Modelización Garch [Bitcoin-S&P 500] - Estrategias 2020 Directv
Econ. Jesús B. Zerpa
23/3/2020
BTCSP <- read.csv("C:/Users/Personal/Desktop/BTCSP.csv", sep=";")
apple<-BTCSPRevisión de valores de inicio y finales de la base de datos.
head(apple)## Date BTC.Close SP.Close
## 1 01.01.2014 740.3 1842.95
## 2 02.01.2014 775.0 1826.50
## 3 03.01.2014 812.1 1825.50
## 4 06.01.2014 934.5 1820.75
## 5 07.01.2014 791.0 1830.75
## 6 08.01.2014 828.5 1832.50tail(apple)## Date BTC.Close SP.Close
## 1599 24.01.2020 8447.1 3293.50
## 1600 26.01.2020 8621.6 3259.12
## 1601 27.01.2020 8912.0 3239.50
## 1602 28.01.2020 9393.7 3278.25
## 1603 29.01.2020 9304.2 3272.50
## 1604 30.01.2020 9512.7 3289.38library(zoo)##
## Attaching package: 'zoo'## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numericConstrucción de objeto zoo y gráfico de series de tiempo.
apple.zoo=zoo(apple[,-1], order.by=as.Date(strptime(as.character(apple[,1]), "%d.%m.%Y")))
plot(apple.zoo, main="Precios de Cierre BTC y S&P 500 (2014-2020)")
###### Análisis y suavización de datos medias móviles.
library(chron)
plot(rollapply(apple.zoo, width=120, mean, na.rm=T), main="Mean of Rolling 120 Obs.")
plot(rollapply(apple.zoo, width=120, mean, by=120, na.rm=T),main="Mean of Each 120 Obs.")
Análisis de retornos
library(PerformanceAnalytics)## Loading required package: xts##
## Attaching package: 'PerformanceAnalytics'## The following object is masked from 'package:graphics':
##
## legendtmp <- merge(apple.zoo[,"BTC.Close"], apple.zoo[,"SP.Close"])
tmp.ret <- CalculateReturns(tmp)
colnames(tmp) <- colnames(tmp.ret) <- c("BTC.Close","SP.Close")
plot(tmp, main="Precios de Cierre BTC y S&P 500 (2014-2020)", xlab="Date")
plot(tmp.ret, main="Retornos Precios Cierre BTC y S&P 500 (2014-2020)", xlab="Date")
###### Función coredate
plot(coredata(na.omit(tmp.ret)), pch=".", main="Retornos Precios Cierre BTC y S&P 500 (2014-2020)")
Coeficientes de regresión precios de cierre BTC a través de S&P 500
rr <- rollapply(na.approx(na.trim(tmp, side="both")), width = 120,
FUN = function(z) coef(lm(BTC.Close ~ SP.Close, data = as.data.frame(z))),
by.column = FALSE, align = "right")
rr.var <- rollapply(na.approx(na.trim(tmp, side="both")), width = 120,
FUN = function(z) sd(residuals(lm(BTC.Close ~ SP.Close, data = as.data.frame(z)))),
by.column = FALSE, align = "right")
res <- merge(rr,rr.var)
colnames(res)[3] <- "Desv Estandar Res."
plot(res, main="Coeficiente de Regresion.", xlab="Date")
Resumen y distribución de datos del modelo.
summary(res)## Index (Intercept) SP.Close
## Min. :2014-06-18 Min. :-120844.4 Min. :-10.3194
## 1st Qu.:2015-11-13 1st Qu.: -14978.2 1st Qu.: -0.1529
## Median :2017-04-11 Median : -903.8 Median : 0.8113
## Mean :2017-04-11 Mean : -10054.0 Mean : 5.2066
## 3rd Qu.:2018-09-06 3rd Qu.: 702.8 3rd Qu.: 7.5255
## Max. :2020-01-30 Max. : 40337.8 Max. : 50.1830
## Desv Estandar Res.
## Min. : 17.97
## 1st Qu.: 65.97
## Median : 108.01
## Mean : 673.01
## 3rd Qu.: 997.44
## Max. :3048.28hist(res[,"SP.Close"], breaks=100, main="Histograma de los coeficientes estimados", xlab="Value")
Coeficiente de regresion con los retornos de la Serie.
rr <- rollapply(na.approx(na.trim(tmp.ret, side="both")), width = 120,
FUN = function(z) coef(lm(BTC.Close~ SP.Close, data = as.data.frame(z))),
by.column = FALSE, align = "right")
rr.var <- rollapply(na.approx(na.trim(tmp.ret, side="both")), width = 120,
FUN = function(z) sd(residuals(lm (BTC.Close~ SP.Close, data = as.data.frame(z)))),
by.column = FALSE, align = "right")
res.ret <- merge(rr,rr.var)
colnames(res.ret)[3] <- "St. Dev. Resid."
plot(res.ret, main="Coeficiente de regression de los retornos de las series.", xlab="Date")
Resumen y distribución de errores.
summary(res.ret)## Index (Intercept) SP.Close St. Dev. Resid.
## Min. :2014-06-19 Min. :-0.008115 Min. :-1.90007 Min. :0.01588
## 1st Qu.:2015-11-15 1st Qu.:-0.001573 1st Qu.:-0.50235 1st Qu.:0.03541
## Median :2017-04-11 Median : 0.002882 Median :-0.05253 Median :0.04189
## Mean :2017-04-11 Mean : 0.002795 Mean : 0.08352 Mean :0.04359
## 3rd Qu.:2018-09-06 3rd Qu.: 0.006041 3rd Qu.: 0.39382 3rd Qu.:0.04975
## Max. :2020-01-30 Max. : 0.017093 Max. : 3.41480 Max. :0.06856hist(res.ret[,"SP.Close"], breaks=100, main="Histograma coeficientes estimados de los retornos", xlab="Value")
Análisis de la desviación estándar.
library(xts)
tail(to.yearly(apple.zoo))## apple.zoo.Open apple.zoo.High apple.zoo.Low apple.zoo.Close
## 2015-12-31 313.9 466.5 183.0 429.0
## 2016-12-30 432.9 981.7 358.9 959.3
## 2017-12-29 1019.3 18934.0 778.6 14317.0
## 2018-12-31 13354.0 16917.0 3282.8 3830.5
## 2019-12-31 3963.0 12876.0 3436.1 7208.3
## 2020-01-30 7212.7 9512.7 6989.4 9512.7start(apple.zoo)## [1] "2014-01-01"end(apple.zoo)## [1] "2020-01-30"plot(apply.monthly(window(apple.zoo [,"BTC.Close"], start="2014-01-01") ,function(x) sd(x, na.rm=TRUE)), main="D.E Mensual de los Precios de Cierre de BTC 2014-20", ylab="Desviacion Estandar", xlab="Año")
plot(apply.yearly(window(apple.zoo[,"BTC.Close"], start="2014-01-01",end="2019-12-30") ,function(x) sd(x, na.rm=TRUE)), main="D.E Anual de los Precios de Cierre de BTC 2014-19", ylab="Desviacion Estandar", xlab="Año")
plot(apply.monthly(window(apple.zoo [,"SP.Close"], start="2014-01-01") ,function(x) sd(x, na.rm=TRUE)), main="D.E Mensual de los Precios de Cierre del S&P500 2014-20", ylab="Desviacion Estandar", xlab="Año")
plot(apply.yearly(window(apple.zoo[,"SP.Close"], start="2014-01-01",end="2019-12-30") ,function(x) sd(x, na.rm=TRUE)), main="D.E Anual de los Precios de Cierre del S&P500 2014-19", ylab="Desviacion Estandar", xlab="Año")
Modelización ARIMA
library(vars)## Loading required package: MASS## Loading required package: strucchange## Loading required package: sandwich## Loading required package: urca## Loading required package: lmtestlibrary(forecast)## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoo## Registered S3 methods overwritten by 'forecast':
## method from
## fitted.fracdiff fracdiff
## residuals.fracdiff fracdifflibrary(TSA)## Registered S3 methods overwritten by 'TSA':
## method from
## fitted.Arima forecast
## plot.Arima forecast##
## Attaching package: 'TSA'## The following objects are masked from 'package:PerformanceAnalytics':
##
## kurtosis, skewness## The following objects are masked from 'package:stats':
##
## acf, arima## The following object is masked from 'package:utils':
##
## tarlibrary(ggplot2)
library(tseries)##
## Attaching package: 'tseries'## The following object is masked from 'package:chron':
##
## is.weekendGráficas y aplicación de logaritmos y diferencias.
apple.mod <- na.approx(na.trim(apple.zoo[,"BTC.Close"], side="both"))
head(to.daily(apple.mod))## apple.mod.Open apple.mod.High apple.mod.Low apple.mod.Close
## 2014-01-01 740.3 740.3 740.3 740.3
## 2014-01-02 775.0 775.0 775.0 775.0
## 2014-01-03 812.1 812.1 812.1 812.1
## 2014-01-06 934.5 934.5 934.5 934.5
## 2014-01-07 791.0 791.0 791.0 791.0
## 2014-01-08 828.5 828.5 828.5 828.5apple.mod1 <- to.daily(apple.mod)[,"apple.mod.Close"]
start(apple.mod1)## [1] "2014-01-01"apple.ts <- ts(apple.mod1, start=c(2014,01,01), freq=270)
autoplot(log(apple.ts), main="Log de Los Precios de Cierre de BTC 2014-20")
ggtsdisplay(diff(log(apple.ts)))
adf.test(diff(log(apple.ts)))## Warning in adf.test(diff(log(apple.ts))): p-value smaller than printed p-value##
## Augmented Dickey-Fuller Test
##
## data: diff(log(apple.ts))
## Dickey-Fuller = -10.811, Lag order = 11, p-value = 0.01
## alternative hypothesis: stationarypp.test(diff(log(apple.ts), alternative="stationary"))## Warning in pp.test(diff(log(apple.ts), alternative = "stationary")): p-value
## smaller than printed p-value##
## Phillips-Perron Unit Root Test
##
## data: diff(log(apple.ts), alternative = "stationary")
## Dickey-Fuller Z(alpha) = -1696.1, Truncation lag parameter = 8, p-value
## = 0.01
## alternative hypothesis: stationaryplot(decompose(diff(log(apple.ts))))
arima(log(apple.ts), order = c(0,1,0))##
## Call:
## arima(x = log(apple.ts), order = c(0, 1, 0))
##
##
## sigma^2 estimated as 0.002075: log likelihood = 2677.01, aic = -5354.03arima(log(apple.ts), order = c(1,1,1))##
## Call:
## arima(x = log(apple.ts), order = c(1, 1, 1))
##
## Coefficients:
## ar1 ma1
## 0.1991 -0.2177
## s.e. 0.8046 0.7909
##
## sigma^2 estimated as 0.002074: log likelihood = 2677.31, aic = -5350.62Test de validación
tsdiag(arima(log(apple.ts), order = c(0,1,0)))
tsdiag(arima(log(apple.ts), order = c(1,1,1)))
checkresiduals(arima(log(apple.ts), order = c(0,1,0)))
##
## Ljung-Box test
##
## data: Residuals from ARIMA(0,1,0)
## Q* = 350.21, df = 321, p-value = 0.126
##
## Model df: 0. Total lags used: 321Modelización Garch (Completo)
library(rmgarch)## Loading required package: rugarch## Loading required package: parallel##
## Attaching package: 'rugarch'## The following object is masked from 'package:stats':
##
## sigma##
## Attaching package: 'rmgarch'## The following objects are masked from 'package:xts':
##
## first, lastlibrary(PerformanceAnalytics)
model<- window(apple.zoo [,"BTC.Close"], start="2014-01-01")
model<- na.approx(na.trim(CalculateReturns(model), side="both"))
spec = ugarchspec()
print(spec)##
## *---------------------------------*
## * GARCH Model Spec *
## *---------------------------------*
##
## Conditional Variance Dynamics
## ------------------------------------
## GARCH Model : sGARCH(1,1)
## Variance Targeting : FALSE
##
## Conditional Mean Dynamics
## ------------------------------------
## Mean Model : ARFIMA(1,0,1)
## Include Mean : TRUE
## GARCH-in-Mean : FALSE
##
## Conditional Distribution
## ------------------------------------
## Distribution : norm
## Includes Skew : FALSE
## Includes Shape : FALSE
## Includes Lambda : FALSEdef.fit = ugarchfit(spec = spec, data = model)
print(def.fit)##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : sGARCH(1,1)
## Mean Model : ARFIMA(1,0,1)
## Distribution : norm
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 0.002540 0.001101 2.3077 0.021014
## ar1 0.814833 0.382341 2.1312 0.033075
## ma1 -0.791863 0.402468 -1.9675 0.049124
## omega 0.000125 0.000026 4.7669 0.000002
## alpha1 0.122571 0.020129 6.0893 0.000000
## beta1 0.825323 0.024812 33.2629 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 0.002540 0.001164 2.1824 0.029081
## ar1 0.814833 0.541378 1.5051 0.132296
## ma1 -0.791863 0.565336 -1.4007 0.161305
## omega 0.000125 0.000074 1.6862 0.091765
## alpha1 0.122571 0.033899 3.6158 0.000299
## beta1 0.825323 0.052460 15.7325 0.000000
##
## LogLikelihood : 2788.191
##
## Information Criteria
## ------------------------------------
##
## Akaike -3.4712
## Bayes -3.4511
## Shibata -3.4713
## Hannan-Quinn -3.4638
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.1034 0.7478
## Lag[2*(p+q)+(p+q)-1][5] 1.3352 0.9995
## Lag[4*(p+q)+(p+q)-1][9] 4.7756 0.5055
## d.o.f=2
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.3453 0.5568
## Lag[2*(p+q)+(p+q)-1][5] 1.0215 0.8548
## Lag[4*(p+q)+(p+q)-1][9] 1.3170 0.9692
## d.o.f=2
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[3] 0.2712 0.500 2.000 0.6025
## ARCH Lag[5] 0.3865 1.440 1.667 0.9165
## ARCH Lag[7] 0.4865 2.315 1.543 0.9796
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 1.3331
## Individual Statistics:
## mu 0.32344
## ar1 0.03306
## ma1 0.03301
## omega 0.10592
## alpha1 0.07153
## beta1 0.10984
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 1.49 1.68 2.12
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 1.0648 0.2871
## Negative Sign Bias 1.1088 0.2677
## Positive Sign Bias 0.7929 0.4279
## Joint Effect 1.9171 0.5898
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 286.9 9.624e-50
## 2 30 299.4 1.056e-46
## 3 40 316.5 3.768e-45
## 4 50 329.7 3.034e-43
##
##
## Elapsed time : 1.699994Modelo eGarch (2,1) Distribución de errores T-Student
garch112e2.2.2.spec = ugarchspec(mean.model = list(armaOrder = c(0,0)),
variance.model = list(garchOrder = c(2,1),
model = "eGARCH"), distribution.model = "std")
garch.fit112e2.2.2= ugarchfit(garch112e2.2.2.spec, data = model, fit.control=list(scale=TRUE))
print(garch.fit112e2.2.2)##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : eGARCH(2,1)
## Mean Model : ARFIMA(0,0,0)
## Distribution : std
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 0.001261 0.000528 2.3895 0.016871
## omega -0.098617 0.052158 -1.8908 0.058657
## alpha1 -0.091854 0.062178 -1.4773 0.139602
## alpha2 0.112060 0.062577 1.7908 0.073330
## beta1 0.983072 0.008942 109.9359 0.000000
## gamma1 0.451433 0.099049 4.5577 0.000005
## gamma2 -0.137387 0.080693 -1.7026 0.088644
## shape 2.550534 0.186797 13.6540 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 0.001261 0.000509 2.4788 0.013183
## omega -0.098617 0.070233 -1.4041 0.160275
## alpha1 -0.091854 0.065685 -1.3984 0.161993
## alpha2 0.112060 0.064881 1.7272 0.084139
## beta1 0.983072 0.012533 78.4368 0.000000
## gamma1 0.451433 0.107693 4.1918 0.000028
## gamma2 -0.137387 0.085209 -1.6124 0.106885
## shape 2.550534 0.197290 12.9278 0.000000
##
## LogLikelihood : 3036.887
##
## Information Criteria
## ------------------------------------
##
## Akaike -3.7790
## Bayes -3.7522
## Shibata -3.7791
## Hannan-Quinn -3.7691
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 3.322 0.06836
## Lag[2*(p+q)+(p+q)-1][2] 4.493 0.05561
## Lag[4*(p+q)+(p+q)-1][5] 7.590 0.03721
## d.o.f=0
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.1405 0.7078
## Lag[2*(p+q)+(p+q)-1][8] 0.7473 0.9883
## Lag[4*(p+q)+(p+q)-1][14] 1.9573 0.9920
## d.o.f=3
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[4] 0.01235 0.500 2.000 0.9115
## ARCH Lag[6] 0.38116 1.461 1.711 0.9244
## ARCH Lag[8] 0.58042 2.368 1.583 0.9750
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 2.4443
## Individual Statistics:
## mu 0.51929
## omega 0.17655
## alpha1 0.40823
## alpha2 0.42594
## beta1 0.14497
## gamma1 0.09465
## gamma2 0.09181
## shape 0.13315
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 1.89 2.11 2.59
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 1.0846 0.2783
## Negative Sign Bias 0.4547 0.6494
## Positive Sign Bias 1.4585 0.1449
## Joint Effect 3.0063 0.3907
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 38.41 0.005261
## 2 30 38.43 0.113098
## 3 40 53.32 0.062957
## 4 50 50.24 0.423920
##
##
## Elapsed time : 2.322001garch.fit = ugarchfit(garch112e2.2.2.spec, data = model, fit.control=list(scale=TRUE))
print(garch.fit)##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : eGARCH(2,1)
## Mean Model : ARFIMA(0,0,0)
## Distribution : std
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 0.001261 0.000528 2.3895 0.016871
## omega -0.098617 0.052158 -1.8908 0.058657
## alpha1 -0.091854 0.062178 -1.4773 0.139602
## alpha2 0.112060 0.062577 1.7908 0.073330
## beta1 0.983072 0.008942 109.9359 0.000000
## gamma1 0.451433 0.099049 4.5577 0.000005
## gamma2 -0.137387 0.080693 -1.7026 0.088644
## shape 2.550534 0.186797 13.6540 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 0.001261 0.000509 2.4788 0.013183
## omega -0.098617 0.070233 -1.4041 0.160275
## alpha1 -0.091854 0.065685 -1.3984 0.161993
## alpha2 0.112060 0.064881 1.7272 0.084139
## beta1 0.983072 0.012533 78.4368 0.000000
## gamma1 0.451433 0.107693 4.1918 0.000028
## gamma2 -0.137387 0.085209 -1.6124 0.106885
## shape 2.550534 0.197290 12.9278 0.000000
##
## LogLikelihood : 3036.887
##
## Information Criteria
## ------------------------------------
##
## Akaike -3.7790
## Bayes -3.7522
## Shibata -3.7791
## Hannan-Quinn -3.7691
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 3.322 0.06836
## Lag[2*(p+q)+(p+q)-1][2] 4.493 0.05561
## Lag[4*(p+q)+(p+q)-1][5] 7.590 0.03721
## d.o.f=0
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.1405 0.7078
## Lag[2*(p+q)+(p+q)-1][8] 0.7473 0.9883
## Lag[4*(p+q)+(p+q)-1][14] 1.9573 0.9920
## d.o.f=3
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[4] 0.01235 0.500 2.000 0.9115
## ARCH Lag[6] 0.38116 1.461 1.711 0.9244
## ARCH Lag[8] 0.58042 2.368 1.583 0.9750
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 2.4443
## Individual Statistics:
## mu 0.51929
## omega 0.17655
## alpha1 0.40823
## alpha2 0.42594
## beta1 0.14497
## gamma1 0.09465
## gamma2 0.09181
## shape 0.13315
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 1.89 2.11 2.59
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 1.0846 0.2783
## Negative Sign Bias 0.4547 0.6494
## Positive Sign Bias 1.4585 0.1449
## Joint Effect 3.0063 0.3907
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 38.41 0.005261
## 2 30 38.43 0.113098
## 3 40 53.32 0.062957
## 4 50 50.24 0.423920
##
##
## Elapsed time : 2.003004plot(garch.fit, which=3)
###### Gráfica de Valor en Riesgo VaR
plot(garch.fit, which=2)##
## please wait...calculating quantiles...
###### Valor en riesgo y reportes.
garchroll <- ugarchroll(garch112e2.2.2.spec, data = model, n.start =500,
refit.window = "moving"
, refit.every = 100)
garchVaR <- quantile(garchroll, probs=0.01)
actual <- xts(as.data.frame(garchroll)$Realized, time(garchVaR))
mean(actual < garchVaR)## [1] 0.008159565VaRplot(alpha = 0.01, actual = actual, VaR = garchVaR)
report(garchroll, type = "VaR", VaR.alpha = 0.01, conf.level = 0.99)## VaR Backtest Report
## ===========================================
## Model: eGARCH-std
## Backtest Length: 1103
## Data:
##
## ==========================================
## alpha: 1%
## Expected Exceed: 11
## Actual VaR Exceed: 9
## Actual %: 0.8%
##
## Unconditional Coverage (Kupiec)
## Null-Hypothesis: Correct Exceedances
## LR.uc Statistic: 0.403
## LR.uc Critical: 6.635
## LR.uc p-value: 0.526
## Reject Null: NO
##
## Conditional Coverage (Christoffersen)
## Null-Hypothesis: Correct Exceedances and
## Independence of Failures
## LR.cc Statistic: 0.551
## LR.cc Critical: 9.21
## LR.cc p-value: 0.759
## Reject Null: NOGráficos de residuos del modelo.
plot(garch.fit, which=1)
plot(garch.fit, which=8)
plot(garch.fit, which=9)
plot(garch.fit, which=12)
plot(garch.fit, which = "all")##
## please wait...calculating quantiles...
###### Interpretación y pronósticos.
forecast1<-ugarchforecast(garch.fit,n.ahead = 3)
forecast1##
## *------------------------------------*
## * GARCH Model Forecast *
## *------------------------------------*
## Model: eGARCH
## Horizon: 3
## Roll Steps: 0
## Out of Sample: 0
##
## 0-roll forecast [T0=2020-01-30]:
## Series Sigma
## T+1 0.001261 0.04461
## T+2 0.001261 0.04622
## T+3 0.001261 0.04635plot(forecast1,which=1)
plot(forecast1,which=3)
###### Método Forecast Rolling.
modelfit=ugarchfit(garch112e2.2.2.spec,data=model, solver="hybrid", out.sample=5)
modelforecast<-ugarchforecast(modelfit, data = NULL, n.ahead = 10, n.roll = 5, external.forecasts = list(mregfor = NULL, vregfor = NULL))
modelforecast##
## *------------------------------------*
## * GARCH Model Forecast *
## *------------------------------------*
## Model: eGARCH
## Horizon: 10
## Roll Steps: 5
## Out of Sample: 5
##
## 0-roll forecast [T0=2020-01-24]:
## Series Sigma
## T+1 0.001192 0.03927
## T+2 0.001192 0.04096
## T+3 0.001192 0.04116
## T+4 0.001192 0.04136
## T+5 0.001192 0.04155
## T+6 0.001192 0.04174
## T+7 0.001192 0.04193
## T+8 0.001192 0.04212
## T+9 0.001192 0.04230
## T+10 0.001192 0.04249Pronósticos a 10 días.
plot(modelforecast,which=2)
plot(modelforecast,which=4)
Modelo Garch de correlacion dinamica condicional-DCC Garch
garch1 <- merge(apple.zoo[,"BTC.Close"], apple.zoo[,"SP.Close"])
colnames(garch1)<-c("BTC","SP")
tst <- na.approx(na.trim(CalculateReturns(garch1), side="both"))
garch112e2.2.2.spec= ugarchspec(mean.model = list(armaOrder = c(0,0)),
variance.model = list(garchOrder = c(2,1),
model = "eGARCH"), distribution.model = "std")dcc.garch12.1.spec = dccspec(uspec = multispec( replicate(2, garch112e2.2.2.spec )), dccOrder = c(1,1),model = "aDCC",distribution ="mvt")
dcc.fit.1 = dccfit(dcc.garch12.1.spec, data = tst, fit.control=list(scale=TRUE))
print(dcc.fit.1)##
## *---------------------------------*
## * DCC GARCH Fit *
## *---------------------------------*
##
## Distribution : mvt
## Model : aDCC(1,1)
## No. Parameters : 21
## [VAR GARCH DCC UncQ] : [0+16+4+1]
## No. Series : 2
## No. Obs. : 1603
## Log-Likelihood : 8717.84
## Av.Log-Likelihood : 5.44
##
## Optimal Parameters
## -----------------------------------
## Estimate Std. Error t value Pr(>|t|)
## [BTC].mu 0.001261 0.000443 2.845261 0.004437
## [BTC].omega -0.098617 0.067614 -1.458534 0.144694
## [BTC].alpha1 -0.091854 0.059079 -1.554772 0.120000
## [BTC].alpha2 0.112060 0.059290 1.890041 0.058753
## [BTC].beta1 0.983072 0.012050 81.580138 0.000000
## [BTC].gamma1 0.451433 0.105853 4.264710 0.000020
## [BTC].gamma2 -0.137387 0.080808 -1.700162 0.089100
## [BTC].shape 2.550534 0.075947 33.583264 0.000000
## [SP].mu 0.000503 0.000472 1.065980 0.286433
## [SP].omega -0.588570 0.317145 -1.855837 0.063477
## [SP].alpha1 -0.213872 0.117771 -1.816000 0.069370
## [SP].alpha2 -0.042003 0.050273 -0.835489 0.403442
## [SP].beta1 0.941702 0.032926 28.600350 0.000000
## [SP].gamma1 0.220626 0.133934 1.647270 0.099503
## [SP].gamma2 -0.025682 0.122223 -0.210124 0.833571
## [SP].shape 4.896249 1.087639 4.501721 0.000007
## [Joint]dcca1 0.012674 0.008973 1.412385 0.157837
## [Joint]dccb1 0.947733 0.038296 24.747789 0.000000
## [Joint]dccg1 0.000410 0.010705 0.038321 0.969431
## [Joint]mshape 4.000001 0.329756 12.130200 0.000000
##
## Information Criteria
## ---------------------
##
## Akaike -10.851
## Bayes -10.780
## Shibata -10.851
## Hannan-Quinn -10.825
##
##
## Elapsed time : 22.07168Retornos de las series.
garch.fit = ugarchfit(garch112e2.2.2.spec, data = tst[,1], fit.control=list(scale=TRUE))
print(garch.fit)##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : eGARCH(2,1)
## Mean Model : ARFIMA(0,0,0)
## Distribution : std
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 0.001261 0.000528 2.3895 0.016871
## omega -0.098617 0.052158 -1.8908 0.058657
## alpha1 -0.091854 0.062178 -1.4773 0.139602
## alpha2 0.112060 0.062577 1.7908 0.073330
## beta1 0.983072 0.008942 109.9359 0.000000
## gamma1 0.451433 0.099049 4.5577 0.000005
## gamma2 -0.137387 0.080693 -1.7026 0.088644
## shape 2.550534 0.186797 13.6540 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 0.001261 0.000509 2.4788 0.013183
## omega -0.098617 0.070233 -1.4041 0.160275
## alpha1 -0.091854 0.065685 -1.3984 0.161993
## alpha2 0.112060 0.064881 1.7272 0.084139
## beta1 0.983072 0.012533 78.4368 0.000000
## gamma1 0.451433 0.107693 4.1918 0.000028
## gamma2 -0.137387 0.085209 -1.6124 0.106885
## shape 2.550534 0.197290 12.9278 0.000000
##
## LogLikelihood : 3036.887
##
## Information Criteria
## ------------------------------------
##
## Akaike -3.7790
## Bayes -3.7522
## Shibata -3.7791
## Hannan-Quinn -3.7691
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 3.322 0.06836
## Lag[2*(p+q)+(p+q)-1][2] 4.493 0.05561
## Lag[4*(p+q)+(p+q)-1][5] 7.590 0.03721
## d.o.f=0
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.1405 0.7078
## Lag[2*(p+q)+(p+q)-1][8] 0.7473 0.9883
## Lag[4*(p+q)+(p+q)-1][14] 1.9573 0.9920
## d.o.f=3
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[4] 0.01235 0.500 2.000 0.9115
## ARCH Lag[6] 0.38116 1.461 1.711 0.9244
## ARCH Lag[8] 0.58042 2.368 1.583 0.9750
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 2.4443
## Individual Statistics:
## mu 0.51929
## omega 0.17655
## alpha1 0.40823
## alpha2 0.42594
## beta1 0.14497
## gamma1 0.09465
## gamma2 0.09181
## shape 0.13315
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 1.89 2.11 2.59
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 1.0846 0.2783
## Negative Sign Bias 0.4547 0.6494
## Positive Sign Bias 1.4585 0.1449
## Joint Effect 3.0063 0.3907
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 38.41 0.005261
## 2 30 38.43 0.113098
## 3 40 53.32 0.062957
## 4 50 50.24 0.423920
##
##
## Elapsed time : 3.765648plot(garch.fit, which=3)
plot(tst, main="Retornos de Precios de BTC y S&P500", xlab="Date")
###### Media condicional.
plot(dcc.fit.1, which=1)## Warning in plot.window(...): relative range of values ( 50 * EPS) is small (axis
## 2)## Warning in plot.window(...): relative range of values ( 27 * EPS) is small (axis
## 2)
###### Sigma Vs Returns.
plot(dcc.fit.1, which=2)
###### Covarianza y correlación condicional.
plot(dcc.fit.1, which=3)
plot(dcc.fit.1, which=4)
Portafolio y VaR al 1%.
plot(dcc.fit.1, which=5)
###### Forecast.
fit01 = dccfit(dcc.garch12.1.spec, data = tst, out.sample = 15, fit.control = list(eval.se=FALSE))
forc2 = dccforecast(fit01, n.ahead = 1, n.roll = 10)
plot(forc2, which=1)
plot(forc2, which=2)
plot(forc2, which=3)
plot(forc2, which=5)
forc2##
## *---------------------------------*
## * DCC GARCH Forecast *
## *---------------------------------*
##
## Distribution : mvt
## Model : aDCC(1,1)
## Horizon : 1
## Roll Steps : 10
## -----------------------------------
##
## 0-roll forecast:
## , , 1
##
## [,1] [,2]
## [1,] 1.00000 -0.07547
## [2,] -0.07547 1.00000Otros gráficos del modelo.
r1=rcor(dcc.fit.1, type="R")
r1.z=zoo(r1[1,2,], order.by=time(tst))
plot(r1.z, main=paste(colnames(garch1)[1],"-", colnames(garch1)[2], "Correlacion Condicional", sep=" "),
ylab="Correlacion Condicional",
xlab="Date")
abline(h=mean(r1.z), lty=2, lwd=1, col="blue")
abline(h=(mean(r1.z)+sd(r1.z)), lty=2, lwd=1, col="blue")
abline(h=(mean(r1.z)-sd(r1.z)), lty=2, lwd=1, col="blue")
###### Predicciones.
mr1z <- mean(window(r1.z, start="2020-01-01"))
sr1z <- sd(window(r1.z, start="2020-01-01"))
plot(window(r1.z, start="2020-01-01"), main=paste(colnames(garch1)[1],"-", colnames(garch1)[2], "Correlacion Condicional", sep=" "),
ylab="Correlacion Condicional", sub=paste("mean:", round(mr1z,3),"sd:", round(sr1z,3)),
xlab="Date")
abline(h=mr1z, lty=2, lwd=1, col="blue")
abline(h=(mr1z+sr1z), lty=2, lwd=1, col="red")
abline(h=(mr1z-sr1z), lty=2, lwd=1, col="red")