000	491	0.0162933	9.969730e-02	-8.944033	-8.878945	-8.944746	-8.917871
USDGBP	csGARCH	0.0000001	491	0.0162933	9.923350e-02	-8.922918	-8.816914	-8.924679	-8.880311
USD/CNY
USDCHF	sGARCH	0.0000039	491	0.0162933	4.474730e-01	-7.429201	-7.346922	-7.430282	-7.396127
USDCHF	fGARCH.GARCH	0.0000041	491	0.0162933	4.484460e-01	-7.430015	-7.347736	-7.431096	-7.396941
USDCHF	fGARCH.TGARCH	0.0000016	491	0.0162933	3.909388e-01	-7.489543	-7.393608	-7.490989	-7.450980
USDCHF	fGARCH.NGARCH	0.0000027	491	0.0162933	1.475722e+04	-32.815922	-32.719987	-32.817368	-32.777360
USDCHF	fGARCH.NAGARCH	0.0000019	491	0.0162933	5.718066e+01	-6.702690	-6.606755	-6.704136	-6.664127
USDCHF	fGARCH.GJRGARCH	0.0000024	491	0.0162933	4.235669e-01	-7.480131	-7.384196	-7.481577	-7.441568
USDCHF	gjrGARCH	0.0000024	491	0.0162933	4.304650e-01	-7.499152	-7.403217	-7.500598	-7.460589
USDCHF	iGARCH	0.0000040	491	0.0162933	5.032206e-01	-7.405834	-7.337211	-7.406605	-7.378250
USDCHF	csGARCH	0.0000039	491	0.0162933	4.547895e-01	-7.413347	-7.303756	-7.415210	-7.369295
USD/EUR
USDCAD	sGARCH	0.0000002	491	0.0162933	2.029649e-01	-7.968274	-7.888079	-7.969305	-7.936039
USDCAD	fGARCH.GARCH	0.0000002	491	0.0162933	2.032142e-01	-7.968190	-7.887995	-7.969221	-7.935955
USDCAD	fGARCH.TGARCH	0.0000012	491	0.0162933	6.358517e-01	-7.746684	-7.652836	-7.748071	-7.708961
USDCAD	fGARCH.NGARCH	0.0000046	491	0.0162933	1.146625e+04	-28.549116	-28.455267	-28.550502	-28.511392
USDCAD	fGARCH.NAGARCH	0.0000002	491	0.0162933	2.025619e-01	-7.976993	-7.883145	-7.978380	-7.939270
USDCAD	fGARCH.GJRGARCH	0.0000002	491	0.0162933	2.071406e-01	-7.976217	-7.882369	-7.977604	-7.938494
USDCAD	gjrGARCH	0.0000002	491	0.0162933	2.054251e-01	-7.982640	-7.888791	-7.984026	-7.944916
USDCAD	iGARCH	0.0000003	491	0.0162933	2.060356e-01	-7.966705	-7.900163	-7.967434	-7.939957
USDCAD	csGARCH	0.0000002	491	0.0162933	2.006759e-01	-7.952563	-7.845061	-7.954358	-7.909351
USD/GBP
USDCNY	sGARCH	0.0000082	491	0.0162932	1.803945e-01	-6.899179	-6.808962	-6.900462	-6.862917
USDCNY	fGARCH.GARCH	0.0000080	491	0.0162932	1.802979e-01	-6.899573	-6.809356	-6.900855	-6.863310
USDCNY	fGARCH.TGARCH	0.0000104	491	0.0162932	7.798437e-01	-6.665817	-6.561958	-6.667493	-6.624071
USDCNY	fGARCH.NGARCH	0.0000201	491	0.0162932	1.385188e+03	-9.314223	-9.210364	-9.315899	-9.272477
USDCNY	fGARCH.NAGARCH	0.0000082	491	0.0162932	1.949349e-01	-6.913952	-6.810094	-6.915629	-6.872206
USDCNY	fGARCH.GJRGARCH	0.0000071	491	0.0162933	1.921778e-01	-6.926290	-6.822431	-6.927966	-6.884544
USDCNY	gjrGARCH	0.0000070	491	0.0162933	1.711430e-01	-6.958038	-6.854179	-6.959714	-6.916292
USDCNY	iGARCH	0.0000090	491	0.0162932	1.909882e-01	-6.885120	-6.808545	-6.886062	-6.854341
USDCNY	csGARCH	0.0000067	491	0.0162933	1.968595e-01	-6.915382	-6.797881	-6.917505	-6.868153
USD/JPY
USDJPY	sGARCH	0.0100690	491	0.0162523	1.672705e-01	1.770600	1.856801	1.769395	1.805248
USDJPY	fGARCH.GARCH	0.0099535	491	0.0162527	1.670901e-01	1.770829	1.857030	1.769625	1.805477
USDJPY	fGARCH.TGARCH	0.0068442	491	0.0162654	1.831416e-01	1.774305	1.874148	1.772723	1.814437
USDJPY	fGARCH.NGARCH	0.0310700	491	0.0161667	9.912952e+03	-17.954323	-17.854480	-17.955905	-17.914191
USDJPY	fGARCH.NAGARCH	0.0057596	491	0.0162698	1.787575e-01	1.758502	1.858344	1.756919	1.798633
USDJPY	fGARCH.GJRGARCH	0.0068569	491	0.0162653	1.734335e-01	1.767464	1.867306	1.765881	1.807595
USDJPY	gjrGARCH	0.0056543	491	0.0162702	1.806214e-01	1.757351	1.857193	1.755768	1.797482
USDJPY	iGARCH	0.0102367	491	0.0162516	1.692992e-01	1.767210	1.839769	1.766330	1.796374
USDJPY	csGARCH	0.0097956	491	0.0162534	1.646165e-01	1.776146	1.889630	1.774133	1.821760

6.5.2.2A : Table summary

Close Price Summary : Selected Models

Model	MSE	n	AIC.MSE	MSE.AIC	Akaike	Bayes	Shibata	Hannan.Quinn
sGARCH	0.0014404	3437	0.0023268	11.79193	-6.419263	-6.336211	-6.420369	-6.385880
fGARCH.GARCH	0.0014239	3437	0.0023268	11.79336	-6.419523	-6.336471	-6.420629	-6.386140
fGARCH.TGARCH	0.0009802	3437	0.0023270	11.68510	-6.285683	-6.188982	-6.287155	-6.246813
fGARCH.NGARCH	0.0044450	3437	0.0023250	9579.41289	-22.943684	-22.846983	-22.945156	-22.904815
fGARCH.NAGARCH	0.0008244	3437	0.0023271	37.01305	-6.249765	-6.153064	-6.251237	-6.210895
fGARCH.GJRGARCH	0.0009811	3437	0.0023270	11.83265	-6.437795	-6.341095	-6.439268	-6.398926
gjrGARCH	0.0008093	3437	0.0023271	11.84065	-6.452145	-6.355444	-6.453617	-6.413276
iGARCH	0.0014645	3437	0.0023268	11.78994	-6.415663	-6.346259	-6.416455	-6.387766
csGARCH	0.0014012	3437	0.0023268	11.77385	-6.409246	-6.298897	-6.411138	-6.364891

6.5.2.2B : Table summary

Close Price Summary : Selected Models

Model	n

6.5.2.2C : Table summary

Hi-Lo Price Summary : Selected Models

.id	Model	Date	Price	Price.T1	Akaike	Bayes	Shibata	Hannan.Quinn	diff	se

6.5.2.2D : Table summary

6.6 HiLo Price

Here I also measure the accuracy of mean value of highest and lowest. It may need to compare with the multivariate models.

6.6.1 All Models

## filtered bias hi-lo price.
hl <- fx %>% separate(Type, c('Cur', 'Type')) %>% 
  dplyr::filter(Type == 'Hi'|Type == 'Lo') %>% 
  dplyr::select(-Cur, -Type)

ntmID <- hl %>% dplyr::filter(se == 1) %>% .$Date %>% unlist %>% sort

acc <- hl %>% dplyr::filter(!Date %in% ntmID & Date %in% ntimeID2) %>% 
  ddply(.(.id, Model), summarise, 
        MSE = mean((Price.T1 - Price)^2), 
        n = length(Price), 
        AIC.MSE = (-2*MSE)/n+2*4/n, 
        MSE.AIC = mean((Akaike - mean(Akaike))^2),
        Akaike = mean(Akaike), 
        Bayes = mean(Bayes), 
        Shibata = mean(Shibata), 
        Hannan.Quinn = mean(Hannan.Quinn)) %>% 
  tbl_df %>% mutate(MSE = round(MSE, 7))

Hi-Lo Price Summary : All Models

.id	Model	MSE	n	AIC.MSE	MSE.AIC	Akaike	Bayes	Shibata	Hannan.Quinn
USD/AUD
USDAUD	sGARCH	0.0000003	932	0.0085837	1.648792e-01	-7.4119702	-7.334184	-7.4129300	-7.380703
USDAUD	fGARCH.GARCH	0.0000003	932	0.0085837	1.648695e-01	-7.4120664	-7.334280	-7.4130263	-7.380799
USDAUD	fGARCH.TGARCH	0.0000034	932	0.0085837	8.513587e-01	-7.0981018	-7.006662	-7.0994082	-7.061347
USDAUD	fGARCH.AVGARCH	0.0000000	96	0.0833333	1.027210e+02	-6.6630037	-6.563157	-6.6645378	-6.622869
USDAUD	fGARCH.NGARCH	0.0000036	932	0.0085837	8.855356e+03	-24.9571459	-24.865706	-24.9584523	-24.920391
USDAUD	fGARCH.NAGARCH	0.0000005	932	0.0085837	1.805113e-01	-7.4171641	-7.325725	-7.4184705	-7.380409
USDAUD	fGARCH.APARCH	0.0000027	568	0.0140845	5.220720e+03	-16.7726063	-16.666685	-16.7743355	-16.730028
USDAUD	fGARCH.GJRGARCH	0.0000008	932	0.0085837	1.787077e-01	-7.4084725	-7.317033	-7.4097789	-7.371717
USDAUD	fGARCH.ALLGARCH	0.0000004	394	0.0203046	5.181377e+03	-16.6299045	-16.508303	-16.6321749	-16.581025
USDAUD	eGARCH	0.0000004	834	0.0095923	4.360711e+00	-7.4046875	-7.312429	-7.4060177	-7.367603
USDAUD	gjrGARCH	0.0000008	932	0.0085837	1.804271e-01	-7.4144112	-7.322972	-7.4157177	-7.377656
USDAUD	apARCH	0.0000003	152	0.0526316	4.991800e-03	-7.9006388	-7.794431	-7.9023949	-7.857946
USDAUD	iGARCH	0.0000008	932	0.0085837	1.745408e-01	-7.4115892	-7.347456	-7.4122564	-7.385810
USDAUD	csGARCH	0.0000005	932	0.0085837	1.745604e-01	-7.3942776	-7.289185	-7.3959837	-7.352034
USD/CAD
USDEUR	sGARCH	0.0000005	932	0.0085837	2.662179e-01	-8.4067157	-8.325171	-8.4077785	-8.373938
USDEUR	fGARCH.GARCH	0.0000005	932	0.0085837	2.655665e-01	-8.4069570	-8.325413	-8.4080198	-8.374179
USDEUR	fGARCH.TGARCH	0.0000014	932	0.0085837	4.353595e-01	-8.2333149	-8.138118	-8.2347388	-8.195049
USDEUR	fGARCH.AVGARCH	0.0000002	50	0.1600000	3.974652e-01	-7.8654915	-7.755734	-7.8673388	-7.821373
USDEUR	fGARCH.NGARCH	0.0000043	932	0.0085837	1.115418e+04	-27.5051597	-27.409962	-27.5065836	-27.466894
USDEUR	fGARCH.NAGARCH	0.0000005	932	0.0085837	7.306654e+01	-8.1321148	-8.036917	-8.1335386	-8.093849
USDEUR	fGARCH.APARCH	0.0000027	208	0.0384615	4.430175e+03	-16.1940403	-16.080899	-16.1960343	-16.148562
USDEUR	fGARCH.GJRGARCH	0.0000005	932	0.0085837	2.639775e-01	-8.4091774	-8.313980	-8.4106013	-8.370912
USDEUR	fGARCH.ALLGARCH	0.0000004	608	0.0131579	2.511709e+03	-13.1087241	-12.987125	-13.1110062	-13.059845
USDEUR	eGARCH	0.0000004	840	0.0095238	4.999288e+00	-8.4256815	-8.330173	-8.4271176	-8.387291
USDEUR	gjrGARCH	0.0000005	932	0.0085837	2.611554e-01	-8.4301511	-8.334954	-8.4315750	-8.391886
USDEUR	apARCH	0.0000001	152	0.0526316	7.732810e-02	-8.2448046	-8.134019	-8.2467087	-8.200273
USDEUR	iGARCH	0.0000005	932	0.0085837	2.604802e-01	-8.4049789	-8.337088	-8.4057344	-8.377689
USDEUR	csGARCH	0.0000005	932	0.0085837	2.396449e-01	-8.3990411	-8.290191	-8.4008788	-8.355287
USD/CHF
USDGBP	sGARCH	0.0000001	932	0.0085837	9.731170e-02	-9.0757528	-8.996031	-9.0767785	-9.043709
USDGBP	fGARCH.GARCH	0.0000001	932	0.0085837	9.806740e-02	-9.0743033	-8.994582	-9.0753291	-9.042260
USDGBP	fGARCH.TGARCH	0.0000002	932	0.0085837	4.786164e-01	-8.7976178	-8.704257	-8.7989967	-8.760092
USDGBP	fGARCH.AVGARCH	0.0000001	58	0.1379310	9.400883e+01	-7.6242767	-7.518611	-7.6260178	-7.581808
USDGBP	fGARCH.NGARCH	0.0000014	932	0.0085837	1.434271e+03	-10.7715250	-10.678164	-10.7729039	-10.733999
USDGBP	fGARCH.NAGARCH	0.0000001	932	0.0085837	3.068059e+01	-8.8295939	-8.736233	-8.8309728	-8.792068
USDGBP	fGARCH.APARCH	0.0000002	570	0.0140351	1.547959e+03	-12.0698179	-11.964987	-12.0715310	-12.027681
USDGBP	fGARCH.GJRGARCH	0.0000001	932	0.0085837	9.977000e-02	-9.0870527	-8.993692	-9.0884317	-9.049527
USDGBP	fGARCH.ALLGARCH	0.0000002	612	0.0130719	1.244235e+03	-11.4991308	-11.379478	-11.5013388	-11.451036
USDGBP	eGARCH	0.0000001	832	0.0096154	4.019435e+00	-9.0501706	-8.957006	-9.0515480	-9.012723
USDGBP	gjrGARCH	0.0000001	932	0.0085837	8.937850e-02	-9.1015747	-9.008214	-9.1029536	-9.064049
USDGBP	apARCH	0.0000002	152	0.0526316	1.377456e-01	-9.1076928	-9.001783	-9.1094466	-9.065125
USDGBP	iGARCH	0.0000001	932	0.0085837	9.938420e-02	-9.0736792	-9.007596	-9.0744054	-9.047118
USDGBP	csGARCH	0.0000001	932	0.0085837	6.897400e-02	-9.0669338	-8.959934	-9.0687187	-9.023926
USD/CNY
USDCHF	sGARCH	0.0000063	932	0.0085837	3.828590e-01	-7.6377615	-7.555827	-7.6388270	-7.604827
USDCHF	fGARCH.GARCH	0.0000063	932	0.0085837	3.826268e-01	-7.6375311	-7.555597	-7.6385967	-7.604596
USDCHF	fGARCH.TGARCH	0.0000003	932	0.0085837	2.587293e-01	-7.6415832	-7.545993	-7.6430115	-7.603159
USDCHF	fGARCH.AVGARCH	0.0000002	32	0.2500000	6.180160e-02	-7.9112727	-7.802933	-7.9130885	-7.867718
USDCHF	fGARCH.NGARCH	0.0000049	932	0.0085837	9.604493e+02	-9.1812081	-9.085617	-9.1826365	-9.142784
USDCHF	fGARCH.NAGARCH	0.0000034	932	0.0085837	8.512336e+01	-7.1170238	-7.021433	-7.1184521	-7.078600
USDCHF	fGARCH.APARCH	0.0000049	566	0.0141343	4.084659e+03	-16.8636128	-16.755664	-16.8654258	-16.820219
USDCHF	fGARCH.GJRGARCH	0.0000038	932	0.0085837	3.464026e-01	-7.6665767	-7.570986	-7.6680051	-7.628153
USDCHF	fGARCH.ALLGARCH	0.0000003	606	0.0132013	4.715382e+03	-15.5641595	-15.442340	-15.5664422	-15.515191
USDCHF	eGARCH	0.0000148	838	0.0095465	9.730179e-01	-7.7213878	-7.627059	-7.7227817	-7.683471
USDCHF	gjrGARCH	0.0000046	932	0.0085837	3.587954e-01	-7.6861873	-7.590597	-7.6876157	-7.647763
USDCHF	apARCH	0.0000001	150	0.0533333	2.632400e-03	-8.0075738	-7.902455	-8.0092775	-7.965317
USDCHF	iGARCH	0.0001641	932	0.0085833	6.198796e-01	-7.4976643	-7.429386	-7.4984206	-7.470219
USDCHF	csGARCH	0.0000471	932	0.0085836	4.622719e-01	-7.5736941	-7.464448	-7.5755382	-7.529781
USD/EUR
USDCAD	sGARCH	0.0000006	932	0.0085837	1.846559e-01	-8.0893334	-8.007394	-8.0904069	-8.056397
USDCAD	fGARCH.GARCH	0.0000006	932	0.0085837	1.848084e-01	-8.0893424	-8.007403	-8.0904159	-8.056406
USDCAD	fGARCH.TGARCH	0.0000016	932	0.0085837	8.127251e-01	-7.8295745	-7.733982	-7.8310106	-7.791150
USDCAD	fGARCH.AVGARCH	0.0000000	70	0.1142857	1.291440e+02	-6.8729740	-6.771942	-6.8745506	-6.832363
USDCAD	fGARCH.NGARCH	0.0000161	932	0.0085837	1.103237e+04	-30.8466049	-30.751013	-30.8480410	-30.808180
USDCAD	fGARCH.NAGARCH	0.0000005	932	0.0085837	1.837784e-01	-8.0972899	-8.001698	-8.0987260	-8.058865
USDCAD	fGARCH.APARCH	0.0000004	564	0.0141844	3.100086e+03	-15.4533350	-15.349038	-15.4550084	-15.411410
USDCAD	fGARCH.GJRGARCH	0.0000005	932	0.0085837	1.823809e-01	-8.0899410	-7.994349	-8.0913771	-8.051517
USDCAD	fGARCH.ALLGARCH	0.0000005	608	0.0131579	3.027263e+03	-14.5004167	-14.381576	-14.5025752	-14.452646
USDCAD	eGARCH	0.0000005	826	0.0096852	1.576666e+00	-8.0906686	-7.995309	-8.0920967	-8.052338
USDCAD	gjrGARCH	0.0000004	932	0.0085837	1.811391e-01	-8.0950992	-7.999507	-8.0965352	-8.056675
USDCAD	apARCH	0.0000000	150	0.0533333	5.354100e-03	-8.4413977	-8.339791	-8.4429948	-8.400555
USDCAD	iGARCH	0.0000007	932	0.0085837	1.853070e-01	-8.0899692	-8.021683	-8.0907337	-8.062521
USDCAD	csGARCH	0.0000006	932	0.0085837	1.833947e-01	-8.0729304	-7.963685	-8.0747819	-8.029018
USD/GBP
USDCNY	sGARCH	0.0011492	932	0.0085812	1.502393e+00	-6.3872078	-6.295469	-6.3885434	-6.350333
USDCNY	fGARCH.GARCH	0.0006407	932	0.0085823	1.510695e+00	-6.3856212	-6.293883	-6.3869568	-6.348747
USDCNY	fGARCH.TGARCH	0.0021150	932	0.0085792	2.779777e+00	-6.1473473	-6.041967	-6.1490829	-6.104990
USDCNY	fGARCH.AVGARCH	0.0000002	24	0.3333333	3.333900e-03	-7.0303704	-6.918114	-7.0322781	-6.985254
USDCNY	fGARCH.NGARCH	0.2988267	932	0.0079424	1.093385e+03	-8.2856309	-8.180251	-8.2873665	-8.243273
USDCNY	fGARCH.NAGARCH	0.0003913	932	0.0085829	1.560094e+00	-6.4016729	-6.296293	-6.4034085	-6.359315
USDCNY	fGARCH.APARCH	0.0013851	564	0.0141795	8.778234e+03	-21.5574721	-21.435549	-21.5597582	-21.508464
USDCNY	fGARCH.GJRGARCH	0.0009124	932	0.0085817	1.734800e+00	-6.3656190	-6.260239	-6.3673546	-6.323261
USDCNY	fGARCH.ALLGARCH	0.0013794	608	0.0131534	2.955634e+03	-11.8437098	-11.708425	-11.8465034	-11.789332
USDCNY	eGARCH	0.0012983	834	0.0095892	2.958090e+00	-6.1061162	-6.001109	-6.1078431	-6.063909
USDCNY	gjrGARCH	0.0009319	932	0.0085817	1.511723e+00	-6.4117818	-6.306402	-6.4135175	-6.369424
USDCNY	apARCH	0.0000094	152	0.0526315	3.464470e-02	-6.9359394	-6.821784	-6.9379235	-6.890058
USDCNY	iGARCH	0.0011934	932	0.0085811	1.735624e+00	-6.3165905	-6.238494	-6.3175791	-6.285200
USDCNY	csGARCH	0.0013067	932	0.0085809	1.779049e+00	-6.3396861	-6.220664	-6.3418739	-6.291845
USD/JPY
USDJPY	sGARCH	0.0123463	932	0.0085572	1.531779e-01	1.5172976	1.607609	1.5159817	1.553598
USDJPY	fGARCH.GARCH	0.0121946	932	0.0085575	1.528495e-01	1.5175935	1.607905	1.5162776	1.553894
USDJPY	fGARCH.TGARCH	0.0110268	932	0.0085600	2.159302e-01	1.5471582	1.651112	1.5454481	1.588942
USDJPY	fGARCH.AVGARCH	0.0507600	70	0.1128354	3.751932e-01	0.9725055	1.107126	0.9697069	1.026612
USDJPY	fGARCH.NGARCH	0.1262078	932	0.0083129	4.478307e+03	-7.1533983	-7.049445	-7.1551084	-7.111614
USDJPY	fGARCH.NAGARCH	0.0090602	932	0.0085642	1.590694e-01	1.5001238	1.604077	1.4984137	1.541908
USDJPY	fGARCH.APARCH	190.5823016	212	-1.7602104	1.314159e+04	-22.3648852	-22.235279	-22.3674832	-22.312793
USDJPY	fGARCH.GJRGARCH	0.0111482	932	0.0085598	1.558683e-01	1.5131676	1.617121	1.5114575	1.554952
USDJPY	fGARCH.ALLGARCH	0.0189279	370	0.0215193	2.183352e+03	-2.7140743	-2.575823	-2.7169997	-2.658504
USDJPY	eGARCH	0.0314204	834	0.0095170	6.954058e-01	1.5672646	1.671789	1.5655364	1.609278
USDJPY	gjrGARCH	0.0104402	932	0.0085613	1.616354e-01	1.5087563	1.612710	1.5070462	1.550540
USDJPY	apARCH	0.1455181	150	0.0513931	1.266300e+05	-97.4327888	-97.301222	-97.4354591	-97.379909
USDJPY	iGARCH	0.0116146	932	0.0085588	1.552551e-01	1.5156137	1.592283	1.5146389	1.546431
USDJPY	csGARCH	0.0192035	932	0.0085425	1.486592e-01	1.5242103	1.641806	1.5220537	1.571478

6.6.1.1 : Table summary

Hi-Lo Price Summary : All Models

Model	MSE	n	AIC.MSE	MSE.AIC	Akaike	Bayes	Shibata	Hannan.Quinn
sGARCH	0.0019290	6524	0.0012257	11.70907	-6.498778	-6.415210	-6.499898	-6.465187
fGARCH.GARCH	0.0018347	6524	0.0012257	11.70996	-6.498318	-6.414750	-6.499438	-6.464728
fGARCH.TGARCH	0.0018784	6524	0.0012257	11.74064	-6.314340	-6.217124	-6.315829	-6.275264
fGARCH.AVGARCH	0.0088831	400	0.0199556	70.87457	-5.775133	-5.665487	-5.777010	-5.731061
fGARCH.NGARCH	0.0607235	6524	0.0012076	5663.79028	-16.957239	-16.860023	-16.958727	-16.918162
fGARCH.NAGARCH	0.0013509	6524	0.0012258	38.09790	-6.356391	-6.259175	-6.357879	-6.317314
fGARCH.APARCH	12.4244263	3252	-0.0051811	5104.44249	-16.892759	-16.782177	-16.894661	-16.848309
fGARCH.GJRGARCH	0.0017237	6524	0.0012257	11.74896	-6.501953	-6.404737	-6.503442	-6.462876
fGARCH.ALLGARCH	0.0020607	3806	0.0021009	3069.97961	-12.615100	-12.490414	-12.617494	-12.564981
eGARCH	0.0046764	5838	0.0013687	14.26714	-6.461398	-6.364233	-6.462887	-6.422342
gjrGARCH	0.0016255	6524	0.0012257	11.73871	-6.518636	-6.421419	-6.520124	-6.479559
apARCH	0.0206326	1058	0.0075224	18924.50792	-20.770325	-20.659571	-20.772234	-20.725807
iGARCH	0.0018535	6524	0.0012257	11.73061	-6.468408	-6.398488	-6.469213	-6.440303
csGARCH	0.0029370	6524	0.0012253	11.72684	-6.474622	-6.363757	-6.476532	-6.430059

6.6.1.2 : Table summary

Hi-Lo Price Summary : All Models

Model	n
sGARCH	2
fGARCH.GARCH	4
fGARCH.TGARCH	2
fGARCH.NGARCH	56
fGARCH.NAGARCH	9
fGARCH.APARCH	15
fGARCH.GJRGARCH	4
fGARCH.ALLGARCH	56
eGARCH	10
gjrGARCH	3
apARCH	8
iGARCH	9
csGARCH	4

6.6.1.3 : Table summary

Hi-Lo Price Summary : Selected Models

.id	Model	Date	Price	Price.T1	Akaike	Bayes	Shibata	Hannan.Quinn	diff	se
USDAUD	fGARCH.NGARCH	2013-06-27	1.077	2.542027e+00	-590.320340	-590.197426	-590.322615	-590.270933	2.360285e+00	1
USDAUD	fGARCH.NGARCH	2017-03-26	1.307	1.111220e-02	-586.980288	-586.857373	-586.982562	-586.930880	8.502100e-03	1
USDAUD	apARCH	2013-05-16	1.030	5.216021e+74	363.188288	363.379488	363.182914	363.265144	5.064098e+74	1
USDEUR	fGARCH.GARCH	2015-02-05	0.884	2.683682e+92	412.262447	412.385024	412.260190	412.311713	3.035839e+92	1
USDEUR	fGARCH.NGARCH	2014-10-14	0.779	-2.018651e+51	-468.909622	-468.759806	-468.912961	-468.849407	2.591336e+51	1
USDEUR	fGARCH.NGARCH	2015-03-02	0.890	-4.015994e+07	83.346290	83.510176	83.342305	83.412167	4.512353e+07	1
USDEUR	fGARCH.NGARCH	2015-06-04	0.887	-1.394863e+18	-545.380537	-545.244340	-545.383310	-545.325796	1.572562e+18	1
USDEUR	fGARCH.NGARCH	2015-06-24	0.891	1.892803e+10	77.586765	77.722962	77.583992	77.641506	2.124358e+10	1
USDEUR	fGARCH.NGARCH	2016-04-28	0.880	4.510825e-01	-594.671515	-594.535319	-594.674288	-594.616775	5.125938e-01	1
USDGBP	fGARCH.TGARCH	2014-06-19	0.586	-3.465523e+73	364.832355	365.037213	364.826216	364.914701	5.913861e+73	1
USDGBP	fGARCH.NGARCH	2014-06-19	0.586	4.316118e-01	-160.018385	-159.813528	-160.024525	-159.936039	7.365389e-01	1
USDGBP	fGARCH.NGARCH	2016-07-20	0.759	7.366569e+74	-405.810489	-405.701830	-405.812268	-405.766822	9.705624e+74	1
USDGBP	csGARCH	2014-12-05	0.637	9.285102e+149	758.957433	759.107249	758.954093	759.017647	1.457630e+150	1
USDCHF	sGARCH	2015-01-16	0.850	1.189676e+00	-6.687989	-6.606271	-6.689007	-6.655145	1.399619e+00	1
USDCHF	fGARCH.GARCH	2014-05-25	0.897	-3.484066e+62	366.067877	366.273301	366.061692	366.150461	3.884132e+62	1
USDCHF	fGARCH.GARCH	2015-01-16	0.850	1.189676e+00	-6.687989	-6.606271	-6.689007	-6.655145	1.399619e+00	1
USDCHF	fGARCH.TGARCH	2015-01-16	0.850	1.182560e+00	-6.882116	-6.786779	-6.883495	-6.843798	1.391247e+00	1
USDCHF	fGARCH.NGARCH	2015-01-16	0.850	1.182556e+00	-6.811955	-6.716617	-6.813334	-6.773637	1.391243e+00	1
USDCHF	fGARCH.NGARCH	2015-09-07	0.970	-8.823318e+01	-587.029347	-586.920390	-587.031140	-586.985555	9.096204e+01	1
USDCHF	fGARCH.NGARCH	2015-10-30	0.991	-1.889325e+01	-584.267632	-584.158374	-584.269437	-584.223714	1.906483e+01	1
USDCHF	fGARCH.NAGARCH	2015-01-16	0.850	1.188451e+00	-6.758750	-6.663413	-6.760129	-6.720432	1.398178e+00	1
USDCHF	fGARCH.GJRGARCH	2015-01-16	0.850	1.189203e+00	-6.775060	-6.679723	-6.776439	-6.736742	1.399062e+00	1
USDCHF	fGARCH.ALLGARCH	2015-01-16	0.850	1.184971e+00	-6.882670	-6.760093	-6.884927	-6.833404	1.394083e+00	1
USDCHF	eGARCH	2015-01-16	0.850	1.179679e+00	-6.756294	-6.660957	-6.757673	-6.717976	1.387858e+00	1
USDCHF	eGARCH	2015-01-21	0.851	5.746862e-01	-6.615293	-6.519955	-6.616671	-6.576975	6.753070e-01	1
USDCHF	gjrGARCH	2015-01-16	0.850	1.187461e+00	-6.834457	-6.739119	-6.835835	-6.796138	1.397013e+00	1
USDCHF	gjrGARCH	2015-01-19	0.857	5.503465e-01	-6.799206	-6.703606	-6.800595	-6.760778	6.421780e-01	1
USDCHF	iGARCH	2015-01-16	0.850	1.189656e+00	-6.696311	-6.628212	-6.697021	-6.668940	1.399595e+00	1
USDCHF	iGARCH	2015-01-19	0.857	5.467194e-01	-6.659730	-6.591444	-6.660445	-6.632281	6.379457e-01	1
USDCHF	iGARCH	2015-01-20	0.869	1.169574e+00	-6.632037	-6.563939	-6.632748	-6.604667	1.345885e+00	1
USDCHF	iGARCH	2015-01-21	0.851	5.536845e-01	-6.599117	-6.531019	-6.599827	-6.571747	6.506281e-01	1
USDCHF	iGARCH	2015-01-22	0.853	1.132264e+00	-6.569994	-6.501896	-6.570705	-6.542624	1.327390e+00	1
USDCHF	iGARCH	2015-01-26	0.876	1.153558e+00	-6.519110	-6.450824	-6.519825	-6.491661	1.316847e+00	1
USDCHF	iGARCH	2015-01-27	0.894	6.896106e-01	-6.470927	-6.402829	-6.471637	-6.443557	7.713765e-01	1
USDCHF	iGARCH	2015-02-02	0.920	7.319616e-01	-6.350835	-6.255235	-6.352225	-6.312407	7.956105e-01	1
USDCHF	csGARCH	2015-01-16	0.850	1.193636e+00	-6.688153	-6.579196	-6.689945	-6.644361	1.404278e+00	1
USDCHF	csGARCH	2015-01-22	0.853	1.141360e+00	-6.534724	-6.425767	-6.536516	-6.490932	1.338054e+00	1
USDCHF	csGARCH	2015-01-23	0.868	6.200740e-01	-6.493151	-6.384194	-6.494943	-6.449359	7.143710e-01	1
USDCAD	fGARCH.NGARCH	2015-02-05	1.258	-2.752758e+42	-487.602382	-487.425326	-487.607002	-487.531219	2.188202e+42	1
USDCAD	fGARCH.NGARCH	2015-03-29	1.270	-6.542943e+22	-529.240306	-529.131049	-529.242112	-529.196389	5.151924e+22	1
USDCAD	fGARCH.NGARCH	2015-07-21	1.305	4.139802e+61	-435.142670	-435.006474	-435.145443	-435.087930	3.172262e+61	1
USDCAD	fGARCH.NGARCH	2016-05-02	1.270	2.847428e+37	-493.891329	-493.741100	-493.894693	-493.830942	2.242069e+37	1
USDCAD	eGARCH	2015-08-26	1.330	-3.733849e+102	106.421678	106.557874	106.418905	106.476418	2.807405e+102	1
USDCNY	sGARCH	2014-07-10	2.201	2.987751e+00	-4.665480	-4.583537	-4.666505	-4.632541	1.357452e+00	1
USDCNY	fGARCH.GARCH	2014-07-10	2.201	2.987874e+00	-4.665479	-4.583536	-4.666505	-4.632541	1.357508e+00	1
USDCNY	fGARCH.NGARCH	2014-07-17	6.192	-5.016306e+02	-585.712986	-585.631043	-585.714011	-585.680047	8.101269e+01	1
USDCNY	fGARCH.NGARCH	2014-07-20	6.195	1.194381e+01	-589.430373	-589.348203	-589.431406	-589.397340	1.927975e+00	1
USDCNY	fGARCH.NGARCH	2014-07-22	6.189	1.945038e+01	-591.466725	-591.384782	-591.467750	-591.433786	3.142734e+00	1
USDCNY	fGARCH.NGARCH	2014-07-23	6.182	-3.637318e+01	-588.553531	-588.471588	-588.554557	-588.520593	5.883724e+00	1
USDCNY	fGARCH.NGARCH	2014-07-27	6.176	4.872521e+01	-587.187420	-587.105250	-587.188453	-587.154387	7.889444e+00	1
USDCNY	fGARCH.NGARCH	2014-07-31	6.163	2.769268e+01	-590.455881	-590.373938	-590.456907	-590.422943	4.493377e+00	1
USDCNY	fGARCH.NGARCH	2014-08-03	6.168	3.201427e+01	-587.733648	-587.651478	-587.734681	-587.700615	5.190381e+00	1
USDCNY	fGARCH.NGARCH	2014-08-05	6.153	1.853196e+01	-589.664961	-589.583018	-589.665987	-589.632023	3.011858e+00	1
USDCNY	fGARCH.NGARCH	2014-08-06	6.147	2.635122e+01	-591.728569	-591.646626	-591.729595	-591.695631	4.286842e+00	1
USDCNY	fGARCH.NGARCH	2014-08-10	6.144	5.336958e+01	-588.785684	-588.703514	-588.786717	-588.752651	8.686456e+00	1
USDCNY	fGARCH.NGARCH	2014-08-12	6.144	4.740305e+01	-587.300349	-587.218406	-587.301374	-587.267410	7.715340e+00	1
USDCNY	fGARCH.NGARCH	2014-08-13	6.142	8.825968e+00	-589.224653	-589.142710	-589.225679	-589.191715	1.436986e+00	1
USDCNY	fGARCH.NGARCH	2014-08-14	6.136	4.872331e+01	-586.351874	-586.269931	-586.352899	-586.318935	7.940565e+00	1
USDCNY	fGARCH.NGARCH	2014-08-19	6.130	-1.240483e+01	-590.789977	-590.708034	-590.791003	-590.757039	2.023627e+00	1
USDCNY	fGARCH.NGARCH	2014-08-20	6.130	9.161532e+00	-592.227353	-592.145410	-592.228379	-592.194415	1.494540e+00	1
USDCNY	fGARCH.NGARCH	2014-08-21	6.141	-1.525661e+01	-590.144127	-590.062184	-590.145153	-590.111189	2.484385e+00	1
USDCNY	fGARCH.NGARCH	2014-08-24	6.140	-3.247607e+01	-589.174302	-589.092132	-589.175335	-589.141269	5.289262e+00	1
USDCNY	fGARCH.NGARCH	2014-08-25	6.142	6.174800e+01	-572.956479	-572.874536	-572.957505	-572.923541	1.005340e+01	1
USDCNY	fGARCH.NGARCH	2014-08-26	6.133	9.738678e+01	-587.251542	-587.169599	-587.252568	-587.218604	1.587914e+01	1
USDCNY	fGARCH.NGARCH	2014-08-31	6.129	2.545583e+02	-584.923023	-584.840853	-584.924056	-584.889989	4.153341e+01	1
USDCNY	fGARCH.NGARCH	2014-09-01	6.132	1.596999e+02	-584.161053	-584.079110	-584.162079	-584.128115	2.604369e+01	1
USDCNY	fGARCH.NGARCH	2014-09-02	6.131	-1.989882e+01	-589.399865	-589.317922	-589.400891	-589.366927	3.245608e+00	1
USDCNY	fGARCH.NGARCH	2014-09-04	6.128	-2.866168e+01	-585.515480	-585.433537	-585.516505	-585.482541	4.677168e+00	1
USDCNY	fGARCH.NGARCH	2014-09-08	6.122	-2.517129e+01	-587.872377	-587.790434	-587.873402	-587.839438	4.111612e+00	1
USDCNY	fGARCH.NGARCH	2014-09-11	6.120	1.708482e+01	-588.380157	-588.298214	-588.381183	-588.347219	2.791637e+00	1
USDCNY	fGARCH.NGARCH	2014-09-14	6.125	-7.626137e+01	-589.072288	-588.990119	-589.073322	-589.039255	1.245084e+01	1
USDCNY	fGARCH.NGARCH	2014-09-16	6.129	-1.759094e+02	-585.597533	-585.515590	-585.598558	-585.564594	2.870116e+01	1
USDCNY	fGARCH.NGARCH	2014-09-21	6.128	-2.039517e+01	-588.488512	-588.406343	-588.489546	-588.455479	3.328194e+00	1
USDCNY	fGARCH.NGARCH	2014-09-23	6.124	1.512941e+01	-590.152856	-590.070913	-590.153882	-590.119918	2.470511e+00	1
USDCNY	fGARCH.NGARCH	2014-10-01	6.128	-1.146657e+02	-584.091459	-584.009516	-584.092485	-584.058521	1.871177e+01	1
USDCNY	fGARCH.NGARCH	2014-10-06	6.129	-2.283202e+01	-579.908511	-579.826568	-579.909537	-579.875573	3.725243e+00	1
USDCNY	fGARCH.NGARCH	2014-10-07	6.125	5.146397e+01	-565.845084	-565.763141	-565.846110	-565.812146	8.402281e+00	1
USDCNY	fGARCH.NGARCH	2014-10-09	6.120	6.182692e+01	-583.758544	-583.676826	-583.759562	-583.725700	1.010244e+01	1
USDCNY	fGARCH.NGARCH	2014-11-26	6.123	6.187566e+01	-583.601907	-583.520189	-583.602924	-583.569062	1.010545e+01	1
USDCNY	fGARCH.NAGARCH	2014-07-10	2.201	2.977219e+00	-4.669064	-4.573464	-4.670453	-4.630636	1.352666e+00	1
USDCNY	fGARCH.NAGARCH	2014-07-24	6.182	-3.603032e+02	14.561667	14.643610	14.560642	14.594606	5.828262e+01	1
USDCNY	fGARCH.NAGARCH	2014-07-29	6.162	-3.579216e+02	14.548624	14.630567	14.547598	14.581562	5.808530e+01	1
USDCNY	fGARCH.NAGARCH	2014-07-31	6.163	-3.531901e+02	14.522470	14.604413	14.521444	14.555409	5.730814e+01	1
USDCNY	fGARCH.NAGARCH	2014-08-04	6.161	-3.492923e+02	14.548440	14.630382	14.547414	14.581378	5.669409e+01	1
USDCNY	fGARCH.NAGARCH	2014-08-26	6.133	4.865151e+00	104.667516	104.749459	104.666490	104.700454	7.932742e-01	1
USDCNY	fGARCH.NAGARCH	2014-09-04	6.128	4.796821e+02	172.167572	172.249515	172.166546	172.200510	7.827710e+01	1
USDCNY	fGARCH.NAGARCH	2014-10-19	6.113	-3.344848e+02	98.972743	99.054686	98.971717	99.005682	5.471696e+01	1
USDCNY	fGARCH.APARCH	2013-10-29	6.134	2.876649e+25	-526.990144	-526.826258	-526.994129	-526.924267	4.689679e+24	1
USDCNY	fGARCH.APARCH	2013-11-07	6.144	-8.647337e+68	-406.983178	-406.819292	-406.987163	-406.917301	1.407444e+68	1
USDCNY	fGARCH.APARCH	2014-06-19	6.221	-7.210200e+39	-479.345003	-479.181117	-479.348988	-479.279126	1.159010e+39	1
USDCNY	fGARCH.APARCH	2014-07-15	6.194	2.096796e+01	-591.356584	-591.260983	-591.357973	-591.318155	3.385206e+00	1
USDCNY	fGARCH.APARCH	2014-07-24	6.182	2.156616e+01	103.442134	103.537734	103.440745	103.480562	3.488541e+00	1
USDCNY	fGARCH.APARCH	2014-08-18	6.127	4.686359e+01	-590.025600	-589.930000	-590.026990	-589.987172	7.648701e+00	1
USDCNY	fGARCH.APARCH	2014-08-20	6.130	-1.738365e+02	-587.118563	-587.022963	-587.119952	-587.080135	2.835831e+01	1
USDCNY	fGARCH.APARCH	2014-09-22	6.128	2.649730e+02	-583.798821	-583.703221	-583.800210	-583.760393	4.323972e+01	1
USDCNY	fGARCH.APARCH	2014-11-20	6.109	-1.204425e+02	-584.497904	-584.402566	-584.499282	-584.459586	1.971558e+01	1
USDCNY	fGARCH.APARCH	2014-11-26	6.123	1.763058e+02	-584.737735	-584.642398	-584.739114	-584.699417	2.879403e+01	1
USDCNY	fGARCH.APARCH	2014-12-19	6.205	1.811908e+02	-585.237794	-585.142457	-585.239173	-585.199476	2.920077e+01	1
USDCNY	fGARCH.GJRGARCH	2014-07-10	2.201	2.979918e+00	-4.677596	-4.581996	-4.678985	-4.639168	1.353893e+00	1
USDCNY	fGARCH.GJRGARCH	2014-09-01	6.132	1.263740e+01	98.054293	98.136236	98.053267	98.087231	2.060893e+00	1
USDCNY	fGARCH.GJRGARCH	2014-11-12	6.114	-3.508494e+01	94.016565	94.098283	94.015548	94.049410	5.738460e+00	1
USDCNY	fGARCH.ALLGARCH	2014-07-10	2.201	2.966190e+00	-4.732654	-4.609740	-4.734928	-4.683247	1.347655e+00	1
USDCNY	fGARCH.ALLGARCH	2014-07-16	6.191	-3.928444e+01	-582.734556	-582.625298	-582.736361	-582.690638	6.345410e+00	1
USDCNY	fGARCH.ALLGARCH	2014-07-17	6.192	1.616838e+02	-583.779418	-583.670160	-583.781223	-583.735500	2.611173e+01	1
USDCNY	fGARCH.ALLGARCH	2014-07-20	6.195	3.493327e+01	-587.564830	-587.455270	-587.566649	-587.520785	5.638946e+00	1
USDCNY	fGARCH.ALLGARCH	2014-07-21	6.193	2.379018e+02	-582.588057	-582.478800	-582.589863	-582.544139	3.841462e+01	1
USDCNY	fGARCH.ALLGARCH	2014-07-27	6.176	6.750841e+01	-588.539587	-588.430027	-588.541406	-588.495542	1.093077e+01	1
USDCNY	fGARCH.ALLGARCH	2014-07-31	6.163	-1.535570e+01	-587.168301	-587.059044	-587.170107	-587.124384	2.491595e+00	1
USDCNY	fGARCH.ALLGARCH	2014-08-03	6.168	-1.336380e+01	-588.926648	-588.817089	-588.928467	-588.882604	2.166635e+00	1
USDCNY	fGARCH.ALLGARCH	2014-08-05	6.153	6.028594e+02	19.084869	19.194126	19.083063	19.128787	9.797812e+01	1
USDCNY	fGARCH.ALLGARCH	2014-08-06	6.147	2.980786e+01	-588.051008	-587.941750	-588.052813	-588.007090	4.849171e+00	1
USDCNY	fGARCH.ALLGARCH	2014-08-07	6.146	-7.094383e+01	-586.949487	-586.840229	-586.951292	-586.905569	1.154309e+01	1
USDCNY	fGARCH.ALLGARCH	2014-08-11	6.144	2.489838e+01	-587.776345	-587.667088	-587.778151	-587.732427	4.052471e+00	1
USDCNY	fGARCH.ALLGARCH	2014-08-12	6.144	6.297337e+01	-587.294543	-587.185286	-587.296349	-587.250625	1.024957e+01	1
USDCNY	fGARCH.ALLGARCH	2014-08-13	6.142	-2.219940e+01	-590.296221	-590.186964	-590.298027	-590.252303	3.614361e+00	1
USDCNY	fGARCH.ALLGARCH	2014-08-14	6.136	-1.404711e+02	-587.700902	-587.591645	-587.702708	-587.656984	2.289295e+01	1
USDCNY	fGARCH.ALLGARCH	2014-08-17	6.133	5.944981e+02	109.501754	109.611314	109.499935	109.545799	9.693430e+01	1
USDCNY	fGARCH.ALLGARCH	2014-08-19	6.130	-5.155929e+01	-585.152751	-585.043494	-585.154557	-585.108833	8.410978e+00	1
USDCNY	fGARCH.ALLGARCH	2014-08-20	6.130	-1.929233e+02	-586.176906	-586.067649	-586.178711	-586.132988	3.147199e+01	1
USDCNY	fGARCH.ALLGARCH	2014-08-24	6.140	1.671067e+01	-588.414218	-588.304658	-588.416037	-588.370173	2.721608e+00	1
USDCNY	fGARCH.ALLGARCH	2014-08-25	6.142	2.016595e+01	-590.032967	-589.923710	-590.034773	-589.989049	3.283287e+00	1
USDCNY	fGARCH.ALLGARCH	2014-08-26	6.133	-9.193458e+00	-592.028938	-591.919680	-592.030743	-591.985020	1.499015e+00	1
USDCNY	fGARCH.ALLGARCH	2014-08-27	6.132	9.527845e+01	-586.491601	-586.382343	-586.493406	-586.447683	1.553791e+01	1
USDCNY	fGARCH.ALLGARCH	2014-09-03	6.125	-3.275840e+02	13.412488	13.521745	13.410682	13.456406	5.348311e+01	1
USDCNY	fGARCH.ALLGARCH	2014-09-10	6.119	3.412713e+01	-588.214319	-588.105062	-588.216125	-588.170401	5.577240e+00	1
USDCNY	fGARCH.ALLGARCH	2014-09-11	6.120	1.713551e+02	-585.306314	-585.197057	-585.308120	-585.262397	2.799920e+01	1
USDCNY	fGARCH.ALLGARCH	2014-09-14	6.125	-1.143873e+01	-591.115129	-591.005570	-591.116949	-591.071085	1.867548e+00	1
USDCNY	fGARCH.ALLGARCH	2014-09-15	6.132	6.270890e+01	-587.125551	-587.016294	-587.127357	-587.081633	1.022650e+01	1
USDCNY	fGARCH.ALLGARCH	2014-09-17	6.129	1.185828e+01	-590.965879	-590.856622	-590.967685	-590.921961	1.934781e+00	1
USDCNY	fGARCH.ALLGARCH	2014-09-18	6.127	5.849842e+01	-586.243193	-586.133936	-586.244999	-586.199275	9.547645e+00	1
USDCNY	fGARCH.ALLGARCH	2014-09-22	6.128	-7.554483e+01	-585.523762	-585.414505	-585.525568	-585.479844	1.232781e+01	1
USDCNY	fGARCH.ALLGARCH	2014-09-23	6.124	6.743292e+01	-586.611629	-586.502371	-586.613434	-586.567711	1.101125e+01	1
USDCNY	fGARCH.ALLGARCH	2014-09-24	6.125	-1.361419e+02	-583.665628	-583.556371	-583.667434	-583.621710	2.222725e+01	1
USDCNY	fGARCH.ALLGARCH	2014-09-28	6.117	-1.470848e+00	-589.397050	-589.287490	-589.398869	-589.353005	2.404524e-01	1
USDCNY	fGARCH.ALLGARCH	2014-10-02	6.128	-1.655563e+01	-586.788690	-586.679433	-586.790496	-586.744772	2.701636e+00	1
USDCNY	fGARCH.ALLGARCH	2014-10-05	6.129	1.461850e+01	-590.597425	-590.487865	-590.599244	-590.553380	2.385136e+00	1
USDCNY	fGARCH.ALLGARCH	2014-10-07	6.125	-2.893222e+00	-592.477892	-592.368634	-592.479697	-592.433974	4.723629e-01	1
USDCNY	fGARCH.ALLGARCH	2014-10-13	6.113	6.047961e+01	-587.057935	-586.948978	-587.059727	-587.014143	9.893606e+00	1
USDCNY	fGARCH.ALLGARCH	2014-10-15	6.112	-2.322660e+02	-584.723325	-584.614368	-584.725117	-584.679533	3.800164e+01	1
USDCNY	fGARCH.ALLGARCH	2014-10-28	6.103	5.800710e+01	-589.031088	-588.922131	-589.032880	-588.987295	9.504686e+00	1
USDCNY	fGARCH.ALLGARCH	2014-11-04	6.105	-1.520227e+02	-585.103628	-584.994670	-585.105420	-585.059835	2.490134e+01	1
USDCNY	fGARCH.ALLGARCH	2014-11-07	6.102	3.102281e+01	-590.154705	-590.045748	-590.156497	-590.110913	5.084040e+00	1
USDCNY	fGARCH.ALLGARCH	2014-11-10	6.105	-1.387418e+02	-584.273462	-584.164205	-584.275268	-584.229544	2.272592e+01	1
USDCNY	fGARCH.ALLGARCH	2014-11-20	6.109	-4.671149e+01	-588.176614	-588.067656	-588.178406	-588.132821	7.646340e+00	1
USDCNY	fGARCH.ALLGARCH	2014-11-25	6.126	-3.509017e+01	-588.097661	-587.988704	-588.099453	-588.053869	5.728072e+00	1
USDCNY	fGARCH.ALLGARCH	2014-11-27	6.125	-4.766673e+01	-589.227416	-589.118459	-589.229208	-589.183624	7.782323e+00	1
USDCNY	fGARCH.ALLGARCH	2014-12-02	6.137	-3.559250e+01	-586.845104	-586.736147	-586.846896	-586.801311	5.799658e+00	1
USDCNY	fGARCH.ALLGARCH	2014-12-05	6.140	-1.335011e+00	-590.219456	-590.110499	-590.221248	-590.175664	2.174285e-01	1
USDCNY	fGARCH.ALLGARCH	2014-12-18	6.187	2.127975e+01	-591.310725	-591.201768	-591.312518	-591.266933	3.439430e+00	1
USDCNY	fGARCH.ALLGARCH	2014-12-19	6.205	1.828485e+01	-589.889033	-589.780075	-589.890825	-589.845240	2.946793e+00	1
USDCNY	eGARCH	2014-07-10	2.201	2.758887e+00	-4.752441	-4.656841	-4.753830	-4.714013	1.253470e+00	1
USDCNY	gjrGARCH	2014-07-10	2.201	2.894085e+00	-4.702450	-4.606850	-4.703839	-4.664022	1.314895e+00	1
USDCNY	iGARCH	2014-07-10	2.201	2.988228e+00	-4.673441	-4.605156	-4.674157	-4.645993	1.357668e+00	1
USDJPY	fGARCH.NGARCH	2013-05-20	102.872	1.639729e+20	126.895461	127.031657	126.892687	126.950201	1.593951e+18	1
USDJPY	fGARCH.NGARCH	2013-06-16	95.106	-2.728130e+05	179.131969	179.268541	179.129175	179.186867	2.868516e+03	1
USDJPY	fGARCH.NGARCH	2013-06-17	95.753	3.511368e+02	10.570756	10.706952	10.567983	10.625496	3.667111e+00	1
USDJPY	fGARCH.NGARCH	2013-06-19	98.239	4.076553e+124	740.361014	740.497210	740.358240	740.415754	4.149628e+122	1
USDJPY	fGARCH.NGARCH	2013-07-01	100.438	4.397652e+23	-244.819452	-244.683255	-244.822225	-244.764711	4.378474e+21	1
USDJPY	fGARCH.NGARCH	2013-07-22	100.170	-7.099425e+16	107.520826	107.657022	107.518052	107.575566	7.087376e+14	1
USDJPY	fGARCH.APARCH	2013-02-07	93.093	-3.970675e+14	-210.537651	-210.401828	-210.540404	-210.483067	4.265278e+12	1
USDJPY	fGARCH.APARCH	2013-03-29	94.255	1.067074e+03	-571.141577	-570.936720	-571.147717	-571.059231	1.132114e+01	1
USDJPY	fGARCH.APARCH	2013-05-13	102.261	1.875536e+63	-401.564171	-401.441594	-401.566428	-401.514904	1.834068e+61	1
USDJPY	fGARCH.APARCH	2013-06-12	95.930	-1.338837e+49	118.941807	119.091623	118.938467	119.002021	1.395639e+47	1
USDJPY	fGARCH.ALLGARCH	2013-04-08	98.639	2.419383e+10	-45.341071	-45.164015	-45.345691	-45.269908	2.452765e+08	1
USDJPY	fGARCH.ALLGARCH	2013-04-14	97.623	1.365824e+02	9.689241	9.866784	9.684586	9.760608	1.399080e+00	1
USDJPY	fGARCH.ALLGARCH	2013-05-15	101.850	1.719010e+30	-497.287445	-497.124010	-497.291401	-497.221757	1.687786e+28	1
USDJPY	fGARCH.ALLGARCH	2013-06-19	96.211	-8.650911e+03	78.994799	79.117376	78.992542	79.044066	8.991603e+01	1
USDJPY	fGARCH.ALLGARCH	2013-12-03	103.369	3.656304e+138	-201.516514	-201.352628	-201.520499	-201.450637	3.537137e+136	1
USDJPY	fGARCH.ALLGARCH	2013-12-12	103.077	-3.572408e+44	285.951103	286.128646	285.946448	286.022470	3.465767e+42	1
USDJPY	eGARCH	2013-03-19	94.770	2.936350e+60	155.742660	155.919716	155.738040	155.813823	3.098396e+58	1
USDJPY	eGARCH	2013-04-07	99.016	-1.249428e+80	167.045855	167.196083	167.042490	167.106242	1.261845e+78	1
USDJPY	eGARCH	2013-04-14	97.623	-5.344121e+15	115.987973	116.138202	115.984609	116.048361	5.474244e+13	1
USDJPY	eGARCH	2013-05-13	102.261	1.483098e+63	161.813922	161.922879	161.812130	161.857714	1.450307e+61	1
USDJPY	eGARCH	2013-06-16	95.106	2.867306e+54	123.668672	123.805244	123.665878	123.723570	3.014853e+52	1
USDJPY	eGARCH	2013-11-18	100.333	-1.192013e+13	283.354744	283.491693	283.351929	283.409799	1.188057e+11	1
USDJPY	apARCH	2013-01-29	90.990	-1.175138e+50	-1305.505004	-1305.341568	-1305.508959	-1305.439315	1.291503e+48	1
USDJPY	apARCH	2013-03-15	95.160	-1.758223e+61	315.688639	315.824835	315.685866	315.743379	1.847649e+59	1
USDJPY	apARCH	2013-04-04	95.817	6.156224e+02	8.903971	9.094646	8.898637	8.980607	6.424981e+00	1
USDJPY	apARCH	2013-04-09	99.694	-7.412985e+02	-1357.528473	-1357.392277	-1357.531246	-1357.473733	7.435739e+00	1
USDJPY	apARCH	2013-04-17	97.640	-4.147166e+22	-1334.100214	-1333.950398	-1334.103553	-1334.039999	4.247405e+20	1
USDJPY	apARCH	2013-05-09	101.949	-3.960522e+122	494.605046	494.727623	494.602789	494.654312	3.884807e+120	1
USDJPY	apARCH	2013-05-14	102.760	6.892843e+01	-1352.815761	-1352.652325	-1352.819717	-1352.750072	6.707710e-01	1

6.6.1.4 : Table summary

6.6.2 Selected Models

## selected models' filtered hi-lo price.
hl <- united.fx2 %>% 
  separate(Type, c('Cur', 'Type')) %>% 
  dplyr::filter(Type == 'Hi'|Type == 'Lo') %>% dplyr::select(-Cur, -Type)

acc <- hl %>% 
  ddply(.(.id, Model), summarise, 
        MSE = mean((Price.T1 - Price)^2), 
        n = length(Price), 
        AIC.MSE = (-2*MSE)/n+2*4/n, 
        MSE.AIC = mean((Akaike - mean(Akaike))^2),
        Akaike = mean(Akaike), 
        Bayes = mean(Bayes), 
        Shibata = mean(Shibata), 
        Hannan.Quinn = mean(Hannan.Quinn)) %>% 
  tbl_df %>% mutate(MSE = round(MSE, 7))

Hi-Lo Price Summary : Selected Models

.id	Model	MSE	n	AIC.MSE	MSE.AIC	Akaike	Bayes	Shibata	Hannan.Quinn
USD/AUD
USDAUD	sGARCH	3.000000e-07	1118	7.155600e-03	1.582012e-01	-7.455870	-7.377139	-7.456862	-7.424223
USDAUD	fGARCH.GARCH	3.000000e-07	1118	7.155600e-03	1.581702e-01	-7.455926	-7.377194	-7.456917	-7.424279
USDAUD	fGARCH.TGARCH	3.000000e-06	1118	7.155600e-03	7.782652e-01	-7.170306	-7.077921	-7.171647	-7.133171
USDAUD	fGARCH.NGARCH	1.924000e-03	1118	7.152200e-03	8.292556e+03	-23.550094	-23.457709	-23.551435	-23.512959
USDAUD	fGARCH.NAGARCH	5.000000e-07	1118	7.155600e-03	1.723509e-01	-7.462533	-7.370148	-7.463874	-7.425397
USDAUD	fGARCH.GJRGARCH	7.000000e-07	1118	7.155600e-03	1.704597e-01	-7.453286	-7.360901	-7.454627	-7.416150
USDAUD	gjrGARCH	7.000000e-07	1118	7.155600e-03	1.720178e-01	-7.459266	-7.366882	-7.460608	-7.422131
USDAUD	iGARCH	8.000000e-07	1118	7.155600e-03	1.664171e-01	-7.455925	-7.390847	-7.456620	-7.429766
USDAUD	csGARCH	5.000000e-07	1118	7.155600e-03	1.664264e-01	-7.438474	-7.332436	-7.440219	-7.395851
USD/CAD
USDEUR	sGARCH	5.000000e-07	1118	7.155600e-03	2.925489e-01	-8.487218	-8.404988	-8.488301	-8.454165
USDEUR	fGARCH.GARCH	5.000000e-07	1118	7.155600e-03	2.918912e-01	-8.487353	-8.405123	-8.488435	-8.454299
USDEUR	fGARCH.TGARCH	1.300000e-06	1118	7.155600e-03	4.576922e-01	-8.317263	-8.221381	-8.318710	-8.278722
USDEUR	fGARCH.NGARCH	1.740288e+33	1118	-3.113216e+30	1.049421e+04	-26.150349	-26.054466	-26.151795	-26.111808
USDEUR	fGARCH.NAGARCH	5.000000e-07	1118	7.155600e-03	6.102942e+01	-8.258624	-8.162741	-8.260070	-8.220082
USDEUR	fGARCH.GJRGARCH	5.000000e-07	1118	7.155600e-03	2.906279e-01	-8.489274	-8.393391	-8.490720	-8.450733
USDEUR	gjrGARCH	5.000000e-07	1118	7.155600e-03	2.859653e-01	-8.508256	-8.412373	-8.509702	-8.469715
USDEUR	iGARCH	5.000000e-07	1118	7.155600e-03	2.872873e-01	-8.485325	-8.416749	-8.486097	-8.457760
USDEUR	csGARCH	5.000000e-07	1118	7.155600e-03	2.670724e-01	-8.476752	-8.367216	-8.478615	-8.432723
USD/CHF
USDGBP	sGARCH	1.000000e-07	1118	7.155600e-03	1.084039e-01	-9.131230	-9.050187	-9.132297	-9.098655
USDGBP	fGARCH.GARCH	1.000000e-07	1118	7.155600e-03	1.090407e-01	-9.129881	-9.048837	-9.130947	-9.097305
USDGBP	fGARCH.TGARCH	1.074226e+144	1118	-1.921692e+141	1.252931e+02	-8.517466	-8.422782	-8.518891	-8.479408
USDGBP	fGARCH.NGARCH	2.250000e-05	1118	7.155600e-03	1.216355e+03	-10.656341	-10.561658	-10.657767	-10.618284
USDGBP	fGARCH.NAGARCH	1.000000e-07	1118	7.155600e-03	8.166163e+01	-8.702257	-8.607573	-8.703682	-8.664199
USDGBP	fGARCH.GJRGARCH	1.000000e-07	1118	7.155600e-03	1.101912e-01	-9.142290	-9.047607	-9.143715	-9.104233
USDGBP	gjrGARCH	1.000000e-07	1118	7.155600e-03	1.006238e-01	-9.155120	-9.060437	-9.156546	-9.117063
USDGBP	iGARCH	1.000000e-07	1118	7.155600e-03	1.101402e-01	-9.129211	-9.061807	-9.129973	-9.102118
USDGBP	csGARCH	1.000000e-07	1118	7.155600e-03	8.317250e-02	-9.119910	-9.011586	-9.121746	-9.076369
USD/CNY
USDCHF	sGARCH	1.087000e-04	1118	7.155400e-03	4.092381e-01	-7.722373	-7.641136	-7.723421	-7.689718
USDCHF	fGARCH.GARCH	1.087000e-04	1118	7.155400e-03	4.089882e-01	-7.722128	-7.640891	-7.723176	-7.689473
USDCHF	fGARCH.TGARCH	9.940000e-05	1118	7.155500e-03	2.775534e-01	-7.708387	-7.613494	-7.709795	-7.670243
USDCHF	fGARCH.NGARCH	7.471115e+00	1118	-6.209500e-03	2.008525e+03	-11.047600	-10.952708	-11.049008	-11.009457
USDCHF	fGARCH.NAGARCH	1.055000e-04	1118	7.155400e-03	7.116145e+01	-7.296029	-7.201136	-7.297437	-7.257885
USDCHF	fGARCH.GJRGARCH	1.062000e-04	1118	7.155400e-03	3.705886e-01	-7.748789	-7.653896	-7.750197	-7.710645
USDCHF	gjrGARCH	1.059000e-04	1118	7.155400e-03	3.762108e-01	-7.769725	-7.674832	-7.771133	-7.731581
USDCHF	iGARCH	5.389000e-04	1118	7.154700e-03	6.395539e-01	-7.595948	-7.528367	-7.596690	-7.568783
USDCHF	csGARCH	2.745000e-04	1118	7.155100e-03	4.938373e-01	-7.657306	-7.548758	-7.659127	-7.613673
USD/EUR
USDCAD	sGARCH	5.000000e-07	1118	7.155600e-03	1.747242e-01	-8.129379	-8.047234	-8.130458	-8.096360
USDCAD	fGARCH.GARCH	6.000000e-07	1118	7.155600e-03	1.748543e-01	-8.129428	-8.047283	-8.130507	-8.096409
USDCAD	fGARCH.TGARCH	1.500000e-06	1118	7.155600e-03	7.456206e-01	-7.885495	-7.789697	-7.886938	-7.846988
USDCAD	fGARCH.NGARCH	1.532912e+120	1118	-2.742240e+117	9.787606e+03	-28.329640	-28.233843	-28.331083	-28.291134
USDCAD	fGARCH.NAGARCH	4.000000e-07	1118	7.155600e-03	1.743589e-01	-8.138303	-8.042505	-8.139746	-8.099796
USDCAD	fGARCH.GJRGARCH	4.000000e-07	1118	7.155600e-03	1.724530e-01	-8.129573	-8.033775	-8.131016	-8.091066
USDCAD	gjrGARCH	4.000000e-07	1118	7.155600e-03	1.710668e-01	-8.134137	-8.038339	-8.135580	-8.095630
USDCAD	iGARCH	7.000000e-07	1118	7.155600e-03	1.750959e-01	-8.129990	-8.061499	-8.130760	-8.102460
USDCAD	csGARCH	6.000000e-07	1118	7.155600e-03	1.736392e-01	-8.113110	-8.003659	-8.114969	-8.069115
USD/GBP
USDCNY	sGARCH	1.162900e-03	1118	7.153600e-03	1.968217e+00	-6.184628	-6.094604	-6.185916	-6.148443
USDCNY	fGARCH.GARCH	7.262000e-04	1118	7.154300e-03	1.971790e+00	-6.183813	-6.093790	-6.185101	-6.147628
USDCNY	fGARCH.TGARCH	1.899600e-03	1118	7.152200e-03	2.815785e+00	-5.980778	-5.877112	-5.982459	-5.939109
USDCNY	fGARCH.NGARCH	3.871562e+02	1118	-6.854315e-01	1.107828e+04	-26.060588	-25.956922	-26.062269	-26.018919
USDCNY	fGARCH.NAGARCH	6.530016e+02	1118	-1.161005e+00	5.275165e+01	-5.777868	-5.674202	-5.779549	-5.736199
USDCNY	fGARCH.GJRGARCH	3.887800e-02	1118	7.086100e-03	1.199275e+01	-6.062658	-5.958992	-6.064339	-6.020990
USDCNY	gjrGARCH	1.029600e-03	1118	7.153800e-03	1.941339e+00	-6.212800	-6.109134	-6.214481	-6.171131
USDCNY	iGARCH	1.480000e-03	1118	7.153000e-03	2.135927e+00	-6.120921	-6.044541	-6.121869	-6.090220
USDCNY	csGARCH	1.245800e-03	1118	7.153400e-03	2.214865e+00	-6.139775	-6.022466	-6.141902	-6.092623
USD/JPY
USDJPY	sGARCH	1.281240e-02	1118	7.132700e-03	1.660750e-01	1.453319	1.543812	1.451996	1.489692
USDJPY	fGARCH.GARCH	1.296530e-02	1118	7.132400e-03	1.657860e-01	1.453661	1.544154	1.452338	1.490034
USDJPY	fGARCH.TGARCH	1.128230e-02	1118	7.135500e-03	2.235525e-01	1.480725	1.584860	1.479007	1.522582
USDJPY	fGARCH.NGARCH	1.486430e+246	1118	-2.659087e+243	5.560993e+03	-7.128731	-7.024596	-7.130449	-7.086874
USDJPY	fGARCH.NAGARCH	1.004380e-02	1118	7.137700e-03	1.724612e-01	1.435101	1.539237	1.433383	1.476959
USDJPY	fGARCH.GJRGARCH	1.179720e-02	1118	7.134500e-03	1.692636e-01	1.448632	1.552768	1.446915	1.490490
USDJPY	gjrGARCH	1.132000e-02	1118	7.135400e-03	1.760297e-01	1.442378	1.546513	1.440660	1.484235
USDJPY	iGARCH	1.267330e-02	1118	7.133000e-03	1.680264e-01	1.451435	1.528286	1.450454	1.482325
USDJPY	csGARCH	1.842660e-02	1118	7.122700e-03	1.613351e-01	1.461124	1.578902	1.458959	1.508465

6.6.2.1A : Table summary

Hi-Lo Price Summary : Selected Models

Model	MSE	n	AIC.MSE	MSE.AIC	Akaike	Bayes	Shibata	Hannan.Quinn
sGARCH	2.012200e-03	7826	1.021700e-03	11.79482	-6.522483	-6.438783	-6.523608	-6.488839
fGARCH.GARCH	1.971700e-03	7826	1.021700e-03	11.79515	-6.522124	-6.438423	-6.523249	-6.488480
fGARCH.TGARCH	1.534609e+143	7826	-3.921821e+139	29.35350	-6.299853	-6.202504	-6.301347	-6.260723
fGARCH.NGARCH	2.123471e+245	7826	-5.426709e+241	6988.71934	-18.989049	-18.891700	-18.990544	-18.949919
fGARCH.NAGARCH	9.328739e+01	7826	-2.281810e-02	48.93661	-6.314359	-6.217010	-6.315853	-6.275229
fGARCH.GJRGARCH	7.254700e-03	7826	1.020400e-03	13.24431	-6.511034	-6.413685	-6.512529	-6.471904
gjrGARCH	1.779600e-03	7826	1.021800e-03	11.80858	-6.542418	-6.445069	-6.543913	-6.503288
iGARCH	2.099200e-03	7826	1.021700e-03	11.81105	-6.495126	-6.425075	-6.495937	-6.466969
csGARCH	2.849800e-03	7826	1.021500e-03	11.80904	-6.497743	-6.386746	-6.499660	-6.453127

6.6.2.1B : Table summary

Hi-Lo Price Summary : Selected Models

Model	n
sGARCH	1
fGARCH.GARCH	1
fGARCH.TGARCH	2
fGARCH.NGARCH	45
fGARCH.NAGARCH	7
fGARCH.GJRGARCH	2
gjrGARCH	1
iGARCH	6
csGARCH	3

6.6.2.1C : Table summary

Hi-Lo Price Summary : Selected Models

.id	Model	Date	Price	Price.T1	Akaike	Bayes	Shibata	Hannan.Quinn	diff	se
USDAUD	fGARCH.NGARCH	2013-06-27	1.077	2.542027e+00	-590.320340	-590.197426	-590.322615	-590.270933	2.360285e+00	1
USDEUR	fGARCH.NGARCH	2015-03-02	0.890	-4.015994e+07	83.346290	83.510176	83.342305	83.412167	4.512353e+07	1
USDEUR	fGARCH.NGARCH	2015-06-04	0.887	-1.394863e+18	-545.380537	-545.244340	-545.383310	-545.325796	1.572562e+18	1
USDEUR	fGARCH.NGARCH	2015-06-24	0.891	1.892803e+10	77.586765	77.722962	77.583992	77.641506	2.124358e+10	1
USDGBP	fGARCH.TGARCH	2014-06-19	0.586	-3.465523e+73	364.832355	365.037213	364.826216	364.914701	5.913861e+73	1
USDGBP	fGARCH.NGARCH	2014-06-19	0.586	4.316118e-01	-160.018385	-159.813528	-160.024525	-159.936039	7.365389e-01	1
USDCHF	sGARCH	2015-01-16	0.850	1.189676e+00	-6.687989	-6.606271	-6.689007	-6.655145	1.399619e+00	1
USDCHF	fGARCH.GARCH	2015-01-16	0.850	1.189676e+00	-6.687989	-6.606271	-6.689007	-6.655145	1.399619e+00	1
USDCHF	fGARCH.TGARCH	2015-01-16	0.850	1.182560e+00	-6.882116	-6.786779	-6.883495	-6.843798	1.391247e+00	1
USDCHF	fGARCH.NGARCH	2015-01-16	0.850	1.182556e+00	-6.811955	-6.716617	-6.813334	-6.773637	1.391243e+00	1
USDCHF	fGARCH.NGARCH	2015-09-07	0.970	-8.823318e+01	-587.029347	-586.920390	-587.031140	-586.985555	9.096204e+01	1
USDCHF	fGARCH.NGARCH	2015-10-30	0.991	-1.889325e+01	-584.267632	-584.158374	-584.269437	-584.223714	1.906483e+01	1
USDCHF	fGARCH.NAGARCH	2015-01-16	0.850	1.188451e+00	-6.758750	-6.663413	-6.760129	-6.720432	1.398178e+00	1
USDCHF	fGARCH.GJRGARCH	2015-01-16	0.850	1.189203e+00	-6.775060	-6.679723	-6.776439	-6.736742	1.399062e+00	1
USDCHF	gjrGARCH	2015-01-16	0.850	1.187461e+00	-6.834457	-6.739119	-6.835835	-6.796138	1.397013e+00	1
USDCHF	iGARCH	2015-01-16	0.850	1.189656e+00	-6.696311	-6.628212	-6.697021	-6.668940	1.399595e+00	1
USDCHF	iGARCH	2015-01-20	0.869	1.169574e+00	-6.632037	-6.563939	-6.632748	-6.604667	1.345885e+00	1
USDCHF	iGARCH	2015-01-21	0.851	5.536845e-01	-6.599117	-6.531019	-6.599827	-6.571747	6.506281e-01	1
USDCHF	iGARCH	2015-01-22	0.853	1.132264e+00	-6.569994	-6.501896	-6.570705	-6.542624	1.327390e+00	1
USDCHF	iGARCH	2015-01-27	0.894	6.896106e-01	-6.470927	-6.402829	-6.471637	-6.443557	7.713765e-01	1
USDCHF	iGARCH	2015-02-02	0.920	7.319616e-01	-6.350835	-6.255235	-6.352225	-6.312407	7.956105e-01	1
USDCHF	csGARCH	2015-01-16	0.850	1.193636e+00	-6.688153	-6.579196	-6.689945	-6.644361	1.404278e+00	1
USDCHF	csGARCH	2015-01-22	0.853	1.141360e+00	-6.534724	-6.425767	-6.536516	-6.490932	1.338054e+00	1
USDCHF	csGARCH	2015-01-23	0.868	6.200740e-01	-6.493151	-6.384194	-6.494943	-6.449359	7.143710e-01	1
USDCAD	fGARCH.NGARCH	2015-03-29	1.270	-6.542943e+22	-529.240306	-529.131049	-529.242112	-529.196389	5.151924e+22	1
USDCAD	fGARCH.NGARCH	2015-07-21	1.305	4.139802e+61	-435.142670	-435.006474	-435.145443	-435.087930	3.172262e+61	1
USDCNY	fGARCH.NGARCH	2014-07-17	6.192	-5.016306e+02	-585.712986	-585.631043	-585.714011	-585.680047	8.101269e+01	1
USDCNY	fGARCH.NGARCH	2014-07-20	6.195	1.194381e+01	-589.430373	-589.348203	-589.431406	-589.397340	1.927975e+00	1
USDCNY	fGARCH.NGARCH	2014-07-22	6.189	1.945038e+01	-591.466725	-591.384782	-591.467750	-591.433786	3.142734e+00	1
USDCNY	fGARCH.NGARCH	2014-07-23	6.182	-3.637318e+01	-588.553531	-588.471588	-588.554557	-588.520593	5.883724e+00	1
USDCNY	fGARCH.NGARCH	2014-07-27	6.176	4.872521e+01	-587.187420	-587.105250	-587.188453	-587.154387	7.889444e+00	1
USDCNY	fGARCH.NGARCH	2014-07-31	6.163	2.769268e+01	-590.455881	-590.373938	-590.456907	-590.422943	4.493377e+00	1
USDCNY	fGARCH.NGARCH	2014-08-03	6.168	3.201427e+01	-587.733648	-587.651478	-587.734681	-587.700615	5.190381e+00	1
USDCNY	fGARCH.NGARCH	2014-08-05	6.153	1.853196e+01	-589.664961	-589.583018	-589.665987	-589.632023	3.011858e+00	1
USDCNY	fGARCH.NGARCH	2014-08-06	6.147	2.635122e+01	-591.728569	-591.646626	-591.729595	-591.695631	4.286842e+00	1
USDCNY	fGARCH.NGARCH	2014-08-12	6.144	4.740305e+01	-587.300349	-587.218406	-587.301374	-587.267410	7.715340e+00	1
USDCNY	fGARCH.NGARCH	2014-08-13	6.142	8.825968e+00	-589.224653	-589.142710	-589.225679	-589.191715	1.436986e+00	1
USDCNY	fGARCH.NGARCH	2014-08-14	6.136	4.872331e+01	-586.351874	-586.269931	-586.352899	-586.318935	7.940565e+00	1
USDCNY	fGARCH.NGARCH	2014-08-19	6.130	-1.240483e+01	-590.789977	-590.708034	-590.791003	-590.757039	2.023627e+00	1
USDCNY	fGARCH.NGARCH	2014-08-20	6.130	9.161532e+00	-592.227353	-592.145410	-592.228379	-592.194415	1.494540e+00	1
USDCNY	fGARCH.NGARCH	2014-08-21	6.141	-1.525661e+01	-590.144127	-590.062184	-590.145153	-590.111189	2.484385e+00	1
USDCNY	fGARCH.NGARCH	2014-08-24	6.140	-3.247607e+01	-589.174302	-589.092132	-589.175335	-589.141269	5.289262e+00	1
USDCNY	fGARCH.NGARCH	2014-08-25	6.142	6.174800e+01	-572.956479	-572.874536	-572.957505	-572.923541	1.005340e+01	1
USDCNY	fGARCH.NGARCH	2014-08-26	6.133	9.738678e+01	-587.251542	-587.169599	-587.252568	-587.218604	1.587914e+01	1
USDCNY	fGARCH.NGARCH	2014-08-31	6.129	2.545583e+02	-584.923023	-584.840853	-584.924056	-584.889989	4.153341e+01	1
USDCNY	fGARCH.NGARCH	2014-09-01	6.132	1.596999e+02	-584.161053	-584.079110	-584.162079	-584.128115	2.604369e+01	1
USDCNY	fGARCH.NGARCH	2014-09-02	6.131	-1.989882e+01	-589.399865	-589.317922	-589.400891	-589.366927	3.245608e+00	1
USDCNY	fGARCH.NGARCH	2014-09-04	6.128	-2.866168e+01	-585.515480	-585.433537	-585.516505	-585.482541	4.677168e+00	1
USDCNY	fGARCH.NGARCH	2014-09-08	6.122	-2.517129e+01	-587.872377	-587.790434	-587.873402	-587.839438	4.111612e+00	1
USDCNY	fGARCH.NGARCH	2014-09-11	6.120	1.708482e+01	-588.380157	-588.298214	-588.381183	-588.347219	2.791637e+00	1
USDCNY	fGARCH.NGARCH	2014-09-14	6.125	-7.626137e+01	-589.072288	-588.990119	-589.073322	-589.039255	1.245084e+01	1
USDCNY	fGARCH.NGARCH	2014-09-16	6.129	-1.759094e+02	-585.597533	-585.515590	-585.598558	-585.564594	2.870116e+01	1
USDCNY	fGARCH.NGARCH	2014-10-01	6.128	-1.146657e+02	-584.091459	-584.009516	-584.092485	-584.058521	1.871177e+01	1
USDCNY	fGARCH.NGARCH	2014-10-06	6.129	-2.283202e+01	-579.908511	-579.826568	-579.909537	-579.875573	3.725243e+00	1
USDCNY	fGARCH.NGARCH	2014-10-07	6.125	5.146397e+01	-565.845084	-565.763141	-565.846110	-565.812146	8.402281e+00	1
USDCNY	fGARCH.NGARCH	2014-10-09	6.120	6.182692e+01	-583.758544	-583.676826	-583.759562	-583.725700	1.010244e+01	1
USDCNY	fGARCH.NGARCH	2014-11-26	6.123	6.187566e+01	-583.601907	-583.520189	-583.602924	-583.569062	1.010545e+01	1
USDCNY	fGARCH.NAGARCH	2014-07-24	6.182	-3.603032e+02	14.561667	14.643610	14.560642	14.594606	5.828262e+01	1
USDCNY	fGARCH.NAGARCH	2014-07-31	6.163	-3.531901e+02	14.522470	14.604413	14.521444	14.555409	5.730814e+01	1
USDCNY	fGARCH.NAGARCH	2014-08-04	6.161	-3.492923e+02	14.548440	14.630382	14.547414	14.581378	5.669409e+01	1
USDCNY	fGARCH.NAGARCH	2014-08-26	6.133	4.865151e+00	104.667516	104.749459	104.666490	104.700454	7.932742e-01	1
USDCNY	fGARCH.NAGARCH	2014-09-04	6.128	4.796821e+02	172.167572	172.249515	172.166546	172.200510	7.827710e+01	1
USDCNY	fGARCH.NAGARCH	2014-10-19	6.113	-3.344848e+02	98.972743	99.054686	98.971717	99.005682	5.471696e+01	1
USDCNY	fGARCH.GJRGARCH	2014-09-01	6.132	1.263740e+01	98.054293	98.136236	98.053267	98.087231	2.060893e+00	1
USDJPY	fGARCH.NGARCH	2013-05-20	102.872	1.639729e+20	126.895461	127.031657	126.892687	126.950201	1.593951e+18	1
USDJPY	fGARCH.NGARCH	2013-06-16	95.106	-2.728130e+05	179.131969	179.268541	179.129175	179.186867	2.868516e+03	1
USDJPY	fGARCH.NGARCH	2013-06-19	98.239	4.076553e+124	740.361014	740.497210	740.358240	740.415754	4.149628e+122	1
USDJPY	fGARCH.NGARCH	2013-07-22	100.170	-7.099425e+16	107.520826	107.657022	107.518052	107.575566	7.087376e+14	1

6.6.2.1D : Table summary

## selected models' filtered hi-lo price.
hl <- united.fx3 %>% 
  separate(Type, c('Cur', 'Type')) %>% 
  dplyr::filter(Type == 'Hi'|Type == 'Lo') %>% dplyr::select(-Cur, -Type)

acc <- hl %>% 
  ddply(.(.id, Model), summarise, 
        MSE = mean((Price.T1 - Price)^2), 
        n = length(Price), 
        AIC.MSE = (-2*MSE)/n+2*4/n, 
        MSE.AIC = mean((Akaike - mean(Akaike))^2),
        Akaike = mean(Akaike), 
        Bayes = mean(Bayes), 
        Shibata = mean(Shibata), 
        Hannan.Quinn = mean(Hannan.Quinn)) %>% 
  tbl_df %>% mutate(MSE = round(MSE, 7))

Hi-Lo Price Summary : Selected Models

.id	Model	MSE	n	AIC.MSE	MSE.AIC	Akaike	Bayes	Shibata	Hannan.Quinn
USD/AUD
USDAUD	sGARCH	0.0000003	982	0.0081466	1.664181e-01	-7.435101	-7.357380	-7.436061	-7.403860
USDAUD	fGARCH.GARCH	0.0000003	982	0.0081466	1.663901e-01	-7.435192	-7.357471	-7.436152	-7.403951
USDAUD	fGARCH.TGARCH	0.0000032	982	0.0081466	7.946351e-01	-7.137939	-7.046565	-7.139246	-7.101210
USDAUD	fGARCH.NGARCH	0.0000028	982	0.0081466	8.381684e+03	-24.282136	-24.190763	-24.283443	-24.245407
USDAUD	fGARCH.NAGARCH	0.0000004	982	0.0081466	1.819828e-01	-7.441341	-7.349967	-7.442647	-7.404612
USDAUD	fGARCH.GJRGARCH	0.0000008	982	0.0081466	1.800733e-01	-7.432244	-7.340870	-7.433550	-7.395515
USDAUD	gjrGARCH	0.0000008	982	0.0081466	1.818250e-01	-7.438332	-7.346958	-7.439639	-7.401603
USDAUD	iGARCH	0.0000008	982	0.0081466	1.757568e-01	-7.434918	-7.370851	-7.435586	-7.409165
USDAUD	csGARCH	0.0000005	982	0.0081466	1.757037e-01	-7.417554	-7.312527	-7.419260	-7.375337
USD/CAD
USDEUR	sGARCH	0.0000005	982	0.0081466	2.759457e-01	-8.430450	-8.348496	-8.431525	-8.397508
USDEUR	fGARCH.GARCH	0.0000005	982	0.0081466	2.753612e-01	-8.430711	-8.348757	-8.431786	-8.397769
USDEUR	fGARCH.TGARCH	0.0000013	982	0.0081466	4.464373e-01	-8.252996	-8.157389	-8.254433	-8.214566
USDEUR	fGARCH.NGARCH	0.0000040	982	0.0081466	1.048876e+04	-26.197042	-26.101434	-26.198479	-26.158611
USDEUR	fGARCH.NAGARCH	0.0000005	982	0.0081466	6.938555e+01	-8.169526	-8.073919	-8.170964	-8.131096
USDEUR	fGARCH.GJRGARCH	0.0000004	982	0.0081466	2.738930e-01	-8.432666	-8.337058	-8.434103	-8.394235
USDEUR	gjrGARCH	0.0000004	982	0.0081466	2.702596e-01	-8.453055	-8.357447	-8.454492	-8.414624
USDEUR	iGARCH	0.0000005	982	0.0081466	2.703513e-01	-8.428586	-8.360285	-8.429351	-8.401132
USDEUR	csGARCH	0.0000005	982	0.0081466	2.500170e-01	-8.421820	-8.312559	-8.423673	-8.377901
USD/CHF
USDGBP	sGARCH	0.0000001	982	0.0081466	1.019276e-01	-9.094116	-9.014148	-9.095149	-9.061974
USDGBP	fGARCH.GARCH	0.0000001	982	0.0081466	1.018041e-01	-9.094048	-9.014080	-9.095081	-9.061906
USDGBP	fGARCH.TGARCH	0.0000002	982	0.0081466	4.762497e-01	-8.820149	-8.726542	-8.821536	-8.782524
USDGBP	fGARCH.NGARCH	0.0000002	982	0.0081466	1.012082e+03	-10.111457	-10.017850	-10.112844	-10.073832
USDGBP	fGARCH.NAGARCH	0.0000001	982	0.0081466	2.913131e+01	-8.864259	-8.770652	-8.865646	-8.826634
USDGBP	fGARCH.GJRGARCH	0.0000001	982	0.0081466	1.044637e-01	-9.105787	-9.012180	-9.107174	-9.068162
USDGBP	gjrGARCH	0.0000001	982	0.0081466	9.399530e-02	-9.119260	-9.025653	-9.120647	-9.081635
USDGBP	iGARCH	0.0000001	982	0.0081466	1.029364e-01	-9.093255	-9.026926	-9.093987	-9.066594
USDGBP	csGARCH	0.0000001	982	0.0081466	7.455580e-02	-9.084697	-8.977451	-9.086491	-9.041590
USD/CNY
USDCHF	sGARCH	0.0000060	982	0.0081466	3.910510e-01	-7.681502	-7.599733	-7.682564	-7.648634
USDCHF	fGARCH.GARCH	0.0000060	982	0.0081466	3.908978e-01	-7.681312	-7.599544	-7.682375	-7.648444
USDCHF	fGARCH.TGARCH	0.0000005	982	0.0081466	2.683395e-01	-7.669874	-7.574449	-7.671299	-7.631517
USDCHF	fGARCH.NGARCH	0.0000051	982	0.0081466	1.610019e+03	-10.367573	-10.272148	-10.368997	-10.329215
USDCHF	fGARCH.NAGARCH	0.0000033	982	0.0081466	8.087329e+01	-7.184891	-7.089466	-7.186315	-7.146533
USDCHF	fGARCH.GJRGARCH	0.0000036	982	0.0081466	3.543108e-01	-7.708629	-7.613204	-7.710053	-7.670271
USDCHF	gjrGARCH	0.0000044	982	0.0081466	3.651351e-01	-7.727887	-7.632462	-7.729312	-7.689530
USDCHF	iGARCH	0.0001553	982	0.0081463	6.234484e-01	-7.552138	-7.484025	-7.552891	-7.524759
USDCHF	csGARCH	0.0000447	982	0.0081465	4.634969e-01	-7.622024	-7.512943	-7.623863	-7.578177
USD/EUR
USDCAD	sGARCH	0.0000005	982	0.0081466	1.825993e-01	-8.109976	-8.028439	-8.111038	-8.077201
USDCAD	fGARCH.GARCH	0.0000005	982	0.0081466	1.827439e-01	-8.109983	-8.028446	-8.111045	-8.077209
USDCAD	fGARCH.TGARCH	0.0000015	982	0.0081466	7.961756e-01	-7.853303	-7.758113	-7.854726	-7.815040
USDCAD	fGARCH.NGARCH	0.0000152	982	0.0081466	1.036153e+04	-29.468386	-29.373195	-29.469809	-29.430123
USDCAD	fGARCH.NAGARCH	0.0000004	982	0.0081466	1.818049e-01	-8.117968	-8.022777	-8.119391	-8.079705
USDCAD	fGARCH.GJRGARCH	0.0000004	982	0.0081466	1.802579e-01	-8.110214	-8.015024	-8.111637	-8.071951
USDCAD	gjrGARCH	0.0000004	982	0.0081466	1.788733e-01	-8.115061	-8.019870	-8.116484	-8.076798
USDCAD	iGARCH	0.0000006	982	0.0081466	1.832824e-01	-8.110511	-8.042627	-8.111265	-8.083224
USDCAD	csGARCH	0.0000005	982	0.0081466	1.813697e-01	-8.093333	-7.984489	-8.095170	-8.049582
USD/GBP
USDCNY	sGARCH	0.0011614	982	0.0081443	1.651781e+00	-6.331884	-6.240622	-6.333205	-6.295201
USDCNY	fGARCH.GARCH	0.0006728	982	0.0081453	1.649043e+00	-6.331834	-6.240572	-6.333156	-6.295151
USDCNY	fGARCH.TGARCH	0.0020546	982	0.0081425	2.782459e+00	-6.111601	-6.006698	-6.113321	-6.069435
USDCNY	fGARCH.NGARCH	0.2841700	982	0.0075679	1.733471e+03	-9.342278	-9.237375	-9.343998	-9.300112
USDCNY	fGARCH.NAGARCH	0.0004274	982	0.0081458	2.086466e+00	-6.326863	-6.221960	-6.328583	-6.284697
USDCNY	fGARCH.GJRGARCH	0.0009456	982	0.0081447	1.956618e+00	-6.301342	-6.196438	-6.303061	-6.259176
USDCNY	gjrGARCH	0.0010041	982	0.0081446	1.627139e+00	-6.360214	-6.255311	-6.361934	-6.318048
USDCNY	iGARCH	0.0012725	982	0.0081440	1.870693e+00	-6.263319	-6.185699	-6.264295	-6.232119
USDCNY	csGARCH	0.0012875	982	0.0081440	1.932317e+00	-6.282028	-6.163483	-6.284198	-6.234379
USD/JPY
USDJPY	sGARCH	0.0137815	982	0.0081186	1.615589e-01	1.490880	1.582037	1.489538	1.527520
USDJPY	fGARCH.GARCH	0.0137270	982	0.0081187	1.613116e-01	1.491116	1.582272	1.489773	1.527756
USDJPY	fGARCH.TGARCH	0.0122792	982	0.0081216	2.247962e-01	1.520669	1.625467	1.518929	1.562792
USDJPY	fGARCH.NGARCH	0.1207667	982	0.0079007	4.565911e+03	-7.293489	-7.188690	-7.295228	-7.251365
USDJPY	fGARCH.NAGARCH	0.0105250	982	0.0081252	1.679075e-01	1.473158	1.577956	1.471418	1.515281
USDJPY	fGARCH.GJRGARCH	0.0122762	982	0.0081216	1.645223e-01	1.486441	1.591239	1.484701	1.528565
USDJPY	gjrGARCH	0.0118956	982	0.0081224	1.712452e-01	1.480756	1.585554	1.479016	1.522880
USDJPY	iGARCH	0.0135686	982	0.0081190	1.634892e-01	1.489276	1.566791	1.488278	1.520433
USDJPY	csGARCH	0.0205310	982	0.0081048	1.566149e-01	1.498631	1.617071	1.496442	1.546238

6.6.2.2A : Table summary

Hi-Lo Price Summary : Selected Models

Model	MSE	n	AIC.MSE	MSE.AIC	Akaike	Bayes	Shibata	Hannan.Quinn
sGARCH	0.0021357	6874	0.0011632	11.73299	-6.513164	-6.429540	-6.514286	-6.479551
fGARCH.GARCH	0.0020582	6874	0.0011632	11.73306	-6.513138	-6.429514	-6.514260	-6.479525
fGARCH.TGARCH	0.0020486	6874	0.0011632	11.73386	-6.332171	-6.234898	-6.333662	-6.293071
fGARCH.NGARCH	0.0578520	6874	0.0011470	5527.18482	-16.723194	-16.625922	-16.724685	-16.684095
fGARCH.NAGARCH	0.0015653	6874	0.0011634	36.83598	-6.375956	-6.278683	-6.377447	-6.336856
fGARCH.GJRGARCH	0.0018896	6874	0.0011633	11.78332	-6.514920	-6.417648	-6.516411	-6.475821
gjrGARCH	0.0018437	6874	0.0011633	11.75204	-6.533293	-6.436021	-6.534784	-6.494194
iGARCH	0.0021426	6874	0.0011632	11.75602	-6.484779	-6.414803	-6.485586	-6.456651
csGARCH	0.0031235	6874	0.0011629	11.75321	-6.488975	-6.378054	-6.490888	-6.444390

6.6.2.2B : Table summary

Hi-Lo Price Summary : Selected Models

Model	n

6.6.2.2C : Table summary

Hi-Lo Price Summary : Selected Models

.id	Model	Date	Price	Price.T1	Akaike	Bayes	Shibata	Hannan.Quinn	diff	se

6.6.2.2D : Table summary

7 GARCH(1,1)?

I had optimised the mean.model but not yet optimise the variance.model, Binary.com Interview Q1 - Tick-Data-HiLo For Daily Trading (Blooper) has provides an example for GARCH(m,n) comparison while below are the papers studied on the optimal GARCH order.

• Optimal lag order selection for a GARCH model
• Does anything NOT beat the GARCH(1,1)?
• How to choose the order of a GARCH model?

Above article states that the task of jointly determining the ARMA-GARCH orders is difficult…

8 Distribution Model

I set snorm as the default distribution from the comparison of ROI in Binary-Q1⁹. rgarchdist - Distribution:Rugarch Distribution Functions list the available distribution function for rugarch.

Does anything NOT beat the GARCH(1,1)? had compared few GARCH models which are :

• GARCH
• GJR
• EGARCH
• APARCH
• component GARCH
• AVGARCH
• NGARCH
• NAGARCH

with four distributions, the Normal, Skew-Student (Fernandez and Steel version), Normal Inverse Gaussian (NIG) and Johnson’s SU (JSU). The conditional mean was based on an ARMA(2,1) model, while the GARCH order was set at (1,1) and (2,1), giving a total combination of 64 models. To create the rolling forecasts, the ugarchroll() was used…

The author concludes that the normality assumption does not realistically capture the observed market dynamics, and neither does the GARCH(1,1)-N model. There were few models which did not beat it in this application. In fact, higher order GARCH models were shown to provide significant out performance on a range of tail related measures, and distributions such as the NIG and JSU appeared to provide the most realistic representation of the observed dynamics.

The author proof that the matrix relationship¹⁰ among the distribution and models in order to get the best fit model. However there are couple of thesises proof that the best fit model for forex, stocks market is difference.

Here I skipped the distribution section due to above model comparison in section GARCH Models has compare the models… Binary.com Interview Q1 has compare the models as well.

• norm for normal distribution.
• snorm for skew-normal distribution.
• std for student-t distribution.
• sstd for skew-student distribution.
• ged for generalized error distribution.
• sged for skew-generalized error distribution.
• nig for normal inverse gaussian distribution.
• ghyp for generalized hyperbolic distribution.
• jsu for Johnson’s SU distribution.

9 Solver

The article Does anything NOT beat the GARCH(1,1)? using hybrid same with my previous paper Binary.com Interview Q1 where my paper test and choose it since it is best fit for gjrGARCH model.

• nlminb
• solnp
• lbfgs
• gosolnp
• nloptr
• hybrid

10 Review on Binary-Q1

GARCH模型中的ARMA(p,d,q)参数最优化 compare the accuracy of the model and the paper Binary.com Interview Q1 - Tick-Data-HiLo For Daily Trading (Blooper) states the wrong of the staking model in Binary.com Interview Q1 as I use the price as odds price without calculate the loss.¹¹ However, here I try to review on paper Binary.com Interview Q1 to compare the accuracy of prediction.

In order to validate the accuracy of prediction, here I added this section to compare among the models. I added a mean mse for Hi and Lo in order to know the long term accuracy between Hi-Lo since an order stand upon the accuracy of both Hi and Lo. binary-Q1 Multivariate GARCH Models will be another study for both punter and banker.

## read files
fls <- list.files('data', patter = '.snorm.hybrid.rds$')
mds <- llply(fls, function(txt) {
    tryCatch(readRDS(paste0('data/', txt)), 
             error = function(e) cat(paste0('data/', txt, ' error!\n')))
    })

## data/fGARCH.ALLGARCH.Mn.Cl.snorm.hybrid.rds error!
## data/fGARCH.AVGARCH.Mn.Cl.snorm.hybrid.rds error!
## data/fGARCH.NAGARCH.Mn.Cl.snorm.hybrid.rds error!
## data/fGARCH.NGARCH.Mn.Cl.snorm.hybrid.rds error!
## data/fGARCH.TGARCH.Mn.Cl.snorm.hybrid.rds error!

names(mds) <- str_replace_all(fls, '.rds', '')

## measure mse.
mds <- llply(names(mds), function(x) {
  HiLo <- x %>% str_extract_all('Hi.Lo|Lo.Hi|Hi.Cl|Lo.Cl|Op.Hi|
                                 Op.Lo|Op.Cl') %>% unlist
  if (length(HiLo) > 0) {
    dfm <- mds[[x]]
    
    if (HiLo == 'Hi.Lo') {
      dfm %<>% mutate(mse.Hi = mean((Point.Forecast - USDJPY.High)^2), 
                     mse.Lo = mean((forClose - USDJPY.Low)^2)) %>% unique
      
    } else if (HiLo == 'Lo.Hi') {
      dfm %<>% mutate(mse.Lo = mean((Point.Forecast - USDJPY.Low)^2), 
                     mse.Hi = mean((forClose - USDJPY.High)^2)) %>% unique

    } else if (HiLo == 'Hi.Cl') {
      dfm %<>% mutate(mse.Hi = mean((Point.Forecast - USDJPY.High)^2), 
                     mse.Cl = mean((forClose - USDJPY.Close)^2)) %>% unique

    } else if (HiLo == 'Lo.Cl') {
      dfm %<>% mutate(mse.Lo = mean((Point.Forecast - USDJPY.Low)^2), 
                     mse.Cl = mean((forClose - USDJPY.Close)^2)) %>% unique

    } else if (HiLo == 'Op.Hi') {
      dfm %<>% mutate(mse.Op = mean((Point.Forecast - USDJPY.Open)^2), 
                     mse.Hi = mean((forClose - USDJPY.High)^2)) %>% unique

    } else if (HiLo == 'Op.Lo') {
      dfm %<>% mutate(mse.Op = mean((Point.Forecast - USDJPY.Open)^2), 
                     mse.Lo = mean((forClose - USDJPY.Low)^2)) %>% unique

    } else if (HiLo == 'Op.Cl') {
      dfm %<>% mutate(mse.Op = mean((Point.Forecast - USDJPY.Open)^2), 
                     mse.Cl = mean((forClose - USDJPY.Close)^2)) %>% unique

    } else {
      stop('No such option.')
    }
    dfm %<>% .[, -c(1:26)] %>% unique
  }
  })
names(mds) <- str_replace_all(fls, '.rds', '')

mds %<>% ldply

mds %>%  mutate(mse.HiLo = (mse.Hi + mse.Lo)/2) %>% 
  kable(caption = 'Summary') %>% 
  kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive')) %>% 
  scroll_box(width = '100%', height = '400px')

Summary

.id	mse.Hi	mse.Lo	mse.Cl	mse.Op	mse.HiLo
csGARCH.Hi.Lo.snorm.hybrid	8.862459e+156	6.305287e-01	NA	NA	4.431230e+156
csGARCH.Lo.Hi.snorm.hybrid	1.572061e+148	6.306860e-01	NA	NA	7.860305e+147
fGARCH.GARCH.Hi.Lo.snorm.hybrid	4.957576e-01	6.443517e-01	NA	NA	5.700547e-01
fGARCH.GARCH.Lo.Hi.snorm.hybrid	4.936336e-01	6.443517e-01	NA	NA	5.689927e-01
fGARCH.GJRGARCH.Lo.Cl.snorm.hybrid	NA	6.479395e-01	0.5550178	NA	NA
fGARCH.GJRGARCH.Op.Cl.snorm.hybrid	NA	NA	0.5550178	0.5727289	NA
fGARCH.NGARCH.Hi.Lo.snorm.hybrid	1.453179e+173	2.913652e+146	NA	NA	7.265897e+172
fGARCH.NGARCH.Lo.Hi.snorm.hybrid	9.098227e+122	2.319707e+03	NA	NA	4.549113e+122
gjrGARCH.EWMA.est.Hi.Lo.snorm.hybrid	2.038695e+144	6.470051e-01	NA	NA	1.019348e+144
gjrGARCH.EWMA.est.Lo.Hi.snorm.hybrid	3.024325e+77	6.470589e-01	NA	NA	1.512162e+77
gjrGARCH.EWMA.fixed.Hi.Lo.snorm.hybrid	2.022071e+63	6.469073e-01	NA	NA	1.011035e+63
gjrGARCH.EWMA.fixed.Lo.Hi.snorm.hybrid	1.238697e+143	6.470093e-01	NA	NA	6.193487e+142
gjrGARCH.Hi.Cl.snorm.hybrid	4.762089e+145	NA	0.5581871	NA	NA
gjrGARCH.Hi.Lo.snorm.hybrid	7.977139e+79	6.469860e-01	NA	NA	3.988569e+79
gjrGARCH.Lo.Cl.snorm.hybrid	NA	1.221226e+229	0.5581871	NA	NA
gjrGARCH.Lo.Hi.snorm.hybrid	4.901055e-01	6.469729e-01	NA	NA	5.685392e-01
gjrGARCH.Op.Cl.snorm.hybrid	NA	NA	0.5581871	0.5748052	NA
gjrGARCH.Op.Hi.snorm.hybrid	3.599090e+109	NA	NA	0.5746087	NA
iGARCH.EWMA.est.Hi.Lo.snorm.hybrid	4.957351e-01	6.556720e-01	NA	NA	5.757036e-01
iGARCH.EWMA.est.Lo.Hi.snorm.hybrid	8.558115e+73	6.556720e-01	NA	NA	4.279058e+73
iGARCH.EWMA.fixed.Hi.Lo.snorm.hybrid	2.888561e+216	6.556720e-01	NA	NA	1.444280e+216
iGARCH.EWMA.fixed.Lo.Hi.snorm.hybrid	4.958495e-01	6.556720e-01	NA	NA	5.757608e-01
iGARCH.Hi.Lo.snorm.hybrid	4.958608e-01	6.556720e-01	NA	NA	5.757664e-01
iGARCH.Lo.Hi.snorm.hybrid	4.957999e-01	6.556720e-01	NA	NA	5.757359e-01
realGARCH.Hi.Lo.snorm.hybrid	9.856535e+05	8.231377e+06	NA	NA	4.608515e+06
realGARCH.Lo.Hi.snorm.hybrid	9.856535e+05	8.231377e+06	NA	NA	4.608515e+06
sGARCH.Hi.Lo.snorm.hybrid	4.998315e-01	6.383346e-01	NA	NA	5.690830e-01
sGARCH.Lo.Hi.snorm.hybrid	4.958049e-01	6.383346e-01	NA	NA	5.670697e-01

Here I filtered the sd < 20% dataset as below.

## read files
fls <- list.files('data', patter = '.snorm.hybrid.rds$')
mds <- llply(fls, function(txt) {
    tryCatch(readRDS(paste0('data/', txt)), 
             error = function(e) cat(paste0('data/', txt, ' error!\n')))
    })

## data/fGARCH.ALLGARCH.Mn.Cl.snorm.hybrid.rds error!
## data/fGARCH.AVGARCH.Mn.Cl.snorm.hybrid.rds error!
## data/fGARCH.NAGARCH.Mn.Cl.snorm.hybrid.rds error!
## data/fGARCH.NGARCH.Mn.Cl.snorm.hybrid.rds error!
## data/fGARCH.TGARCH.Mn.Cl.snorm.hybrid.rds error!

names(mds) <- str_replace_all(fls, '.rds', '')

## measure mse.
mds <- llply(names(mds), function(x) {
  HiLo <- x %>% str_extract_all('Hi.Lo|Lo.Hi|Hi.Cl|Lo.Cl|Op.Hi|
                                 Op.Lo|Op.Cl') %>% unlist
  if (length(HiLo) > 0) {
    dfm <- mds[[x]]
    
    if (HiLo == 'Hi.Lo') {
      dfm %<>% mutate(diff1 = abs(Point.Forecast/USDJPY.High), 
                      se1 = ifelse(diff1 <= 0.8 | diff1 >= 1.25, 1, 0), 
                      diff2 = abs(forClose/USDJPY.Low), 
                      se2 = ifelse(diff2 <= 0.8 | diff2 >= 1.25, 1, 0)
                      ) %>% 
        dplyr::filter(se1 != 1 & se2 != 1) %>% 
        mutate(mse.Hi = mean((Point.Forecast - USDJPY.High)^2), 
               mse.Lo = mean((forClose - USDJPY.Low)^2)) %>% unique
      
    } else if (HiLo == 'Lo.Hi') {
      dfm %<>% mutate(diff1 = abs(Point.Forecast/USDJPY.Low), 
                      se1 = ifelse(diff1 <= 0.8 | diff1 >= 1.25, 1, 0), 
                      diff2 = abs(forClose/USDJPY.High), 
                      se2 = ifelse(diff2 <= 0.8 | diff2 >= 1.25, 1, 0)
                      ) %>% 
        dplyr::filter(se1 != 1 & se2 != 1) %>% 
        mutate(mse.Lo = mean((Point.Forecast - USDJPY.Low)^2), 
               mse.Hi = mean((forClose - USDJPY.High)^2)) %>% unique

    } else if (HiLo == 'Hi.Cl') {
      dfm %<>% mutate(diff1 = abs(Point.Forecast/USDJPY.High), 
                      se1 = ifelse(diff1 <= 0.8 | diff1 >= 1.25, 1, 0), 
                      diff2 = abs(forClose/USDJPY.Close), 
                      se2 = ifelse(diff2 <= 0.8 | diff2 >= 1.25, 1, 0)
                      ) %>% 
        dplyr::filter(se1 != 1 & se2 != 1) %>% 
        mutate(mse.Hi = mean((Point.Forecast - USDJPY.High)^2), 
               mse.Cl = mean((forClose - USDJPY.Close)^2)) %>% unique

    } else if (HiLo == 'Lo.Cl') {
      dfm %<>% mutate(diff1 = abs(Point.Forecast/USDJPY.Low), 
                      se1 = ifelse(diff1 <= 0.8 | diff1 >= 1.25, 1, 0), 
                      diff2 = abs(forClose/USDJPY.Close), 
                      se2 = ifelse(diff2 <= 0.8 | diff2 >= 1.25, 1, 0)
                      ) %>% 
        dplyr::filter(se1 != 1 & se2 != 1) %>% 
        mutate(mse.Lo = mean((Point.Forecast - USDJPY.Low)^2), 
               mse.Cl = mean((forClose - USDJPY.Close)^2)) %>% unique

    } else if (HiLo == 'Op.Hi') {
      dfm %<>% mutate(diff1 = abs(Point.Forecast/USDJPY.Open), 
                      se1 = ifelse(diff1 <= 0.8 | diff1 >= 1.25, 1, 0), 
                      diff2 = abs(forClose/USDJPY.High), 
                      se2 = ifelse(diff2 <= 0.8 | diff2 >= 1.25, 1, 0)
                      ) %>% 
        dplyr::filter(se1 != 1 & se2 != 1) %>% 
        mutate(mse.Op = mean((Point.Forecast - USDJPY.Open)^2), 
               mse.Hi = mean((forClose - USDJPY.High)^2)) %>% unique

    } else if (HiLo == 'Op.Lo') {
      dfm %<>% mutate(diff1 = abs(Point.Forecast/USDJPY.Open), 
                      se1 = ifelse(diff1 <= 0.8 | diff1 >= 1.25, 1, 0), 
                      diff2 = abs(forClose/USDJPY.Low), 
                      se2 = ifelse(diff2 <= 0.8 | diff2 >= 1.25, 1, 0)
                      ) %>% 
        dplyr::filter(se1 != 1 & se2 != 1) %>% 
        mutate(mse.Op = mean((Point.Forecast - USDJPY.Open)^2), 
               mse.Lo = mean((forClose - USDJPY.Low)^2)) %>% unique

    } else if (HiLo == 'Op.Cl') {
      dfm %<>% mutate(diff1 = abs(Point.Forecast/USDJPY.Open), 
                      se1 = ifelse(diff1 <= 0.8 | diff1 >= 1.25, 1, 0), 
                      diff2 = abs(forClose/USDJPY.Close), 
                      se2 = ifelse(diff2 <= 0.8 | diff2 >= 1.25, 1, 0)
                      ) %>% 
        dplyr::filter(se1 != 1 & se2 != 1) %>% 
        mutate(mse.Op = mean((Point.Forecast - USDJPY.Open)^2), 
               mse.Cl = mean((forClose - USDJPY.Close)^2)) %>% unique

    } else {
      stop('No such option.')
    }
    dfm %<>% .[, -c(1:30)] %>% unique
  }
  })
names(mds) <- str_replace_all(fls, '.rds', '')

mds %<>% ldply

mds %>% mutate(mse.HiLo = (mse.Hi + mse.Lo)/2) %>% 
  kable(caption = 'Summary') %>% 
  kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive')) %>% 
  scroll_box(width = '100%', height = '400px')

Summary

.id	mse.Hi	mse.Lo	mse.Cl	mse.Op	mse.HiLo
csGARCH.Hi.Lo.snorm.hybrid	2.0229955	0.6277246	NA	NA	1.3253601
csGARCH.Lo.Hi.snorm.hybrid	2.0196959	0.6328959	NA	NA	1.3262959
fGARCH.GARCH.Hi.Lo.snorm.hybrid	0.4957576	0.6443517	NA	NA	0.5700547
fGARCH.GARCH.Lo.Hi.snorm.hybrid	0.4936336	0.6443517	NA	NA	0.5689927
fGARCH.GJRGARCH.Lo.Cl.snorm.hybrid	NA	0.6479395	0.5550178	NA	NA
fGARCH.GJRGARCH.Op.Cl.snorm.hybrid	NA	NA	0.5550178	0.5727289	NA
fGARCH.NGARCH.Hi.Lo.snorm.hybrid	0.4907338	1.0560979	NA	NA	0.7734159
fGARCH.NGARCH.Lo.Hi.snorm.hybrid	119.9887775	0.7500664	NA	NA	60.3694219
gjrGARCH.EWMA.est.Hi.Lo.snorm.hybrid	0.4877976	0.6448733	NA	NA	0.5663354
gjrGARCH.EWMA.est.Lo.Hi.snorm.hybrid	0.4913398	0.6479219	NA	NA	0.5696308
gjrGARCH.EWMA.fixed.Hi.Lo.snorm.hybrid	0.4855612	0.6294052	NA	NA	0.5574832
gjrGARCH.EWMA.fixed.Lo.Hi.snorm.hybrid	0.4873248	0.6315175	NA	NA	0.5594211
gjrGARCH.Hi.Cl.snorm.hybrid	0.4903484	NA	0.5591785	NA	NA
gjrGARCH.Hi.Lo.snorm.hybrid	0.4853209	0.6294841	NA	NA	0.5574025
gjrGARCH.Lo.Cl.snorm.hybrid	NA	0.6479054	0.5577813	NA	NA
gjrGARCH.Lo.Hi.snorm.hybrid	0.4901055	0.6469729	NA	NA	0.5685392
gjrGARCH.Op.Cl.snorm.hybrid	NA	NA	0.5581871	0.5748052	NA
gjrGARCH.Op.Hi.snorm.hybrid	0.4897748	NA	NA	0.5756845	NA
iGARCH.EWMA.est.Hi.Lo.snorm.hybrid	0.4957351	0.6556720	NA	NA	0.5757036
iGARCH.EWMA.est.Lo.Hi.snorm.hybrid	0.4966432	0.6566751	NA	NA	0.5766591
iGARCH.EWMA.fixed.Hi.Lo.snorm.hybrid	0.4966460	0.6552626	NA	NA	0.5759543
iGARCH.EWMA.fixed.Lo.Hi.snorm.hybrid	0.4958495	0.6556720	NA	NA	0.5757608
iGARCH.Hi.Lo.snorm.hybrid	0.4958608	0.6556720	NA	NA	0.5757664
iGARCH.Lo.Hi.snorm.hybrid	0.4957999	0.6556720	NA	NA	0.5757359
realGARCH.Hi.Lo.snorm.hybrid	1163.6111434	188.6156300	NA	NA	676.1133867
realGARCH.Lo.Hi.snorm.hybrid	1163.6111434	188.6156300	NA	NA	676.1133867
sGARCH.Hi.Lo.snorm.hybrid	0.4998315	0.6383346	NA	NA	0.5690830
sGARCH.Lo.Hi.snorm.hybrid	0.4958049	0.6383346	NA	NA	0.5670697

Now I filtered the forecast price must be within highest and lowest price in order to made the order stand.

## read files
fls <- list.files('data', patter = '.snorm.hybrid.rds$')
mds <- llply(fls, function(txt) {
    tryCatch(readRDS(paste0('data/', txt)), 
             error = function(e) cat(paste0('data/', txt, ' error!\n')))
    })

## data/fGARCH.ALLGARCH.Mn.Cl.snorm.hybrid.rds error!
## data/fGARCH.AVGARCH.Mn.Cl.snorm.hybrid.rds error!
## data/fGARCH.NAGARCH.Mn.Cl.snorm.hybrid.rds error!
## data/fGARCH.NGARCH.Mn.Cl.snorm.hybrid.rds error!
## data/fGARCH.TGARCH.Mn.Cl.snorm.hybrid.rds error!

names(mds) <- str_replace_all(fls, '.rds', '')

## measure mse.
mds <- llply(names(mds), function(x) {
  HiLo <- x %>% str_extract_all('Hi.Lo|Lo.Hi|Hi.Cl|Lo.Cl|Op.Hi|
                                 Op.Lo|Op.Cl') %>% unlist
  if (length(HiLo) > 0) {
    dfm <- mds[[x]]
    
    if (HiLo == 'Hi.Lo') {
      dfm %<>% dplyr::filter(Point.Forecast <= USDJPY.High & 
                             Point.Forecast >= USDJPY.Low & 
                             forClose <= USDJPY.High & 
                             forClose >= USDJPY.Low) %>% 
        mutate(mse.Hi = mean((Point.Forecast - USDJPY.High)^2), 
               mse.Lo = mean((forClose - USDJPY.Low)^2)) %>% unique
      
    } else if (HiLo == 'Lo.Hi') {
      dfm %<>% dplyr::filter(Point.Forecast <= USDJPY.High & 
                             Point.Forecast >= USDJPY.Low & 
                             forClose <= USDJPY.High & 
                             forClose >= USDJPY.Low) %>% 
        mutate(mse.Lo = mean((Point.Forecast - USDJPY.Low)^2), 
               mse.Hi = mean((forClose - USDJPY.High)^2)) %>% unique

    } else if (HiLo == 'Hi.Cl') {
      dfm %<>% dplyr::filter(Point.Forecast <= USDJPY.High & 
                             Point.Forecast >= USDJPY.Low & 
                             forClose <= USDJPY.High & 
                             forClose >= USDJPY.Low) %>% 
        mutate(mse.Hi = mean((Point.Forecast - USDJPY.High)^2), 
               mse.Cl = mean((forClose - USDJPY.Close)^2)) %>% unique

    } else if (HiLo == 'Lo.Cl') {
      dfm %<>% dplyr::filter(Point.Forecast <= USDJPY.High & 
                             Point.Forecast >= USDJPY.Low & 
                             forClose <= USDJPY.High & 
                             forClose >= USDJPY.Low) %>% 
        mutate(mse.Lo = mean((Point.Forecast - USDJPY.Low)^2), 
               mse.Cl = mean((forClose - USDJPY.Close)^2)) %>% unique

    } else if (HiLo == 'Op.Hi') {
      dfm %<>% dplyr::filter(Point.Forecast <= USDJPY.High & 
                             Point.Forecast >= USDJPY.Low & 
                             forClose <= USDJPY.High & 
                             forClose >= USDJPY.Low) %>% 
        mutate(mse.Op = mean((Point.Forecast - USDJPY.Open)^2), 
               mse.Hi = mean((forClose - USDJPY.High)^2)) %>% unique

    } else if (HiLo == 'Op.Lo') {
      dfm %<>% dplyr::filter(Point.Forecast <= USDJPY.High & 
                             Point.Forecast >= USDJPY.Low & 
                             forClose <= USDJPY.High & 
                             forClose >= USDJPY.Low) %>% 
        mutate(mse.Op = mean((Point.Forecast - USDJPY.Open)^2), 
               mse.Lo = mean((forClose - USDJPY.Low)^2)) %>% unique

    } else if (HiLo == 'Op.Cl') {
      dfm %<>% dplyr::filter(Point.Forecast <= USDJPY.High & 
                             Point.Forecast >= USDJPY.Low & 
                             forClose <= USDJPY.High & 
                             forClose >= USDJPY.Low) %>% 
        mutate(mse.Op = mean((Point.Forecast - USDJPY.Open)^2), 
               mse.Cl = mean((forClose - USDJPY.Close)^2)) %>% unique

    } else {
      stop('No such option.')
    }
    dfm %<>% .[, -c(1:26)] %>% unique
  }
  })
names(mds) <- str_replace_all(fls, '.rds', '')

mds %<>% ldply

mds %>% mutate(mse.HiLo = (mse.Hi + mse.Lo)/2) %>% 
  kable(caption = 'Summary') %>% 
  kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive')) %>% 
  scroll_box(width = '100%', height = '400px')

Summary

.id	mse.Hi	mse.Lo	mse.Cl	mse.Op	mse.HiLo
csGARCH.Hi.Lo.snorm.hybrid	0.1725682	0.6189147	NA	NA	0.3957415
csGARCH.Lo.Hi.snorm.hybrid	0.1754137	0.6303761	NA	NA	0.4028949
fGARCH.GARCH.Hi.Lo.snorm.hybrid	0.1925144	0.5379021	NA	NA	0.3652083
fGARCH.GARCH.Lo.Hi.snorm.hybrid	0.1925144	0.5379021	NA	NA	0.3652083
fGARCH.GJRGARCH.Lo.Cl.snorm.hybrid	NA	0.5372528	0.1295187	NA	NA
fGARCH.GJRGARCH.Op.Cl.snorm.hybrid	NA	NA	0.1299436	0.1249402	NA
fGARCH.NGARCH.Hi.Lo.snorm.hybrid	0.2272118	0.5121823	NA	NA	0.3696971
fGARCH.NGARCH.Lo.Hi.snorm.hybrid	0.2123187	0.4634484	NA	NA	0.3378836
gjrGARCH.EWMA.est.Hi.Lo.snorm.hybrid	0.1822257	0.5579749	NA	NA	0.3701003
gjrGARCH.EWMA.est.Lo.Hi.snorm.hybrid	0.1822257	0.5579749	NA	NA	0.3701003
gjrGARCH.EWMA.fixed.Hi.Lo.snorm.hybrid	0.1822257	0.5579749	NA	NA	0.3701003
gjrGARCH.EWMA.fixed.Lo.Hi.snorm.hybrid	0.1822257	0.5579749	NA	NA	0.3701003
gjrGARCH.Hi.Cl.snorm.hybrid	0.2704312	NA	0.1325796	NA	NA
gjrGARCH.Hi.Lo.snorm.hybrid	0.1822257	0.5579749	NA	NA	0.3701003
gjrGARCH.Lo.Cl.snorm.hybrid	NA	0.5373148	0.1373641	NA	NA
gjrGARCH.Lo.Hi.snorm.hybrid	0.1822257	0.5579749	NA	NA	0.3701003
gjrGARCH.Op.Cl.snorm.hybrid	NA	NA	0.1292683	0.1156056	NA
gjrGARCH.Op.Hi.snorm.hybrid	0.2381400	NA	NA	0.1411032	NA
iGARCH.EWMA.est.Hi.Lo.snorm.hybrid	0.1290527	0.5816668	NA	NA	0.3553598
iGARCH.EWMA.est.Lo.Hi.snorm.hybrid	0.1269647	0.5866267	NA	NA	0.3567957
iGARCH.EWMA.fixed.Hi.Lo.snorm.hybrid	0.1290527	0.5816668	NA	NA	0.3553598
iGARCH.EWMA.fixed.Lo.Hi.snorm.hybrid	0.1290527	0.5816668	NA	NA	0.3553598
iGARCH.Hi.Lo.snorm.hybrid	0.1290527	0.5816668	NA	NA	0.3553598
iGARCH.Lo.Hi.snorm.hybrid	0.1277353	0.5866267	NA	NA	0.3571810
realGARCH.Hi.Lo.snorm.hybrid	0.1321052	1.1086522	NA	NA	0.6203787
realGARCH.Lo.Hi.snorm.hybrid	0.1321052	1.1086522	NA	NA	0.6203787
sGARCH.Hi.Lo.snorm.hybrid	0.1054852	0.6143042	NA	NA	0.3598947
sGARCH.Lo.Hi.snorm.hybrid	0.1054852	0.6143042	NA	NA	0.3598947

11 Conclusion

11.1 Conclusion Words

Due to some unknown reason, the NGARCH and NAGARCH (and other models, some currencies as well.)¹² always bias, therefore the AIC/BIC value and the mse value opposite site to made we hard to judge if it is good to fit. Fortunately I try to filter the bias where \(\sigma \geq 20\%\) and count the number of occurance to pick the model. You can compare the average MSE, AIC, BIC values of all models but skip the bias model(s) which bias hundred times or almost x2 of average of the rest of models. You can also refer to the number of bias or even look into the details of the bias observation.

If we compare the model which most accurate for all currencies prediction, gjrGARCH still be the best model among all models however you can select other model for specific currency.

11.2 Future Works

Perhaps the other day will compare the matrix models fit with distribution and solver. The multivariate GARCH model is also on going. There will be perfect if I saved the VaR 1% and 5% since it will be required in order to test the efficiency of ROI with multivariate models.

We can use specific model for different currencies for multivariate models.

12 Appendix

12.1 Speech and Blooper

There are a lot of time I waste just for verify and rerun the coding. ugarchroll function always interrupted after running few hours. The simulation wrote by me always interrupt as well, there are 14 GARCH models while I running 6 models at the meantime. ugarchroll for refit.windows = 'recrusive' cost me few days time while refit.windows = 'moving' cost me weeks time and all in 24 hours without any rest.

After get the MSE value and AIC value, I forced to debug the codes upon unexpected results especially bias. For example, the MSE value judge the best fit model but AIC and BIC judge as worst model. Here I also looking for some reference like AIC for MSE which applied AIC for compare the best MSE as introduced by a professor.

Below are the blooper (behind the scene) for GARCH模型中的ARMA(p,d,q)参数最优化 where I use almost a week to review and filter couple times.

This paper compares 14 models with 3 mthods but GARCH模型中的ARMA(p,d,q)参数最优化 only compares 2 models.

12.2 Documenting File Creation

It’s useful to record some information about how your file was created.

• File creation date: 2018-08-12
• File latest updated date: 2018-08-27
• R version 3.5.1 (2018-07-02)
• R version (short form): 3.5.1
• rmarkdown package version: 1.10
• File version: 1.0.1
• Author Profile: ®γσ, Eng Lian Hu
• GitHub: Source Code
• Additional session information:

Additional session information:

Category	session_info	Category	Sys.info
version	R version 3.5.1 (2018-07-02)	sysname	Windows
system	x86_64, mingw32	release	10 x64
ui	RTerm	version	build 16299
language	en	nodename	RSTUDIO-SCIBROK
collate	Japanese_Japan.932	machine	x86-64
tz	Asia/Tokyo	login	scibr
date	2018-08-27	user	scibr
Current time	2018-08-27 16:56:31 JST	effective_user	scibr

12.3 Reference

1. GARCH模型中的ARMA(p,d,q)参数最优化
2. Binary.com Interview Q1 (Old link or Alternate link)
3. Binary.com Interview Q1 (Extention) or (Alternate link)
4. Binary.com Interview Q1 - Tick-Data-HiLo For Daily Trading (Blooper)
5. 41901 Probability and Statistics
6. A Comparison of Volatility Models - Does Anything Beat a GARCH(1,1)
7. A Winners Curse for Econometric Models - On the Joint Distribution of In-Sample Fit and Out-of-Sample Fit and Its Implications for Model Selection
8. AMATH546 - ECON589 HW3
9. ARMA(1,1)-GARCH(1,1) Estimation and Forecast using rugarch 1.2-2
10. EGARCH, GKR-GARCH, TGARCH, AVGARCH, NGARCH, IGARCH and APARCH Models for Pathogens at Marine Recreational Sites
11. GARCH Models in Value at Risk Estimation Empirical Evidence from Montenegrin Stock Exchange
12. Predicting Stock Price Returns using Garch Model
13. Predictive Accuracy of GARCH, GJR and EGARCH Models Select Exchange Rates Application
14. Which GARCH Model is Best for Value-at-Risk
15. Optimal lag order selection for a GARCH model
16. Does anything NOT beat the GARCH(1,1)?
17. How to choose the order of a GARCH model?

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1. Kindly refer to paper in Reference↩

2. Only the solver=solnp stable but the other solvers not stable, the fluctuation of AIC value is quite high.↩

3. Due to some errors↩

4. Kindly refer to paper in Reference↩

5. Kindly refer to paper in Reference↩

6. tryCatch() might useful for llply() or else we can use for() to skip NULL or error result. Normally I will add cat() upon completion of one prediction to know the progress of whole simulation.↩

7. Markov Chain theory explain the statiscal predicton only can predict the next stage based on current stage. For example in soccer In-Play : 1-0 or 0-1 can be predicted during 0-0, the fit for 0-0 will not be usable anymore once there has scored. Similar concept with scoring intensity in Dixon & Robinson 1997, the armaOrder and arfima parameters optimised the preditive accuracy at every single stage.↩

8. gjrGARCH model generated highest ROI.↩

9. Kindly refer to paper in Reference↩

10. Therefore I skip [2nd Stage Model Comparison], my previous paper use 2nd stage parameter adjustment but noticed that the matrix relationship will correct.↩

11. VaR or other risk amount, the loss amount will be 1 for the exchange rate since \(\frac{100yen}{1}=100yen\) while I use the closed price as settled price if the forecast settled price has no within the range of Hi-Lo price within a trading day. There will be a leverage and slot unit required for financial market while a risk amount will be required for financial betting.↩

12. Kindly refer to section MSE, AIC and BIC.↩