1 Introduction

From paper Binary Q1 or (Alternate link) and also Binary Q1 (Extention) or (Alternate link). Both papers test the accuracy of various statistical models and gain a high ROI per annum. However, as stated in the paper there has a concern which is don’t know highest or lowest price came first, therefore the paper compared all possible outcomes. Finally the Hi-Lo and Lo-Hi models made highest returns. The research on this paper will be applicable to the real-life.

In order to test the timeline of daily highest and lowest price when I am writing Real Time Trading System (Trial), here I created this file to read the tick-data-history to test the ROI (Return On Investment) per annum. Kindly refer to section Reference for further information.

2 Data

2.1 Read Data

I use more than 3 years data (from week 1 2015 until week 27 2018)1 for the question as experiment, 1st year data is burn-in data for statistical modelling and prediction purpose while following 2 years data for forecasting and staking. There have 52 trading weeks within a year.

There will be a certain spread charged by operators but the OHLC dataset does not provide the information for the course of the exchange rate. The tick-data history will be similar with rebirth model in soccer betting for normal FOREX trading market. The financial betting market similar with pre-match soccer betting.

I gathered the 3 datasets from below websites:

  • 1st Dataset - quantmod::getSymbols(src = 'yahoo'): which contains OHLCV data price (timezone in GMT). The place orders function required highest or lowest price come first, therefore I gathered the data via FXCMTickData.
  • 2nd Dataset - FXCMTickData : which contain the timeline of highest and lowest price within a day (timezone in UTC). The daily dataset used for forecast daily price.
  • 3rd Dataset - TFX::queryFX(): which shows the current price. The place orders function required data history, therefore I gathered the data via FXCMTickData.

There will probably occurs inconsistancy of data price among 3 datasets, however there will be cost few years time to gather all real time price via TFX::queryFX(). Otherwise all data gather via 1 channel (queryFX()) will be perfect. However, you can feel free to read futher in this paper where verified the consistancy of datasets.

The will be another research project for Real Time High Frequency Trading where collect the real-time data and also high-frquency trading for tick-data. You are feel free to browse over Real Time FXCM.

Below is the dataset gather via getSymbols(src = 'yahoo').

## read saved dataset.
mbase <- readRDS('./data/USDJPY/USDJPY.rds')
## [1] "mbase : [911 x 6]"
Table Summary
Category Freq
Index Min. :2015-01-05
Index 1st Qu.:2015-11-19
Index Median :2016-10-03
Index Mean :2016-10-03
Index 3rd Qu.:2017-08-18
Index Max. :2018-07-05
USDJPY.Open Min. : 99.89
USDJPY.Open 1st Qu.:109.33
USDJPY.Open Median :112.59
USDJPY.Open Mean :113.21
USDJPY.Open 3rd Qu.:118.97
USDJPY.Open Max. :125.60
USDJPY.High Min. :100.4
USDJPY.High 1st Qu.:109.6
USDJPY.High Median :112.9
USDJPY.High Mean :113.6
USDJPY.High 3rd Qu.:119.4
USDJPY.High Max. :125.8
USDJPY.Low Min. : 99.57
USDJPY.Low 1st Qu.:108.90
USDJPY.Low Median :112.15
USDJPY.Low Mean :112.79
USDJPY.Low 3rd Qu.:118.67
USDJPY.Low Max. :124.97
USDJPY.Close Min. : 99.91
USDJPY.Close 1st Qu.:109.32
USDJPY.Close Median :112.58
USDJPY.Close Mean :113.21
USDJPY.Close 3rd Qu.:118.97
USDJPY.Close Max. :125.63
USDJPY.Volume Min. :0
USDJPY.Volume 1st Qu.:0
USDJPY.Volume Median :0
USDJPY.Volume Mean :0
USDJPY.Volume 3rd Qu.:0
USDJPY.Volume Max. :0
USDJPY.Adjusted Min. : 99.91
USDJPY.Adjusted 1st Qu.:109.32
USDJPY.Adjusted Median :112.58
USDJPY.Adjusted Mean :113.21
USDJPY.Adjusted 3rd Qu.:118.97
USDJPY.Adjusted Max. :125.63

Table 2.1.1 : 1st dataset - summary of daily price dataset.

2.2 Tidy Data

For 2nd dataset, here I gather the tick data via FXCMTickData, there are more than million rows dataset (million rows per file while there are 52 files over 52 weeks) while I tidy and filter only highest and lowest bid/ask price. From the table below we can know the timeline which is weather highest or lowest price came first.

## read tick data.
HL_tick_data <- read_HL_tick_data()
dtID <- unique(HL_tick_data$Date)

## arrange the sequence of highest and lowest price.
HL_tick_data %<>% tbl_df %>% mutate(sq = rep(1:4, length(dtID)))

## Print dataset
HL_tick_data
## # A tibble: 4,228 x 5
##    Date       DateTime              Bid   Ask    sq
##    <date>     <dttm>              <dbl> <dbl> <int>
##  1 2014-12-28 2014-12-28 22:00:00  120.   NA      1
##  2 2014-12-28 2014-12-28 22:36:35   NA   120.     2
##  3 2014-12-28 2014-12-28 22:52:18   NA   120.     3
##  4 2014-12-28 2014-12-28 23:42:36  120.   NA      4
##  5 2014-12-29 2014-12-29 05:10:03   NA   120.     1
##  6 2014-12-29 2014-12-29 05:10:04  120.   NA      2
##  7 2014-12-29 2014-12-29 19:18:16   NA   121.     3
##  8 2014-12-29 2014-12-29 19:36:59  121.   NA      4
##  9 2014-12-30 2014-12-30 00:02:23   NA   121.     1
## 10 2014-12-30 2014-12-30 00:29:35  121.   NA      2
## # ... with 4,218 more rows

Table 2.2.1 : 2nd dataset - daily high-low price tick-data.

For 3rd dataset, due to there is a real-time data, the Real Time Trading System (Trial) web application only stored the real-time bid/ask transaction price but not collect all tick-data in seconds. However, you are feel free to gather from DataCollection.

3 Statistical Modelling

3.1 Forecast Daily Hi-Lo Price

I tried to apply Lasso, Elastic Net and Ridge models to test the accuracy of prediction via shinyApp.

\[\begin{equation} \sigma^2_{t} = \omega + \sum_{i=1}^{\rho}(\alpha_{i} + \gamma_{i} I_{t-i}) \varepsilon_{t-i}^{2} + \sum_{j=1}^{q}\beta_{j}\sigma^{2}_{t-j}\ \cdots\ Equation\ 3.1.1 \end{equation}\]

Here I directly apply GJR-GARCH2 model due to I had compared few statistical models and got the best fitted model. Kindly refer to Binary Q1 for the paper.

  • Auto Arima models (Adjusted and use the optimal AR and MA parameters)
  • Exponential Time Series (27 ETS models)
  • Univariate Garch models (GARCH, T-GARCH, GJR-GARCH, eGARCH, etc altogather 12 models.)
  • Exponential Weighted Moving Average
  • Monte Carlo Markov Chain
  • Bayesian Time Series
  • Midas

Source presentation 3.1.1 : Univariate Garch 2012 (powerpoint)

Here I wrote another extention page for Q1 which is analyse the multiple currencies and also models from minutes to daily. You are feel free to browse over Binary Q1 (Extention). The paper compare and get the optimal predictive model based on the various number of observations.

3.2 GARCH Order

The rugarch package not only provides various GARCH models but also contains below 3 to suite our needs :

  • variance.model
  • mean.model
  • distribution.model

Kindly refer to rugarch包与R语言中的garch族模型 for more information.

Source presentation 3.2.1 : Univariate Garch 2012 (powerpoint)

Source presentation 3.2.2 : Univariate Garch 2012 (powerpoint)

Source presentation 3.2.3 : Univariate Garch 2012 (powerpoint)

Due to above presentation compares the infocriteria of the GARCH order, here I directly set garchOrder(1,1) in my model.

3.3 ARMA Order

For ARMA order, kindly refer to GARCH模型中的ARMA(p,d,q)参数最优化3 for more information. I used old function which is calC() but not calc_fx() in this paper.

Here I read my saved dataset where forecast 1 trading day advanced for daily Hi-Lo price. Kindly refer to Real Time Trading System (Trial) for more information.

##      LatestDate.GMT Lst.Open Lst.High Lst.Low Lst.Close ForecastDate.GMT
##   1:     2016-01-04  120.317  120.448 118.720   120.311              T+1
##   2:     2016-01-05  119.474  119.680 118.801   119.467              T+1
##   3:     2016-01-06  119.100  119.150 118.260   119.102              T+1
##   4:     2016-01-07  118.609  118.753 117.364   118.610              T+1
##   5:     2016-01-08  117.530  118.710 117.512   117.540              T+1
##  ---                                                                    
## 647:     2018-06-28  110.442  110.871 110.388   110.486              T+1
## 648:     2018-07-01  110.745  111.053 110.606   110.710              T+1
## 649:     2018-07-02  110.887  111.126 110.510   110.871              T+1
## 650:     2018-07-03  110.400  110.546 110.282   110.408              T+1
## 651:     2018-07-04  110.497  110.703 110.295   110.502              T+1
##      Fct.Open Fct.High  Fct.Low Fct.Close
##   1: 120.4105 120.2905 119.2893  120.3278
##   2: 119.4793 120.1193 119.2821  119.4786
##   3: 119.0646 119.7417 119.2809  119.0649
##   4: 118.6654 119.4668 119.2840  118.7410
##   5: 117.5048 119.6253 119.2871  117.5493
##  ---                                     
## 647: 110.4233 110.9678 109.8558  110.4686
## 648: 110.8265 111.0962 110.5146  110.7449
## 649: 110.7930 110.9810 110.4011  110.7755
## 650: 110.4582 110.4743 110.0168  110.4741
## 651: 110.5188 110.7678 110.3163  110.5095

Table 3.3.1 : Forecast high-low daily price.

pred.data %>% dplyr::filter(LatestDate.GMT == '2017-01-12') %>% 
  kable(caption = 'Data Error') %>% 
  kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive')) %>%
  scroll_box(width = '100%')
Data Error
LatestDate.GMT Lst.Open Lst.High Lst.Low Lst.Close ForecastDate.GMT Fct.Open Fct.High Fct.Low Fct.Close
2017-01-12 115.055 115.219 113.76 NA T+1 115.1867 110.5123 113.6786 NA

Table 3.3.2 : Forecast daily price missing close price.

Due to the day 2017-01-12 unable forecast the closed price.4, here I omit the transaction on that day.

Below I combine the daily price dataset with forecast Hi-Lo price.

## filter data.
pred.data %<>% dplyr::filter(LatestDate.GMT != '2017-01-12')

## Copied dataset.
mbase <- data.frame(Date = index(mbase), mbase) %>% tbl_df
pred.data %<>% tbl_df

## Add `Date` column as forecasted Date.
pred.data$Date <- lead(pred.data$LatestDate.GMT)
pred.data$Date[length(pred.data$Date)] <- data.table::last(pred.data$LatestDate.GMT) + days(1)

pred.data %<>% select(Date, Fct.Open, Fct.High, Fct.Low, Fct.Close) %>% data.table

## Merge dataset.
pred <- merge(tbl_df(mbase), pred.data, by = 'Date') %>% 
  tbl_df %>% select(-USDJPY.Volume, -USDJPY.Adjusted)
rm(pred.data)

## Print dataset.
pred %>% data.table
##            Date USDJPY.Open USDJPY.High USDJPY.Low USDJPY.Close Fct.Open
##   1: 2016-01-05     119.474     119.680    118.801      119.467 120.4105
##   2: 2016-01-06     119.100     119.150    118.260      119.102 119.4793
##   3: 2016-01-07     118.609     118.753    117.364      118.610 119.0646
##   4: 2016-01-08     117.530     118.710    117.512      117.540 118.6654
##   5: 2016-01-11     117.073     117.992    117.009      117.080 117.5048
##  ---                                                                    
## 646: 2018-07-01     110.745     111.053    110.606      110.710 110.4233
## 647: 2018-07-02     110.887     111.126    110.510      110.871 110.8265
## 648: 2018-07-03     110.400     110.546    110.282      110.408 110.7930
## 649: 2018-07-04     110.497     110.703    110.295      110.502 110.4582
## 650: 2018-07-05     110.555     110.778    110.384      110.579 110.5188
##      Fct.High  Fct.Low Fct.Close
##   1: 120.2905 119.2893  120.3278
##   2: 120.1193 119.2821  119.4786
##   3: 119.7417 119.2809  119.0649
##   4: 119.4668 119.2840  118.7410
##   5: 119.6253 119.2871  117.5493
##  ---                            
## 646: 110.9678 109.8558  110.4686
## 647: 111.0962 110.5146  110.7449
## 648: 110.9810 110.4011  110.7755
## 649: 110.4743 110.0168  110.4741
## 650: 110.7678 110.3163  110.5095

Table 3.3.3 : Tidy dataset for forecast high-low daily price.

Below I test if the dataset scrapped from quantmod::getSymbols(src = 'yahoo') equal to FXCMTickData. Unfortunately the data gathered is not tally each other.

mb.dateID <- unique(mbase$Date)
td.dateID <- unique(HL_tick_data$Date)

## Check the start and end date
data.frame(MB = range(mb.dateID), 
           TD = range(td.dateID)) %>% 
  kable(caption = 'Data Range') %>% 
  kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive'), full_width = FALSE, position = 'float_left') %>%
  footnote(general = 'Date range of 1st and 2nd dataset.',
           general_title = 'Table 3.3.4 : ', footnote_as_chunk = TRUE)
Data Range
MB TD
2015-01-05 2014-12-28
2018-07-05 2018-07-06
Table 3.3.4 : Date range of 1st and 2nd dataset.

Table 3.3.4 shows the date range for both MB (mbase dataset) and TD (tick-data).

Below shows all dates NOT in each dataset. Unfortunately the inconsistancy of dataset gathered from getSymbols(src = 'yahoo') will caused whole predictive models bias, it will affect the staking amount and evetually effect the ROI. The dataset used to working fine few years ago. There will be another research which gather only dataset from operator to solve the issue.

## Check if dateID not in another dataset.
mb.dateID[!mb.dateID %in% td.dateID]
##  [1] "2015-12-25" "2016-01-01" "2016-02-03" "2016-02-04" "2016-02-05"
##  [6] "2016-02-19" "2016-04-20" "2016-04-21" "2016-05-04" "2016-05-05"
## [11] "2016-11-17" "2016-11-18" "2016-12-26" "2017-01-02" "2017-04-17"
## [16] "2017-04-18" "2017-04-19" "2017-04-20" "2017-04-26" "2017-04-27"
## [21] "2017-05-16" "2017-05-17" "2017-05-18" "2017-05-23" "2017-05-24"
## [26] "2017-05-25" "2017-06-29" "2017-08-08" "2017-08-09" "2017-08-10"
## [31] "2017-12-25"
td.dateID[!td.dateID %in% mb.dateID]
##   [1] "2014-12-28" "2014-12-29" "2014-12-30" "2014-12-31" "2015-01-02"
##   [6] "2015-01-04" "2015-01-11" "2015-01-18" "2015-01-25" "2015-02-01"
##  [11] "2015-02-08" "2015-02-15" "2015-02-22" "2015-03-01" "2015-03-08"
##  [16] "2015-03-15" "2015-03-22" "2015-04-03" "2015-04-10" "2015-04-17"
##  [21] "2015-04-24" "2015-05-01" "2015-05-08" "2015-05-15" "2015-05-22"
##  [26] "2015-05-29" "2015-06-05" "2015-06-12" "2015-06-19" "2015-06-26"
##  [31] "2015-07-03" "2015-07-10" "2015-07-17" "2015-07-24" "2015-07-31"
##  [36] "2015-08-07" "2015-08-14" "2015-08-21" "2015-08-28" "2015-09-04"
##  [41] "2015-09-11" "2015-09-21" "2015-09-25" "2015-10-02" "2015-10-09"
##  [46] "2015-10-16" "2015-10-23" "2015-10-25" "2015-11-01" "2015-11-08"
##  [51] "2015-11-15" "2015-11-22" "2015-11-29" "2015-12-06" "2015-12-13"
##  [56] "2015-12-20" "2015-12-27" "2016-01-03" "2016-01-10" "2016-01-17"
##  [61] "2016-01-24" "2016-01-31" "2016-02-07" "2016-02-14" "2016-02-21"
##  [66] "2016-02-28" "2016-03-06" "2016-03-13" "2016-03-20" "2016-04-01"
##  [71] "2016-04-08" "2016-04-29" "2016-05-13" "2016-05-20" "2016-05-27"
##  [76] "2016-06-03" "2016-06-17" "2016-06-24" "2016-07-01" "2016-07-08"
##  [81] "2016-07-15" "2016-07-22" "2016-07-29" "2016-08-05" "2016-08-12"
##  [86] "2016-08-19" "2016-08-26" "2016-09-02" "2016-09-09" "2016-09-16"
##  [91] "2016-09-23" "2016-09-30" "2016-10-07" "2016-10-14" "2016-10-21"
##  [96] "2016-10-28" "2016-10-30" "2016-11-06" "2016-11-13" "2016-11-20"
## [101] "2016-11-27" "2016-12-04" "2016-12-11" "2016-12-18" "2017-01-08"
## [106] "2017-01-15" "2017-01-22" "2017-01-29" "2017-02-05" "2017-02-12"
## [111] "2017-02-19" "2017-02-26" "2017-03-05" "2017-03-12" "2017-03-19"
## [116] "2017-03-31" "2017-04-07" "2017-04-14" "2017-05-05" "2017-05-12"
## [121] "2017-06-02" "2017-06-09" "2017-06-16" "2017-06-23" "2017-07-07"
## [126] "2017-07-10" "2017-07-14" "2017-07-21" "2017-07-28" "2017-08-04"
## [131] "2017-08-18" "2017-08-25" "2017-09-01" "2017-09-08" "2017-09-15"
## [136] "2017-09-22" "2017-09-29" "2017-10-06" "2017-10-13" "2017-10-20"
## [141] "2017-10-27" "2017-10-29" "2017-11-05" "2017-11-12" "2017-11-16"
## [146] "2017-11-17" "2017-11-19" "2017-11-26" "2017-12-03" "2017-12-10"
## [151] "2017-12-17" "2018-01-07" "2018-01-14" "2018-01-21" "2018-01-28"
## [156] "2018-02-04" "2018-02-11" "2018-02-18" "2018-02-25" "2018-03-04"
## [161] "2018-03-11" "2018-03-18" "2018-03-30" "2018-04-06" "2018-04-13"
## [166] "2018-04-20" "2018-04-27" "2018-05-04" "2018-05-11" "2018-05-18"
## [171] "2018-05-25" "2018-06-01" "2018-06-08" "2018-06-15" "2018-06-22"
## [176] "2018-06-29" "2018-07-06"

Graph 3.3.1A : Forecast daily highest price vs real daily highest price.

Graph 3.3.1B : Forecast daily lowest price vs real daily lowest price.

Graph 3.3.1A and Graph 3.3.1B above compare the real price and forecast price. Following section will be compare the MSE (Mean Squared Error).

3.4 Mean Squared Error

## Mean Squared Error : Comparison of accuracy.
## https://cran.r-project.org/web/packages/kableExtra/vignettes/awesome_table_in_html.html
data.frame(
  Category = c('High = ', 'Low = ', 'Close = '), 
  MSE = c(mean((pred$Fct.High - pred$USDJPY.High)^2), 
          mean((pred$Fct.Low - pred$USDJPY.Low)^2), 
          mean((pred$Fct.Close - pred$USDJPY.Close)^2))) %>% 
  kable(caption = 'Mean Squared Error') %>% 
  kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive'), full_width = FALSE, position = 'float_right') %>%
  footnote(general = 'MSE of prediction.',
           general_title = 'Table 3.4.1 : ', footnote_as_chunk = TRUE)
Mean Squared Error
Category MSE
High = 7.747397e+00
Low = 2.978715e+00
Close = 5.109613e+45
Table 3.4.1 : MSE of prediction.

\[\begin{equation} \frac{1}{n}\sum_{t=1}^{n}e_t^2\ \cdots\ Equation\ 3.4.1 \end{equation}\]

Table 3.4.1 at the right-hand-side shows the accuracy of the predictive model. You can also refer to previous studies where compare the accuracy of predicted Open, High, Low and Close price. For accuracy comparison of statistical models, you might refer to GARCH模型中的ARMA(p,d,q)参数最优化 or previous papers for further information.

3.5 Univariate Preditive Error

GARCH模型中的ARMA(p,d,q)参数最优化 compare the accuracy of gjrGARCH and Fi-gjrGARCH model while Multivariate GARCH Models states the statistical predictive error based on univariate and also use more sophistical methods for modelling. This paper I still keep using univariate gjrGARCH in mentioned paper which is not the most accurate.

rx <- pred %>% 
    mutate(diff = Fct.High - Fct.Low) %>% 
    dplyr::filter(diff <= 0)

rx %>% 
  kable(caption = 'Preditive Error for Univariate gjrGARCH') %>% 
  kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive')) %>% 
  scroll_box(width = '100%', height = '400px')
Preditive Error for Univariate gjrGARCH
Date USDJPY.Open USDJPY.High USDJPY.Low USDJPY.Close Fct.Open Fct.High Fct.Low Fct.Close diff
2016-01-12 117.681 118.044 117.240 117.650 1.171339e+02 119.0219 119.3000 116.9629 -0.2780746
2016-01-14 117.400 118.161 117.310 117.425 1.179043e+02 118.4667 119.2978 117.8541 -0.8311305
2016-01-18 117.010 117.434 116.931 116.990 1.181351e+02 118.3154 119.2928 118.4108 -0.9773810
2016-01-21 117.208 117.458 116.478 117.134 1.199554e+02 117.5371 119.2944 117.8787 -1.7573325
2016-01-22 117.925 118.637 117.560 117.924 1.199577e+02 117.6585 119.2953 119.9502 -1.6368143
2016-02-05 116.852 117.359 116.520 116.866 1.180415e+02 118.1581 119.3698 117.9851 -1.2117020
2016-02-08 116.949 117.520 115.583 116.950 1.168444e+02 117.4420 119.3698 116.6408 -1.9278555
2016-02-09 115.650 115.650 114.271 115.668 1.171419e+02 117.6197 119.3706 117.1808 -1.7508385
2016-02-10 115.185 115.185 114.280 115.191 1.155623e+02 117.7806 119.3673 115.5699 -1.5867182
2016-02-11 113.239 113.463 111.081 113.252 1.151618e+02 118.4888 119.3701 115.1483 -0.8813181
2016-02-12 112.483 113.123 111.756 112.497 1.129761e+02 113.3569 119.3690 113.2425 -6.0120831
2016-02-15 113.675 114.547 113.278 113.670 1.123695e+02 113.2573 119.3751 112.3796 -6.1177970
2016-02-26 113.138 113.930 112.560 113.118 1.122336e+02 113.4592 119.4133 112.1477 -5.9540510
2016-03-04 113.680 114.160 113.145 113.670 1.137034e+02 117.5681 119.4274 113.7193 -1.8592487
2016-03-09 112.680 113.143 112.240 112.660 1.134781e+02 117.4694 119.4193 113.2852 -1.9499012
2016-03-16 113.101 113.809 113.021 113.105 1.141090e+02 118.1152 119.4041 114.1218 -1.2888529
2016-03-17 112.794 112.934 110.690 112.752 1.130076e+02 118.8986 119.4034 113.0037 -0.5048306
2016-08-01 102.307 102.795 100.814 102.359 1.022195e+02 102.0382 102.1766 102.2235 -0.1383941
2017-01-11 115.875 116.835 115.681 115.872 1.160022e+02 110.5080 110.9077 115.9959 -0.3996907
2017-01-13 114.696 115.388 114.284 114.664 1.157538e+02 110.5116 115.7639 115.8447 -5.2523310
2017-01-16 114.262 114.449 113.696 114.227 1.145294e+02 110.5143 114.3947 114.4934 -3.8803575
2017-01-17 114.126 114.276 112.740 114.152 1.147558e+02 110.5104 113.5376 114.7966 -3.0272510
2017-01-18 112.908 113.555 112.645 112.878 1.109776e+02 110.5160 112.6626 113.7212 -2.1466118
2017-01-19 114.738 115.521 114.423 114.762 1.130362e+02 110.5222 112.3528 113.0464 -1.8306428
2017-01-20 114.894 115.370 114.546 114.980 1.144277e+02 110.5251 114.5155 115.0250 -3.9904485
2017-01-23 113.853 114.036 112.975 113.810 1.151915e+02 110.5264 114.4629 114.6422 -3.9364849
2017-01-24 112.838 113.468 112.580 112.780 1.136470e+02 110.5234 112.9166 113.6450 -2.3932058
2017-01-27 114.425 115.336 114.401 114.455 1.135213e+02 110.5411 113.0391 113.0678 -2.4979858
2017-01-30 114.683 114.915 113.764 114.668 1.140289e+02 110.5438 114.4871 114.0604 -3.9433415
2017-01-31 113.694 113.932 112.083 113.650 1.149510e+02 110.5442 112.8122 114.9324 -2.2680153
2017-02-01 112.768 113.915 112.768 112.743 1.134872e+02 110.5504 112.0495 113.4452 -1.4990946
2017-02-02 113.243 113.243 112.077 113.311 1.131072e+02 110.5579 112.6554 113.0148 -2.0974911
2017-02-03 112.779 113.232 112.324 112.789 1.130144e+02 110.5637 111.8952 113.0989 -1.3315011
2017-02-06 112.647 112.771 112.028 112.639 1.128467e+02 110.5701 112.3621 112.8554 -1.7919846
2017-02-07 111.798 112.559 111.599 111.827 1.125949e+02 110.5676 111.9942 112.3721 -1.4266635
2017-02-08 112.402 112.520 111.649 112.387 1.119267e+02 110.5795 111.5925 111.9399 -1.0129843
2017-03-20 112.665 112.884 112.467 112.674 1.132525e+02 110.5782 112.5796 113.3871 -2.0013980
2017-09-26 112.434 113.237 112.286 112.377 1.118084e+02 110.7772 111.4461 112.4466 -0.6689662
2017-11-10 113.369 113.624 113.236 113.375 1.135208e+02 111.6006 113.2703 113.9353 -1.6697543
2017-11-13 113.690 113.705 113.246 113.686 1.133465e+02 111.6151 113.2375 113.4610 -1.6224095
2017-12-25 113.295 113.345 113.211 113.308 1.132881e+02 113.3202 113.4133 113.3343 -0.0931218
2018-03-06 106.276 106.453 105.853 106.250 1.054694e+02 109.9114 112.2725 105.4518 -2.3611057
2018-03-07 105.614 106.180 105.511 105.537 1.062154e+02 110.0522 112.2719 106.2335 -2.2196650
2018-03-08 106.169 106.254 105.898 106.186 1.058257e+02 109.7437 112.2648 105.7642 -2.5210451
2018-03-09 106.403 107.029 106.359 106.406 1.060927e+02 110.0195 112.2578 106.1154 -2.2382255
2018-03-12 106.886 106.966 106.374 106.891 1.064310e+02 110.4027 112.2540 106.4393 -1.8513493
2018-03-13 106.318 107.275 106.263 106.260 1.068864e+02 106.8678 112.2470 108.9610 -5.3791502
2018-03-14 106.549 106.734 106.084 106.508 1.064317e+02 107.3842 112.2462 106.3746 -4.8619286
2018-03-15 106.154 106.172 105.790 106.155 1.089557e+02 109.7607 112.2427 108.9263 -2.4820144
2018-03-16 106.328 106.328 105.607 106.309 1.085514e+02 109.9671 112.2387 108.5851 -2.2716455
2018-03-19 105.968 106.298 105.681 105.969 1.086904e+02 106.4472 112.2275 108.6635 -5.7803439
2018-03-20 106.038 106.583 105.984 105.996 1.060489e+02 106.2405 112.1758 106.1186 -5.9353123
2018-03-21 106.480 106.512 106.139 106.469 1.061152e+02 106.7519 112.1760 106.0640 -5.4240734
2018-03-22 105.917 105.961 105.283 105.929 1.065849e+02 106.6064 112.1886 106.5544 -5.5822150
2018-03-23 104.979 105.279 104.667 104.968 1.061759e+02 105.8900 112.1936 106.1328 -6.3035351
2018-03-25 104.840 105.244 104.736 104.859 -2.371204e+78 105.3385 112.1950 105.2540 -6.8564635
2018-03-26 105.546 105.888 105.459 105.500 1.049677e+02 105.4038 112.1988 105.1239 -6.7950154
2018-03-28 106.799 106.926 106.259 106.812 1.056440e+02 106.4399 112.2014 105.7129 -5.7615173
2018-03-29 106.474 106.504 106.116 106.479 1.069839e+02 107.0609 112.2038 106.9786 -5.1429149
2018-04-02 105.805 106.590 105.695 105.799 1.066031e+02 106.6086 112.2066 106.4075 -5.5979435
2018-04-03 106.429 106.680 105.995 106.436 1.061274e+02 106.5891 112.2067 106.0000 -5.6176632
2018-04-04 106.784 107.481 106.716 106.774 1.064474e+02 106.7083 112.2099 106.4452 -5.5015465
2018-04-11 106.814 107.412 106.703 106.829 1.071110e+02 107.1233 112.2176 107.1168 -5.0942802
2018-04-17 107.028 107.378 107.007 107.016 1.071073e+02 107.2334 112.2190 107.1576 -4.9856513
2018-04-19 107.440 107.848 107.405 107.432 1.073801e+02 107.5344 112.2210 107.3638 -4.6866485
2018-04-22 107.843 108.630 107.733 107.869 1.074633e+02 107.9125 112.2219 107.4549 -4.3094062
2018-05-07 108.940 109.331 108.858 108.943 1.091211e+02 109.4594 112.2245 109.1240 -2.7650701
2018-05-08 109.039 109.821 109.001 109.024 1.090087e+02 109.3054 112.2237 109.0137 -2.9182971
2018-06-20 110.344 110.749 109.886 110.352 1.101077e+02 110.3268 111.1784 110.0121 -0.8515311

Table 3.5.1 [69 x 10] : Preditive HiLo Error for Univariate gjrGARCH.

rx <- pred %>% 
    mutate(Range = ifelse(Fct.Close > Fct.High | Fct.Close < Fct.Low, 0, 1)) %>% 
    dplyr::filter(Range == 0)

rx %>% 
  kable(caption = 'Preditive Error for Univariate gjrGARCH') %>% 
  kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive')) %>% 
  scroll_box(width = '100%', height = '400px')
Preditive Error for Univariate gjrGARCH
Date USDJPY.Open USDJPY.High USDJPY.Low USDJPY.Close Fct.Open Fct.High Fct.Low Fct.Close Range
2016-01-05 119.474 119.680 118.801 119.467 1.204105e+02 120.2905 119.28930 1.203278e+02 0
2016-01-07 118.609 118.753 117.364 118.610 1.190646e+02 119.7417 119.28095 1.190649e+02 0
2016-01-08 117.530 118.710 117.512 117.540 1.186654e+02 119.4668 119.28404 1.187410e+02 0
2016-01-11 117.073 117.992 117.009 117.080 1.175048e+02 119.6253 119.28705 1.175493e+02 0
2016-01-12 117.681 118.044 117.240 117.650 1.171339e+02 119.0219 119.29998 1.169629e+02 0
2016-01-13 117.831 118.363 117.780 117.830 1.176806e+02 119.4734 119.29687 1.177372e+02 0
2016-01-14 117.400 118.161 117.310 117.425 1.179043e+02 118.4667 119.29785 1.178541e+02 0
2016-01-15 118.223 118.256 116.650 118.203 1.172975e+02 120.1428 119.29299 1.173248e+02 0
2016-01-18 117.010 117.434 116.931 116.990 1.181351e+02 118.3154 119.29283 1.184108e+02 0
2016-01-21 117.208 117.458 116.478 117.134 1.199554e+02 117.5371 119.29440 1.178787e+02 0
2016-01-22 117.925 118.637 117.560 117.924 1.199577e+02 117.6585 119.29527 1.199502e+02 0
2016-01-25 118.560 118.844 118.182 118.572 1.180532e+02 120.1534 119.29588 1.180728e+02 0
2016-01-29 118.930 121.661 118.520 118.930 1.199500e+02 120.1466 119.29111 1.184693e+02 0
2016-02-01 121.342 121.402 120.699 121.340 1.187472e+02 121.8955 119.28828 1.188890e+02 0
2016-02-02 120.854 121.000 120.200 120.840 1.212201e+02 120.2369 119.37606 1.215636e+02 0
2016-02-05 116.852 117.359 116.520 116.866 1.180415e+02 118.1581 119.36982 1.179851e+02 0
2016-02-08 116.949 117.520 115.583 116.950 1.168444e+02 117.4420 119.36983 1.166408e+02 0
2016-02-09 115.650 115.650 114.271 115.668 1.171419e+02 117.6197 119.37056 1.171808e+02 0
2016-02-10 115.185 115.185 114.280 115.191 1.155623e+02 117.7806 119.36727 1.155699e+02 0
2016-02-11 113.239 113.463 111.081 113.252 1.151618e+02 118.4888 119.37014 1.151483e+02 0
2016-02-12 112.483 113.123 111.756 112.497 1.129761e+02 113.3569 119.36899 1.132425e+02 0
2016-02-15 113.675 114.547 113.278 113.670 1.123695e+02 113.2573 119.37513 1.123796e+02 0
2016-02-19 113.271 113.272 112.731 113.250 1.147310e+02 114.3513 113.49092 1.143935e+02 0
2016-02-23 112.953 112.971 111.789 112.971 1.124546e+02 113.7093 112.97687 1.125245e+02 0
2016-02-24 111.911 112.220 111.112 111.880 1.131695e+02 112.9533 111.83891 1.132103e+02 0
2016-02-26 113.138 113.930 112.560 113.118 1.122336e+02 113.4592 119.41327 1.121477e+02 0
2016-03-02 113.920 114.541 113.736 113.930 1.132065e+02 113.9205 112.14329 1.121172e+02 0
2016-03-03 113.491 114.260 113.460 113.466 1.141882e+02 118.0556 113.97478 1.138755e+02 0
2016-03-04 113.680 114.160 113.145 113.670 1.137034e+02 117.5681 119.42738 1.137193e+02 0
2016-03-09 112.680 113.143 112.240 112.660 1.134781e+02 117.4694 119.41926 1.132852e+02 0
2016-03-11 112.839 113.911 112.830 112.860 1.132965e+02 118.3474 113.37283 1.133331e+02 0
2016-03-15 113.827 113.927 112.670 113.830 1.138588e+02 119.2102 113.87708 1.138725e+02 0
2016-03-16 113.101 113.809 113.021 113.105 1.141090e+02 118.1152 119.40406 1.141218e+02 0
2016-03-17 112.794 112.934 110.690 112.752 1.130076e+02 118.8986 119.40339 1.130037e+02 0
2016-03-22 112.144 112.186 111.412 112.139 1.115238e+02 117.7981 111.59526 1.115176e+02 0
2016-04-10 108.312 108.420 107.664 108.311 1.084021e+02 116.4069 108.46018 1.083571e+02 0
2016-04-12 108.671 109.381 108.540 108.640 1.079416e+02 108.6600 108.11356 1.079566e+02 0
2016-04-13 109.414 109.533 108.901 109.420 1.087493e+02 116.5494 108.73918 1.085916e+02 0
2016-04-21 109.481 111.530 109.280 109.437 1.099109e+02 109.8330 109.43066 1.098751e+02 0
2016-04-27 111.516 111.853 107.950 111.520 1.108108e+02 117.4401 111.19533 1.110706e+02 0
2016-05-01 106.465 106.788 106.196 106.453 1.075310e+02 114.4607 107.50192 1.074747e+02 0
2016-05-09 108.370 109.261 108.317 108.331 1.072117e+02 116.1785 108.15941 1.073600e+02 0
2016-05-10 109.210 109.210 108.440 109.194 1.085179e+02 116.9952 108.33604 1.083310e+02 0
2016-05-12 109.122 109.454 108.514 109.100 1.083034e+02 117.0079 108.42641 1.084150e+02 0
2016-05-17 109.026 109.819 108.753 108.950 1.090570e+02 117.0066 109.14964 1.090800e+02 0
2016-05-22 110.066 110.066 109.340 110.050 1.099273e+02 117.0668 110.17649 1.098986e+02 0
2016-05-29 110.762 111.420 110.720 110.770 1.093641e+02 117.0292 109.70904 1.094018e+02 0
2016-06-07 107.242 107.261 106.606 107.254 1.072276e+02 107.8730 107.52371 1.072731e+02 0
2016-06-08 106.804 106.864 106.278 106.780 1.076409e+02 107.2610 106.61411 1.076436e+02 0
2016-06-12 106.482 106.626 105.745 106.504 1.073823e+02 107.2200 106.47347 1.073866e+02 0
2016-06-19 104.659 104.833 104.300 104.648 1.048329e+02 104.5617 104.10239 1.048136e+02 0
2016-06-28 102.690 102.786 102.190 102.701 1.013915e+02 113.5542 101.26541 1.012485e+02 0
2016-06-30 103.053 103.148 102.456 103.073 1.022789e+02 113.4490 102.88435 1.022669e+02 0
2016-07-04 102.520 102.521 101.460 102.518 1.019806e+02 112.9301 102.44074 1.019598e+02 0
2016-07-11 102.503 104.793 102.465 102.524 1.001126e+02 102.7447 100.64963 1.004375e+02 0
2016-07-12 104.732 104.846 103.963 104.756 1.027253e+02 104.9662 102.41537 1.023703e+02 0
2016-07-14 105.160 106.305 105.150 105.191 1.036660e+02 105.8950 103.99194 1.037290e+02 0
2016-07-26 104.833 106.510 104.833 104.849 1.054931e+02 105.3071 103.83101 1.056387e+02 0
2016-07-27 104.936 105.149 104.521 104.951 1.043491e+02 106.5100 104.77668 1.043480e+02 0
2016-07-28 104.772 104.806 102.278 104.745 1.051606e+02 104.7254 104.25145 1.052063e+02 0
2016-08-01 102.307 102.795 100.814 102.359 1.022195e+02 102.0382 102.17661 1.022235e+02 0
2016-08-03 101.319 101.663 100.867 101.337 1.006473e+02 101.5460 100.92745 1.006059e+02 0
2016-08-08 102.283 102.517 101.800 102.288 1.017217e+02 102.6270 101.91948 1.017132e+02 0
2016-08-11 101.812 102.269 100.862 101.808 1.009178e+02 101.3822 101.02960 1.009545e+02 0
2016-08-15 101.251 101.251 99.573 101.240 1.011768e+02 101.2411 100.85558 1.013252e+02 0
2016-08-17 99.893 100.472 99.652 99.906 9.976146e+01 100.9727 99.83072 9.976095e+01 0
2016-08-21 100.541 100.926 100.225 100.554 1.000215e+02 100.3069 100.16064 9.999052e+01 0
2016-08-31 103.307 103.994 103.082 103.302 1.028015e+02 103.4569 103.05315 1.027613e+02 0
2016-09-05 103.527 103.806 102.048 103.510 1.041375e+02 104.0110 103.29167 1.041380e+02 0
2016-09-12 101.756 102.410 101.472 101.751 1.028754e+02 102.5793 101.94139 1.028031e+02 0
2016-09-18 102.331 102.363 101.581 102.307 1.016396e+02 102.3950 101.87188 1.018497e+02 0
2016-09-19 101.905 102.048 101.573 101.846 1.023871e+02 102.3630 101.36719 1.023782e+02 0
2016-09-27 100.475 100.812 100.423 100.468 1.002824e+02 100.9760 100.22757 9.979007e+01 0
2016-09-29 101.187 101.687 100.756 101.199 1.007434e+02 101.8100 100.85863 1.007217e+02 0
2016-10-04 102.842 103.583 102.682 102.880 1.015676e+02 109.7725 101.69505 1.016112e+02 0
2016-10-17 103.859 104.190 103.689 103.851 1.040284e+02 104.3520 103.87046 1.038180e+02 0
2016-11-01 104.829 105.120 104.457 104.820 1.045201e+02 105.1682 104.54845 1.045087e+02 0
2016-11-25 113.273 113.890 112.610 113.292 1.124095e+02 113.5890 112.64051 1.122854e+02 0
2016-11-29 111.705 113.300 111.705 111.690 1.127768e+02 112.6591 111.55826 1.127039e+02 0
2016-12-02 113.902 114.158 113.334 113.909 1.148876e+02 114.8119 113.94930 1.149185e+02 0
2016-12-06 113.882 114.167 113.515 113.863 1.133557e+02 114.8501 113.46064 1.133332e+02 0
2016-12-07 114.082 114.384 113.519 114.052 1.141544e+02 114.1124 113.40569 1.141438e+02 0
2016-12-16 118.268 118.398 117.926 118.241 1.170918e+02 118.8266 117.85790 1.175458e+02 0
2016-12-20 117.044 118.231 117.000 117.037 1.182737e+02 117.8405 117.41729 1.180001e+02 0
2016-12-22 117.618 117.851 117.317 117.604 1.181771e+02 118.0552 117.43699 1.182134e+02 0
2016-12-23 117.560 117.560 117.176 117.542 1.175915e+02 117.8586 117.37406 1.172250e+02 0
2016-12-26 117.313 117.313 117.001 117.310 1.172673e+02 117.5681 117.18284 1.175935e+02 0
2016-12-27 117.183 117.601 117.183 117.192 1.107531e+02 117.3215 116.74639 1.174492e+02 0
2017-01-03 117.488 118.593 117.286 117.495 1.108060e+02 117.4931 116.74117 1.166882e+02 0
2017-01-06 115.318 116.744 115.263 115.265 1.170907e+02 117.0930 115.17869 1.171657e+02 0
2017-01-09 117.159 117.524 116.183 117.150 1.108753e+02 116.7520 115.32214 1.151178e+02 0
2017-01-11 115.875 116.835 115.681 115.872 1.160022e+02 110.5080 110.90773 1.159959e+02 0
2017-01-13 114.696 115.388 114.284 114.664 1.157538e+02 110.5116 115.76395 1.158447e+02 0
2017-01-16 114.262 114.449 113.696 114.227 1.145294e+02 110.5143 114.39469 1.144934e+02 0
2017-01-17 114.126 114.276 112.740 114.152 1.147558e+02 110.5104 113.53761 1.147966e+02 0
2017-01-18 112.908 113.555 112.645 112.878 1.109776e+02 110.5160 112.66259 1.137212e+02 0
2017-01-19 114.738 115.521 114.423 114.762 1.130362e+02 110.5222 112.35284 1.130464e+02 0
2017-01-20 114.894 115.370 114.546 114.980 1.144277e+02 110.5251 114.51551 1.150250e+02 0
2017-01-23 113.853 114.036 112.975 113.810 1.151915e+02 110.5264 114.46286 1.146422e+02 0
2017-01-24 112.838 113.468 112.580 112.780 1.136470e+02 110.5234 112.91659 1.136450e+02 0
2017-01-27 114.425 115.336 114.401 114.455 1.135213e+02 110.5411 113.03913 1.130678e+02 0
2017-01-30 114.683 114.915 113.764 114.668 1.140289e+02 110.5438 114.48714 1.140604e+02 0
2017-01-31 113.694 113.932 112.083 113.650 1.149510e+02 110.5442 112.81222 1.149324e+02 0
2017-02-01 112.768 113.915 112.768 112.743 1.134872e+02 110.5504 112.04950 1.134452e+02 0
2017-02-02 113.243 113.243 112.077 113.311 1.131072e+02 110.5579 112.65541 1.130148e+02 0
2017-02-03 112.779 113.232 112.324 112.789 1.130144e+02 110.5637 111.89521 1.130989e+02 0
2017-02-06 112.647 112.771 112.028 112.639 1.128467e+02 110.5701 112.36212 1.128554e+02 0
2017-02-07 111.798 112.559 111.599 111.827 1.125949e+02 110.5676 111.99422 1.123721e+02 0
2017-02-08 112.402 112.520 111.649 112.387 1.119267e+02 110.5795 111.59245 1.119399e+02 0
2017-02-13 113.970 114.135 113.452 113.914 1.133315e+02 113.9906 113.39922 1.132473e+02 0
2017-02-14 113.673 114.433 113.271 113.705 1.142276e+02 114.1492 113.43160 1.141844e+02 0
2017-02-24 112.676 112.950 112.064 112.682 1.133713e+02 113.3156 112.57386 1.133921e+02 0
2017-03-07 113.916 114.141 113.739 113.917 1.136974e+02 113.8656 113.61876 1.139655e+02 0
2017-03-20 112.665 112.884 112.467 112.674 1.132525e+02 110.5782 112.57962 1.133871e+02 0
2017-03-28 111.188 111.296 110.755 111.226 1.108421e+02 110.5600 110.31948 1.108461e+02 0
2017-04-20 109.368 109.383 108.943 109.375 1.087041e+02 110.5981 108.76484 1.087224e+02 0
2017-04-26 111.175 111.591 111.052 111.191 1.109776e+02 114.2454 111.01805 1.109709e+02 0
2017-04-30 111.303 111.900 111.303 111.302 1.108528e+02 111.5897 111.55957 1.112584e+02 0
2017-05-11 113.814 113.946 113.213 113.809 1.140786e+02 113.9558 113.63549 1.142211e+02 0
2017-05-15 113.648 113.757 112.981 113.642 1.132890e+02 113.9788 113.36774 1.132042e+02 0
2017-05-23 111.936 112.111 111.707 111.957 1.109440e+02 113.9738 111.05377 1.109214e+02 0
2017-05-25 111.716 111.794 110.887 111.730 1.113975e+02 113.9644 111.68964 1.113937e+02 0
2017-05-31 110.769 111.446 110.769 110.796 1.110870e+02 113.9537 110.55642 -1.822429e+24 0
2017-06-01 111.460 111.699 110.342 111.437 1.105362e+02 113.9513 110.73542 1.106243e+02 0
2017-06-05 110.380 110.437 109.242 110.381 1.102679e+02 113.9559 110.44339 1.102188e+02 0
2017-06-11 110.308 110.316 109.676 110.288 1.098979e+02 113.9460 109.86264 1.098607e+02 0
2017-06-15 111.047 111.404 110.661 110.952 1.096929e+02 113.9348 112.63790 1.097667e+02 0
2017-06-25 111.255 111.711 111.222 111.239 1.116754e+02 111.4224 111.20914 1.114986e+02 0
2017-06-26 111.903 112.438 111.468 111.858 1.111264e+02 111.8163 111.22200 1.111238e+02 0
2017-07-03 113.369 113.370 112.779 113.386 1.124001e+02 113.4239 112.54332 1.124085e+02 0
2017-07-12 113.304 113.514 112.874 113.335 1.140079e+02 113.9186 112.85831 1.140745e+02 0
2017-07-17 112.600 112.617 111.701 112.581 1.123697e+02 112.8243 112.36611 1.121960e+02 0
2017-08-10 109.090 109.379 108.797 109.106 1.101064e+02 110.1632 109.35053 1.102432e+02 0
2017-08-15 110.573 110.941 110.573 110.596 1.099298e+02 113.7011 109.75463 1.096039e+02 0
2017-08-16 109.983 110.312 109.634 109.999 1.109813e+02 111.0133 110.53241 1.104412e+02 0
2017-08-21 109.074 109.530 109.052 108.944 1.095076e+02 109.3806 108.67014 1.093827e+02 0
2017-08-22 109.756 109.806 108.999 109.731 1.091809e+02 109.5802 109.03443 1.089123e+02 0
2017-08-24 109.500 109.797 109.123 109.514 1.090310e+02 113.6575 109.02569 1.089677e+02 0
2017-08-30 110.468 110.645 109.952 110.460 1.096426e+02 110.4865 109.79983 1.096692e+02 0
2017-08-31 110.117 110.369 109.580 110.129 1.104483e+02 110.6410 109.60492 1.108410e+02 0
2017-09-03 109.777 109.908 109.397 109.795 1.104546e+02 110.2892 109.59259 1.104523e+02 0
2017-09-17 111.153 111.581 111.124 111.197 1.099296e+02 111.2947 109.78810 1.097757e+02 0
2017-09-18 111.487 111.862 111.272 111.496 1.110282e+02 111.6023 111.46193 1.110728e+02 0
2017-09-26 112.434 113.237 112.286 112.377 1.118084e+02 110.7772 111.44612 1.124466e+02 0
2017-09-27 112.854 113.190 112.481 112.860 1.125013e+02 113.2893 112.50105 1.124775e+02 0
2017-10-12 112.244 112.249 111.699 112.239 1.123833e+02 112.3807 112.13537 1.124210e+02 0
2017-10-15 111.877 112.076 111.651 111.882 1.122064e+02 112.1289 111.56435 1.122592e+02 0
2017-11-10 113.369 113.624 113.236 113.375 1.135208e+02 111.6006 113.27034 1.139353e+02 0
2017-11-13 113.690 113.705 113.246 113.686 1.133465e+02 111.6151 113.23748 1.134610e+02 0
2017-11-14 113.600 113.907 113.310 113.585 1.135783e+02 113.6092 113.17646 1.136233e+02 0
2017-11-24 111.259 111.572 111.259 111.254 1.121415e+02 111.4082 111.14298 1.121588e+02 0
2017-11-27 111.649 111.649 110.847 111.671 1.122717e+02 111.6365 111.33888 1.122648e+02 0
2017-12-08 113.197 113.585 113.123 113.173 1.123804e+02 113.5431 112.39668 1.123534e+02 0
2017-12-11 113.527 113.681 113.241 113.543 1.131035e+02 113.8103 113.12711 1.130811e+02 0
2017-12-12 113.550 113.739 113.374 113.540 1.135455e+02 113.5218 113.10399 1.135551e+02 0
2017-12-13 113.513 113.527 112.966 113.545 1.135917e+02 113.5286 113.48159 1.131179e+02 0
2017-12-14 112.746 112.873 112.473 112.782 1.135312e+02 113.5275 113.01981 1.135626e+02 0
2017-12-19 112.590 113.026 112.511 112.568 1.126985e+02 112.7850 112.24653 1.128676e+02 0
2017-12-25 113.295 113.345 113.211 113.308 1.132881e+02 113.3202 113.41332 1.133343e+02 0
2017-12-28 113.222 113.264 112.667 113.217 1.132134e+02 113.4818 113.22886 1.132159e+02 0
2018-01-04 112.606 112.854 112.507 112.607 1.122742e+02 112.4603 112.31628 1.122544e+02 0
2018-01-11 111.426 111.871 111.334 111.444 1.127915e+02 112.7302 111.23804 1.127769e+02 0
2018-01-17 110.347 110.909 110.208 110.388 1.107012e+02 111.0334 110.73524 1.106592e+02 0
2018-01-22 110.697 111.148 110.614 110.684 1.111804e+02 111.0692 110.42947 1.112010e+02 0
2018-01-25 109.306 109.462 108.590 109.326 1.102574e+02 110.2357 108.81480 1.102410e+02 0
2018-01-29 108.648 109.189 108.511 108.639 1.098181e+02 109.8435 108.21693 1.098547e+02 0
2018-02-02 109.387 110.467 109.304 109.406 1.092735e+02 109.6837 109.28919 1.092197e+02 0
2018-02-22 107.630 107.757 106.649 107.555 1.075116e+02 108.0684 107.52287 1.074937e+02 0
2018-03-01 106.643 107.193 106.567 106.640 1.075988e+02 107.7021 106.66641 1.077437e+02 0
2018-03-06 106.276 106.453 105.853 106.250 1.054694e+02 109.9114 112.27250 1.054518e+02 0
2018-03-07 105.614 106.180 105.511 105.537 1.062154e+02 110.0522 112.27188 1.062335e+02 0
2018-03-08 106.169 106.254 105.898 106.186 1.058257e+02 109.7437 112.26479 1.057642e+02 0
2018-03-09 106.403 107.029 106.359 106.406 1.060927e+02 110.0195 112.25776 1.061154e+02 0
2018-03-12 106.886 106.966 106.374 106.891 1.064310e+02 110.4027 112.25402 1.064393e+02 0
2018-03-13 106.318 107.275 106.263 106.260 1.068864e+02 106.8678 112.24696 1.089610e+02 0
2018-03-14 106.549 106.734 106.084 106.508 1.064317e+02 107.3842 112.24617 1.063746e+02 0
2018-03-15 106.154 106.172 105.790 106.155 1.089557e+02 109.7607 112.24275 1.089263e+02 0
2018-03-16 106.328 106.328 105.607 106.309 1.085514e+02 109.9671 112.23874 1.085851e+02 0
2018-03-19 105.968 106.298 105.681 105.969 1.086904e+02 106.4472 112.22750 1.086635e+02 0
2018-03-20 106.038 106.583 105.984 105.996 1.060489e+02 106.2405 112.17577 1.061186e+02 0
2018-03-21 106.480 106.512 106.139 106.469 1.061152e+02 106.7519 112.17600 1.060640e+02 0
2018-03-22 105.917 105.961 105.283 105.929 1.065849e+02 106.6064 112.18857 1.065544e+02 0
2018-03-23 104.979 105.279 104.667 104.968 1.061759e+02 105.8900 112.19356 1.061328e+02 0
2018-03-25 104.840 105.244 104.736 104.859 -2.371204e+78 105.3385 112.19497 1.052540e+02 0
2018-03-26 105.546 105.888 105.459 105.500 1.049677e+02 105.4038 112.19878 1.051239e+02 0
2018-03-27 105.522 106.324 105.431 105.493 1.056698e+02 106.1071 105.61172 1.053908e+02 0
2018-03-28 106.799 106.926 106.259 106.812 1.056440e+02 106.4399 112.20139 1.057129e+02 0
2018-03-29 106.474 106.504 106.116 106.479 1.069839e+02 107.0609 112.20378 1.069786e+02 0
2018-04-01 106.318 106.446 105.962 106.312 1.067382e+02 106.4234 106.17705 1.067413e+02 0
2018-04-02 105.805 106.590 105.695 105.799 1.066031e+02 106.6086 112.20658 1.064075e+02 0
2018-04-03 106.429 106.680 105.995 106.436 1.061274e+02 106.5891 112.20675 1.060000e+02 0
2018-04-04 106.784 107.481 106.716 106.774 1.064474e+02 106.7083 112.20989 1.064452e+02 0
2018-04-11 106.814 107.412 106.703 106.829 1.071110e+02 107.1233 112.21758 1.071168e+02 0
2018-04-15 107.488 107.505 107.136 107.498 1.073084e+02 110.6866 107.39906 1.071891e+02 0
2018-04-17 107.028 107.378 107.007 107.016 1.071073e+02 107.2334 112.21904 1.071576e+02 0
2018-04-19 107.440 107.848 107.405 107.432 1.073801e+02 107.5344 112.22102 1.073638e+02 0
2018-04-22 107.843 108.630 107.733 107.869 1.074633e+02 107.9125 112.22190 1.074549e+02 0
2018-04-24 108.802 109.374 108.789 108.803 1.087776e+02 111.3496 108.79896 1.087183e+02 0
2018-05-01 109.846 109.998 109.652 109.872 1.093279e+02 109.9105 109.37096 1.093360e+02 0
2018-05-03 109.119 109.261 108.649 109.096 1.098841e+02 109.8780 108.86835 1.098941e+02 0
2018-05-06 109.139 109.382 108.757 109.146 1.092306e+02 109.1920 108.72659 1.092076e+02 0
2018-05-07 108.940 109.331 108.858 108.943 1.091211e+02 109.4594 112.22448 1.091240e+02 0
2018-05-08 109.039 109.821 109.001 109.024 1.090087e+02 109.3054 112.22367 1.090137e+02 0
2018-05-09 109.826 109.987 109.332 109.847 1.089762e+02 109.9226 109.07330 1.090585e+02 0
2018-05-15 110.283 110.379 110.043 110.297 1.097015e+02 110.4616 109.71590 1.096350e+02 0
2018-05-21 111.007 111.171 110.801 110.978 1.108701e+02 111.4024 110.88708 1.108704e+02 0
2018-05-23 109.909 109.913 108.976 109.869 1.108829e+02 110.8361 109.50223 1.109121e+02 0
2018-05-24 109.330 109.721 109.119 109.312 1.100299e+02 109.8620 108.99522 1.099818e+02 0
2018-05-29 108.449 109.060 108.399 108.394 1.093773e+02 109.3370 108.45294 1.094118e+02 0
2018-06-03 109.598 109.749 109.373 109.598 1.087844e+02 109.8968 108.85207 1.087129e+02 0
2018-06-18 110.169 110.193 109.559 110.138 1.106902e+02 110.5732 110.08983 1.106269e+02 0
2018-06-19 110.081 110.244 109.870 110.071 1.101929e+02 110.1499 109.45053 1.104104e+02 0
2018-06-20 110.344 110.749 109.886 110.352 1.101077e+02 110.3268 111.17836 1.100121e+02 0

Table 3.5.2 [213 x 10] : Preditive Cl Error for Univariate gjrGARCH.

Table 3.5.1 states the forecast highest price lower than forecast lowest price where Table 3.5.2 states forecast closing price not in the range of forecast highest and lowest price. Betting Strategy in next section will omit the error and only trade on the high winning opportunities.

4 Betting Strategy

4.1 Kelly Criterion

\[\begin{equation} f = \frac{Edge}{Odds} = \frac{p^∗ x−(1−p^∗)}{x} \ \cdots Equation\ 4.1.1 \end{equation}\]

The section 1 inside Application of Kelly Criterion model in Sportsbook Investment shows the ROI for betting on sportsbook, where section 2 will be started during spared time after FOREX market.

For the betting strategy, here I need to do correction from Binary Q1 as stated in section Introduction. Below I tidy the dataset to match the bid/ask price for close a transaction.

As we know from previous paper, the closing price will be settled price (closed transaction) if the forecast price has no occured within a day (from 12:00:01 AM until next day 12:00:00 AM, due to system calculate the price spend a minute, therefore the opening price will not in count.). There will be 2 limit orders (but and sell) placed after 12:00:00AM. Once one among the order limit stand (opened transaction), another limit order will be automatically turned to be closed transaction request. Therefore there will only transaction within a trading day unless no any order limit placed stand.

## Here I combine real-time dataset with the daily dataset.
pred <- merge(HL_tick_data, pred,  by = 'Date') %>% 
  tbl_df %>% 
  arrange(DateTime)

## Tidy dataset.
## bid price for sell, ask price for buy orders. bid price always lower than ask price due to banker need to earn vigorish/spread margins. We need to see bid price if we wanna sell and ask price when we wanna buy.
pred %<>% group_by(Date) %>% 
    dplyr::filter(Bid == max(Bid, na.rm = TRUE)|Ask == min(Ask, na.rm = TRUE)) %>% 
    dplyr::select(DateTime, Date, USDJPY.High, USDJPY.Low, USDJPY.Close, sq, Bid, Ask, Fct.High, Fct.Low, Fct.Close) %>% 
    rename(High = USDJPY.High, Low = USDJPY.Low, Close = USDJPY.Close) %>% tbl_df

pred %<>% mutate(
        Fct.High = round(Fct.High, 3), 
        Fct.Low = round(Fct.Low, 3), 
        Fct.Close = round(Fct.Close, 3), 
        Sell = ifelse((Fct.High <= High & 
                       Fct.High >= Low & 
                       Fct.High > Fct.Low) &        # Here I filter the 
                      (Fct.Close > Fct.High |       #  both HiLo and Cl 
                       Fct.Close < Fct.Low), 1, 0), #  predictive error.
        Buy = ifelse((Fct.Low >= Low & 
                      Fct.Low <= High & 
                      Fct.Low < Fct.High) &         # Here I filter the 
                     (Fct.Close > Fct.High |        #  both HiLo and Cl 
                      Fct.Close < Fct.Low), 1, 0))  #  predictive error.

## follow the seq to determine the buy or sell limit order stand within a day. Then the other side will be automatically switch to close transaction limit order but not placed another limit order.
pred <- ldply(split(pred, pred$Date), function(x) {
    x %<>% mutate(Trans = ifelse(!is.na(Bid), 'sell', 'buy'), 
                  Trans = ifelse(Sell == 1|Buy == 1, Trans, 0))
  
  if(x[1,]$Trans == 'sell'|x[1,]$Trans == 'buy') #if open transaction.
    x[nrow(x),]$Trans <- 'close'                 #  then close transaction.
  
  x }) %>% tbl_df

pred$.id <- NULL
pred %<>% mutate(Trans = factor(Trans))

Topic 2.1.4 Staking Model in paper Binary Q1 states that the financial market unable to know the payout rate in advanced, therefore use the forecasted pice based on statistical models. I use the amount calculated by Kelly Criterion as the stakes (possible loss or terms as stop-loss in financial market), variance of forecasted Hi/Lo and also Closed price. However it doesn’t make sense in financial market.

Hedge Fund Market Wizards has a good discussion on this in Ed Thorp’s chapter.

  • Kelly Criterion has highest long-term growth rate, but gives you higher drawdowns and risk of ruin.
  • In gambling you know your theoretical odds, but in trading your win rate is only an estimate.
  • If you estimate your win rate incorrectly, the profits you’d miss out on by underestimating are less than the losses you’d incur by being overconfident.
  • If there’s large uncertainty about your win rate (e.g. trend following systems) Kelly may be inappropriate.
  • “Suppose you have 1MM and your max allowable drawdown is 200K - then from the Kelly perspective you don’t have 1MM, you have 200K in capital.”
  • If you bet .5 K.C. you get .75 of the returns with .5 of the volatility - half Kelly is better psychologically.

Source quote 4.1.1 : Kelly Criterion in Forex primordia • Jul 22, 2017, 7:07 PM

EXAMPLE Let’s look at a trading example.

Say, you have a EURUSD trading strategy that wins approximately 70% of the time. The StopLoss in your strategy is 40 pips and the TakeProfit is 20 pips (spread accounted for).

This means that your B and P parameters are as follows:

B = 20 pips / 40 pips = 0.5 P = 70% = 0.7 Let’s input these values into Kelly’s formula and see what we get:

K = ( PxB – (1–P) ) / B K = ( 0.7 x 0.5 – (1–0.7) ) / 0.5 = 0.1

This means that the optimal risk for this trading strategy that will maximize your profits in the long term is 10%.

If you want to be a bit more conservative, then go with the Half-Kelly of 5%.

Whatever you do, don’t invest more than 10% per trade – it’s pointless.

If you invest more than 20% then you will turn this great strategy into one that will ruin your account.

That’s how you apply the Kelly Criterion in practice.

Source quote 4.1.2 : ForexBoat:Kelly Criterion5

4.2 Staking Model

Chapter 20 Against the Odds: The Mathematics of Gambling6 elaborates the odds price, edge, Kelly Criterion staking model, portfolio, Entropy and also day trading.

\[\begin{eqnarray} g_t(f) &=& \frac{1}{t} \ln \left( \frac{B_t}{B_0} \right) \\ &=& \frac{1}{t} \ln \left( \prod_{i=1}^t [1+r +f(Z_t -r)\varepsilon] \right) \\ &=& \frac{1}{t} \sum_{i=1}^t \ln \left( [1+r +f(Z_t -r)\varepsilon] \right) \end{eqnarray} \ \cdots Equation\ 4.2.1 \]

By applying the law of central limit theorem for large data, here we get:

\[\begin{equation} g(f) = \lim_{t \rightarrow \infty} g_t(f) = E[\ln(1+r + f (Z-r)\varepsilon)] \ \cdots Equation\ 4.2.2 \end{equation}\]

and \(\varepsilon_{i}\) is a weight function where applied statistical models to forecast the price. I used some models and eventually concludes the GJR-GARCH model generated highest ROI. The weight function doesn’t same with different currencies since it using substraction among 2 forecast prices but not in ratio7.

\[\begin{equation} \varepsilon = h(x)_{1} - v \ \cdots Equation\ 4.2.3 \end{equation}\]

\(v\) is a switch function to determine the settled price.

\[\begin{equation} v \left\{\begin{matrix} h(x)_{2} & if(Lo <= h(x)_{2} <= Hi) & \\ Cl & otherwise \end{matrix}\right. \ \cdots Equation\ 4.2.4 \end{equation}\]

where \(Hi\), \(Lo\) and \(Cl\) are the daily highest, lowest and closed price.

Binary Q1 applied a more sophisticated model as stated above to compares all possible outcomes of predicted price and ROI. Due to the financial betting only allows player place bets and awaiting for the settlement (unless placed another bet at other predicted price), there will be no any limit order and close transaction request (similar with FOREX trading market can place more than 1 limit order to lock the profit).

The staking model in previous papers (includes Binary Q1 (Extention)) have only MISTAKE which is wrote for real FOREX trading market but not financial betting since I only think of spread betting but forgot the normal betting :

  • Forecast highest price to sell and forecast lowest price to buy to maximise the profit : I wrote 2nd forecast price as settled price if it was between the daily Hi-Lo range (otherwise daily closed price will be settled price). There will be only applicable to FOREX trading market but NOT financial betting market.
  • However it will be more easily since the settled price will be only daily closed price.

The paper Binary Q1 compares all outcome :

  • Hi-Cl + Lo-Cl generate highest ROI in financial betting market.8
  • Hi-Lo or Lo-Hi will be best betting strategy for noarmal FOREX market.
Return on Investment
.id StartDate LatestDate InitFund LatestFund Profit RR
fundAutoArimaHICL 2015-01-02 2017-01-20 1000 1401.694 401.6938 140.17%
fundAutoArimaLOCL 2015-01-02 2017-01-20 1000 1499.818 499.8177 149.98%
Combine 2015-01-02 2017-01-20 2000 2901.512 901.5115 145.08%

Table 4.2.1 : betting strategy for financial betting.

No               .id  StartDate LatestDate InitFund  LatesFund    Profit        RR
07 fundAutoArimaHILO 2015-01-02 2017-01-20     1000   1637.251 637.25113 163.7251%
10 fundAutoArimaLOHI 2015-01-02 2017-01-20     1000   1716.985 716.98492 171.6985%

Table 4.2.2 : betting strategy for normal FOREX market.

Kindly refer to 2.1.5 Return of Investment in binary Q1 for full table. However, the paper does not filter the univariate preditive error.

4.3 Optimal Edge

I don’t pretend to know the optimal edge for staking. Here I need to compare above models with normal Kelly model.

I used to use Edge1 = ifelse(fB1 > 0, B1, ifelse(fS1 > 0, S1, 0)) to measure the edge for staking while it might be wrong due to I put the edge for selling as secondary edge for Buy as well. Here I use Edge1a = ifelse(fB1 > 0, B1, 0) and Edge1b = ifelse(fS1 > 0, S1, 0) to seperates the edge for Buy and Sell. It means that the buy action will be primary and sell action will be secondary where the edge for both buy and sell will stand. Therefore most of the observation will overcame probabilities 0.5.

4.4 Application of Kelly Criterion to Normal FOREX Market

Previous paper using the forecast HiLo price and forecast closing price as settlement, the stakes will be the edge for pnorm(Hi, mean(Lo), sd(Lo)) and vice verse. It will be \(\frac{\sigma_{Hi}}{\sigma_{Lo}}\) or \(\frac{\sigma_{Lo}}{\sigma_{Hi}}\) but missing the difference of pips between buy/sell price and closed price.

In this paper will count the difference of pips and also leverage ratio. The risk management on leverage will be counted into the staking model.

The papers The Kelly Criterion and the Stock Market and Beat the Market - A Scientific Stock Market System states the application of Kelly criterion onto the stock market. Kindly refer to the paper in Reference for further knowledge.

4.5 Application of Kelly Criterion to Financial Betting Market

Previous paper use Kelly model to placed a certain amount and awaiting for settlement. The forecast closed price will be the settled price if it was within the range of HiLo in the day. There is not workable due to traders not allowed to placed an close transaction limit order in financial betting market.

Due to there has no dataset for financial betting, therefore I do not have the payout rate or odds price for minutely, hourly and daily betting. The sample dataset and research might refer to Application of Kelly Criterion model in Sportsbook Investment where collected AH (Asian-Handicap) and OU (Over-Under) odds price of couple of bookmakers and placed bets9.

I tune a bit in this paper which is set the forecast closed price cannot be settled price. There will be another research which is collect odds price from operators to test the ROI.

5 Return of Investment

5.1 Normal FOREX Market

sim_staking(pred) %>% 
  dplyr::select(Date, Edge1a, Edge1b, Edge2a, Edge2b, Buy, Sell, Trans, BR, Profit, Bal) %>% 
  kable(caption = 'ROI for Normal FOREX Market') %>% 
  kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive')) %>%
  scroll_box(width = '100%', height = '400px')
ROI for Normal FOREX Market
Date Edge1a Edge1b Edge2a Edge2b Buy Sell Trans BR Profit Bal
2016-01-05 0.000000 9.728813 9.844852 0.000000 0 0 sell 10000.00 0.000000 10000.00
2016-01-05 0.000000 9.728813 9.844852 0.000000 0 0 close 10000.00 0.000000 10000.00
2016-01-06 0.000000 9.728381 9.839840 0.000000 0 0 0 10000.00 0.000000 10000.00
2016-01-06 0.000000 9.728381 9.839840 0.000000 0 0 0 10000.00 0.000000 10000.00
2016-01-07 0.000000 9.728319 9.827605 0.000000 0 0 0 10000.00 0.000000 10000.00
2016-01-07 0.000000 9.728319 9.827605 0.000000 0 0 0 10000.00 0.000000 10000.00
2016-01-08 0.000000 9.728504 9.817595 0.000000 0 0 0 10000.00 0.000000 10000.00
2016-01-08 0.000000 9.728504 9.817595 0.000000 0 0 0 10000.00 0.000000 10000.00
2016-01-11 0.000000 9.728689 9.823462 0.000000 0 0 0 10000.00 0.000000 10000.00
2016-01-11 0.000000 9.728689 9.823462 0.000000 0 0 0 10000.00 0.000000 10000.00
2016-01-12 0.000000 9.729490 9.799335 0.000000 0 0 0 10000.00 0.000000 10000.00
2016-01-12 0.000000 9.729490 9.799335 0.000000 0 0 0 10000.00 0.000000 10000.00
2016-01-13 0.000000 9.729305 9.817824 0.000000 0 0 0 10000.00 0.000000 10000.00
2016-01-13 0.000000 9.729305 9.817824 0.000000 0 0 0 10000.00 0.000000 10000.00
2016-01-14 0.000000 9.729367 9.772787 0.000000 0 0 0 10000.00 0.000000 10000.00
2016-01-14 0.000000 9.729367 9.772787 0.000000 0 0 0 10000.00 0.000000 10000.00
2016-01-15 0.000000 9.729059 9.840563 0.000000 0 0 0 10000.00 0.000000 10000.00
2016-01-15 0.000000 9.729059 9.840563 0.000000 0 0 0 10000.00 0.000000 10000.00
2016-01-18 0.000000 9.729059 9.764760 0.000000 0 0 0 10000.00 0.000000 10000.00
2016-01-18 0.000000 9.729059 9.764760 0.000000 0 0 0 10000.00 0.000000 10000.00
2016-01-19 0.000000 9.729182 9.840743 0.000000 0 0 0 10000.00 0.000000 10000.00
2016-01-19 0.000000 9.729182 9.840743 0.000000 0 0 0 10000.00 0.000000 10000.00
2016-01-20 0.000000 9.728998 9.840533 0.000000 0 0 0 10000.00 0.000000 10000.00
2016-01-20 0.000000 9.728998 9.840533 0.000000 0 0 0 10000.00 0.000000 10000.00
2016-01-21 0.000000 9.729121 9.718500 0.000000 0 0 0 10000.00 0.000000 10000.00
2016-01-21 0.000000 9.729121 9.718500 0.000000 0 0 0 10000.00 0.000000 10000.00
2016-01-22 0.000000 9.729182 9.726261 0.000000 0 0 0 10000.00 0.000000 10000.00
2016-01-22 0.000000 9.729182 9.726261 0.000000 0 0 0 10000.00 0.000000 10000.00
2016-01-25 0.000000 9.729244 9.840863 0.000000 0 0 0 10000.00 0.000000 10000.00
2016-01-25 0.000000 9.729244 9.840863 0.000000 0 0 0 10000.00 0.000000 10000.00
2016-01-26 0.000000 9.729428 9.841131 0.000000 0 0 0 10000.00 0.000000 10000.00
2016-01-26 0.000000 9.729428 9.841131 0.000000 0 0 0 10000.00 0.000000 10000.00
2016-01-27 0.000000 9.729121 9.840833 0.000000 0 0 0 10000.00 0.000000 10000.00
2016-01-27 0.000000 9.729121 9.840833 0.000000 0 0 0 10000.00 0.000000 10000.00
2016-01-28 0.000000 9.729059 9.840833 0.000000 0 0 0 10000.00 0.000000 10000.00
2016-01-28 0.000000 9.729059 9.840833 0.000000 0 0 0 10000.00 0.000000 10000.00
2016-01-29 0.000000 9.728936 9.840683 0.000000 1 0 buy 10000.00 0.000000 10000.00
2016-01-29 0.000000 9.728936 9.840683 0.000000 0 0 close 10000.00 0.000000 10000.00
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2018-05-06 9.335739 0.000000 0.000000 9.242315 0 0 buy 10227.09 0.000000 10454.45
2018-05-06 9.335739 0.000000 0.000000 9.242315 0 0 close 10227.09 0.000000 10454.45
2018-05-07 0.000000 9.242584 0.000000 9.236912 0 0 0 10227.09 0.000000 10454.45
2018-05-07 0.000000 9.242584 0.000000 9.236912 0 0 0 10227.09 0.000000 10454.45
2018-05-08 0.000000 9.242584 0.000000 9.239760 0 0 0 10227.09 0.000000 10454.45
2018-05-08 0.000000 9.242584 0.000000 9.239760 0 0 0 10227.09 0.000000 10454.45
2018-05-09 9.312478 0.000000 0.000000 9.232829 0 0 buy 10227.09 0.000000 10454.45
2018-05-09 9.312478 0.000000 0.000000 9.232829 0 0 close 10227.09 0.000000 10454.45
2018-05-10 9.293606 0.000000 9.232799 0.000000 0 0 0 10227.09 0.000000 10454.45
2018-05-10 9.293606 0.000000 9.232799 0.000000 0 0 0 10227.09 0.000000 10454.45
2018-05-13 9.303444 0.000000 0.000000 9.236234 0 0 0 10227.09 0.000000 10454.45
2018-05-13 9.303444 0.000000 0.000000 9.236234 0 0 0 10227.09 0.000000 10454.45
2018-05-14 9.301932 0.000000 0.000000 9.233755 0 0 0 10227.09 0.000000 10454.45
2018-05-14 9.301932 0.000000 0.000000 9.233755 0 0 0 10227.09 0.000000 10454.45
2018-05-15 9.276025 0.000000 9.236646 0.000000 0 0 0 10227.09 0.000000 10454.45
2018-05-15 9.276025 0.000000 9.236646 0.000000 0 0 0 10227.09 0.000000 10454.45
2018-05-16 9.264130 0.000000 9.235050 0.000000 0 0 0 10227.09 0.000000 10454.45
2018-05-16 9.264130 0.000000 9.235050 0.000000 0 0 0 10227.09 0.000000 10454.45
2018-05-17 9.259241 0.000000 9.245070 0.000000 0 0 0 10227.09 0.000000 10454.45
2018-05-17 9.259241 0.000000 9.245070 0.000000 0 0 0 10227.09 0.000000 10454.45
2018-05-20 9.241992 0.000000 9.252299 0.000000 0 0 0 10227.09 0.000000 10454.45
2018-05-20 9.241992 0.000000 9.252299 0.000000 0 0 0 10227.09 0.000000 10454.45
2018-05-21 9.237171 0.000000 9.264659 0.000000 1 0 buy 10227.09 9.237171 10463.68
2018-05-21 9.238072 0.000000 9.265560 0.000000 0 0 close 10236.31 0.000000 10472.90
2018-05-22 9.240125 0.000000 9.256344 0.000000 0 0 0 10236.31 0.000000 10472.90
2018-05-22 9.240125 0.000000 9.256344 0.000000 0 0 0 10236.31 0.000000 10472.90
2018-05-23 9.287992 0.000000 9.245534 0.000000 0 0 sell 10236.31 0.000000 10472.90
2018-05-23 9.287992 0.000000 9.245534 0.000000 0 0 close 10236.31 0.000000 10472.90
2018-05-24 9.318419 0.000000 0.000000 9.233878 0 0 0 10236.31 0.000000 10472.90
2018-05-24 9.318419 0.000000 0.000000 9.233878 0 0 0 10236.31 0.000000 10472.90
2018-05-27 9.307967 0.000000 0.000000 9.234356 0 0 0 10236.31 0.000000 10472.90
2018-05-27 9.307967 0.000000 0.000000 9.234356 0 0 0 10236.31 0.000000 10472.90
2018-05-28 9.299024 0.000000 0.000000 9.234216 0 0 0 10236.31 0.000000 10472.90
2018-05-28 9.299024 0.000000 0.000000 9.234216 0 0 0 10236.31 0.000000 10472.90
2018-05-29 9.356590 0.000000 0.000000 9.240009 0 0 sell 10236.31 0.000000 10472.90
2018-05-29 9.356590 0.000000 0.000000 9.240009 0 0 close 10236.31 0.000000 10472.90
2018-05-30 9.348431 0.000000 0.000000 9.246636 0 0 0 10236.31 0.000000 10472.90
2018-05-30 9.348431 0.000000 0.000000 9.246636 0 0 0 10236.31 0.000000 10472.90
2018-05-31 9.359075 0.000000 0.000000 9.247968 0 0 0 10236.31 0.000000 10472.90
2018-05-31 9.359075 0.000000 0.000000 9.247968 0 0 0 10236.31 0.000000 10472.90
2018-06-03 9.327972 0.000000 0.000000 9.233778 0 0 0 10236.31 0.000000 10472.90
2018-06-03 9.327972 0.000000 0.000000 9.233778 0 0 0 10236.31 0.000000 10472.90
2018-06-04 9.292749 0.000000 0.000000 9.233728 0 0 0 10236.31 0.000000 10472.90
2018-06-04 9.292749 0.000000 0.000000 9.233728 0 0 0 10236.31 0.000000 10472.90
2018-06-05 9.283829 0.000000 9.234642 0.000000 0 0 0 10236.31 0.000000 10472.90
2018-06-05 9.283829 0.000000 9.234642 0.000000 0 0 0 10236.31 0.000000 10472.90
2018-06-06 9.272611 0.000000 9.235134 0.000000 0 0 0 10236.31 0.000000 10472.90
2018-06-06 9.272611 0.000000 9.235134 0.000000 0 0 0 10236.31 0.000000 10472.90
2018-06-07 9.269940 0.000000 9.279905 0.000000 0 0 0 10236.31 0.000000 10472.90
2018-06-07 9.269940 0.000000 9.279905 0.000000 0 0 0 10236.31 0.000000 10472.90
2018-06-10 9.312423 0.000000 0.000000 9.233913 0 0 0 10236.31 0.000000 10472.90
2018-06-10 9.312423 0.000000 0.000000 9.233913 0 0 0 10236.31 0.000000 10472.90
2018-06-11 9.290239 0.000000 9.234035 0.000000 0 0 0 10236.31 0.000000 10472.90
2018-06-11 9.290239 0.000000 9.234035 0.000000 0 0 0 10236.31 0.000000 10472.90
2018-06-12 9.257919 0.000000 9.285125 0.000000 0 0 0 10236.31 0.000000 10472.90
2018-06-12 9.257919 0.000000 9.285125 0.000000 0 0 0 10236.31 0.000000 10472.90
2018-06-13 9.252202 0.000000 9.241657 0.000000 0 0 0 10236.31 0.000000 10472.90
2018-06-13 9.252202 0.000000 9.241657 0.000000 0 0 0 10236.31 0.000000 10472.90
2018-06-14 9.270394 0.000000 9.236519 0.000000 0 0 0 10236.31 0.000000 10472.90
2018-06-14 9.270394 0.000000 9.236519 0.000000 0 0 0 10236.31 0.000000 10472.90
2018-06-17 9.248862 0.000000 9.248784 0.000000 0 0 0 10236.31 0.000000 10472.90
2018-06-17 9.248862 0.000000 9.248784 0.000000 0 0 0 10236.31 0.000000 10472.90
2018-06-18 9.260377 0.000000 9.239467 0.000000 0 0 sell 10236.31 0.000000 10472.90
2018-06-18 9.260377 0.000000 9.239467 0.000000 0 0 close 10236.31 0.000000 10472.90
2018-06-19 9.290793 0.000000 9.234217 0.000000 0 1 sell 10236.31 0.000000 10472.90
2018-06-19 9.290793 0.000000 9.234217 0.000000 0 0 close 10236.31 0.000000 10472.90
2018-06-20 9.234609 0.000000 9.235729 0.000000 0 0 0 10236.31 0.000000 10472.90
2018-06-20 9.234609 0.000000 9.235729 0.000000 0 0 0 10236.31 0.000000 10472.90
2018-06-21 9.266227 0.000000 9.244683 0.000000 0 0 0 10236.31 0.000000 10472.90
2018-06-21 9.266227 0.000000 9.244683 0.000000 0 0 0 10236.31 0.000000 10472.90
2018-06-24 9.272751 0.000000 9.234078 0.000000 0 0 0 10236.31 0.000000 10472.90
2018-06-24 9.272751 0.000000 9.234078 0.000000 0 0 0 10236.31 0.000000 10472.90
2018-06-25 9.292300 0.000000 9.233779 0.000000 0 0 0 10236.31 0.000000 10472.90
2018-06-25 9.292300 0.000000 9.233779 0.000000 0 0 0 10236.31 0.000000 10472.90
2018-06-26 9.280676 0.000000 9.233757 0.000000 0 0 0 10236.31 0.000000 10472.90
2018-06-26 9.280676 0.000000 9.233757 0.000000 0 0 0 10236.31 0.000000 10472.90
2018-06-27 9.293484 0.000000 9.238485 0.000000 0 0 0 10236.31 0.000000 10472.90
2018-06-27 9.293484 0.000000 9.238485 0.000000 0 0 0 10236.31 0.000000 10472.90
2018-06-28 9.264147 0.000000 9.236586 0.000000 0 0 0 10236.31 0.000000 10472.90
2018-06-28 9.264147 0.000000 9.236586 0.000000 0 0 0 10236.31 0.000000 10472.90
2018-07-01 9.270303 0.000000 9.249368 0.000000 0 0 0 10236.31 0.000000 10472.90
2018-07-01 9.270303 0.000000 9.249368 0.000000 0 0 0 10236.31 0.000000 10472.90
2018-07-02 9.246197 0.000000 9.253580 0.000000 0 0 0 10236.31 0.000000 10472.90
2018-07-02 9.246197 0.000000 9.253580 0.000000 0 0 0 10236.31 0.000000 10472.90
2018-07-03 9.249498 0.000000 9.249774 0.000000 0 0 0 10236.31 0.000000 10472.90
2018-07-03 9.249498 0.000000 9.249774 0.000000 0 0 0 10236.31 0.000000 10472.90
2018-07-04 9.263317 0.000000 9.237735 0.000000 0 0 0 10236.31 0.000000 10472.90
2018-07-04 9.263317 0.000000 9.237735 0.000000 0 0 0 10236.31 0.000000 10472.90
2018-07-05 9.252202 0.000000 9.243763 0.000000 0 0 0 10236.31 0.000000 10472.90
2018-07-05 9.252202 0.000000 9.243763 0.000000 0 0 0 10236.31 0.000000 10472.90

Table 5.1.1 : ROI for normal FOREX market.

Graph 5.1.1A : ROI for normal FOREX market. (None)

Graph 5.1.1B : ROI for normal FOREX market. (Mixed Kelly model)

Graph 5.1.1C : ROI for normal FOREX market. (Normal Kelly model)

Graph 5.1.1D : ROI for normal FOREX market. (Adjusted Kelly model 1)

Graph 5.1.1E : ROI for normal FOREX market. (Adjusted Kelly model 2)

Graph 5.1.1F : ROI for normal FOREX market. (Adjusted Kelly model 3)

Graph 5.1.1G : ROI for normal FOREX market. (Adjusted Kelly model 4)

Graph 5.1.1H : ROI for normal FOREX market. (Adjusted Kelly model 5)

Graph 5.1.1G : ROI for normal FOREX market. (Adjusted Kelly model 6)

5.2 Financial Betting Market

sim_staking(pred, financial_bet = TRUE) %>% 
  #mutate(Trans = ifelse(!is.na(Bid), 'sell', 'buy')) %>% 
  dplyr::select(Date, Edge1a, Edge1b, Edge2a, Edge2b, Buy, Sell, Trans, BR, Profit, Bal) %>% 
  kable(caption = 'ROI for Financial Betting Market') %>% 
  kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive')) %>%
  scroll_box(width = '100%', height = '400px')
ROI for Financial Betting Market
Date Edge1a Edge1b Edge2a Edge2b Buy Sell Trans BR Profit Bal
2016-01-05 0 9.210853 9.210853 0 0 0 sell 10000.00 0.000000 10000.00
2016-01-05 0 9.210853 9.210853 0 0 0 close 10000.00 0.000000 10000.00
2016-01-06 0 9.210853 9.210853 0 0 0 0 10000.00 0.000000 10000.00
2016-01-06 0 9.210853 9.210853 0 0 0 0 10000.00 0.000000 10000.00
2016-01-07 0 9.210853 9.210853 0 0 0 0 10000.00 0.000000 10000.00
2016-01-07 0 9.210853 9.210853 0 0 0 0 10000.00 0.000000 10000.00
2016-01-08 0 9.210853 9.210853 0 0 0 0 10000.00 0.000000 10000.00
2016-01-08 0 9.210853 9.210853 0 0 0 0 10000.00 0.000000 10000.00
2016-01-11 0 9.210853 9.210853 0 0 0 0 10000.00 0.000000 10000.00
2016-01-11 0 9.210853 9.210853 0 0 0 0 10000.00 0.000000 10000.00
2016-01-12 0 9.210853 9.210853 0 0 0 0 10000.00 0.000000 10000.00
2016-01-12 0 9.210853 9.210853 0 0 0 0 10000.00 0.000000 10000.00
2016-01-13 0 9.210853 9.210853 0 0 0 0 10000.00 0.000000 10000.00
2016-01-13 0 9.210853 9.210853 0 0 0 0 10000.00 0.000000 10000.00
2016-01-14 0 9.210853 9.210853 0 0 0 0 10000.00 0.000000 10000.00
2016-01-14 0 9.210853 9.210853 0 0 0 0 10000.00 0.000000 10000.00
2016-01-15 0 9.210853 9.210853 0 0 0 0 10000.00 0.000000 10000.00
2016-01-15 0 9.210853 9.210853 0 0 0 0 10000.00 0.000000 10000.00
2016-01-18 0 9.210853 9.210853 0 0 0 0 10000.00 0.000000 10000.00
2016-01-18 0 9.210853 9.210853 0 0 0 0 10000.00 0.000000 10000.00
2016-01-19 0 9.210853 9.210853 0 0 0 0 10000.00 0.000000 10000.00
2016-01-19 0 9.210853 9.210853 0 0 0 0 10000.00 0.000000 10000.00
2016-01-20 0 9.210853 9.210853 0 0 0 0 10000.00 0.000000 10000.00
2016-01-20 0 9.210853 9.210853 0 0 0 0 10000.00 0.000000 10000.00
2016-01-21 0 9.210853 9.210853 0 0 0 0 10000.00 0.000000 10000.00
2016-01-21 0 9.210853 9.210853 0 0 0 0 10000.00 0.000000 10000.00
2016-01-22 0 9.210853 9.210853 0 0 0 0 10000.00 0.000000 10000.00
2016-01-22 0 9.210853 9.210853 0 0 0 0 10000.00 0.000000 10000.00
2016-01-25 0 9.210853 9.210853 0 0 0 0 10000.00 0.000000 10000.00
2016-01-25 0 9.210853 9.210853 0 0 0 0 10000.00 0.000000 10000.00
2016-01-26 0 9.210853 9.210853 0 0 0 0 10000.00 0.000000 10000.00
2016-01-26 0 9.210853 9.210853 0 0 0 0 10000.00 0.000000 10000.00
2016-01-27 0 9.210853 9.210853 0 0 0 0 10000.00 0.000000 10000.00
2016-01-27 0 9.210853 9.210853 0 0 0 0 10000.00 0.000000 10000.00
2016-01-28 0 9.210853 9.210853 0 0 0 0 10000.00 0.000000 10000.00
2016-01-28 0 9.210853 9.210853 0 0 0 0 10000.00 0.000000 10000.00
2016-01-29 0 9.210853 9.210853 0 1 0 buy 10000.00 0.000000 10000.00
2016-01-29 0 9.210853 9.210853 0 0 0 close 10000.00 0.000000 10000.00
2016-02-01 0 9.210853 9.210853 0 0 0 0 10000.00 0.000000 10000.00
2016-02-01 0 9.210853 9.210853 0 0 0 0 10000.00 0.000000 10000.00
2016-02-02 0 9.210853 9.210853 0 0 1 sell 10000.00 9.210853 10009.21
2016-02-02 0 9.211774 9.211774 0 0 0 close 10009.21 0.000000 10018.42
2016-02-08 0 9.211774 9.211774 0 0 0 0 10009.21 0.000000 10018.42
2016-02-08 0 9.211774 9.211774 0 0 0 0 10009.21 0.000000 10018.42
2016-02-09 0 9.211774 9.211774 0 0 0 0 10009.21 0.000000 10018.42
2016-02-09 0 9.211774 9.211774 0 0 0 0 10009.21 0.000000 10018.42
2016-02-10 0 9.211774 9.211774 0 0 0 0 10009.21 0.000000 10018.42
2016-02-10 0 9.211774 9.211774 0 0 0 0 10009.21 0.000000 10018.42
2016-02-11 0 9.211774 9.211774 0 0 0 0 10009.21 0.000000 10018.42
2016-02-11 0 9.211774 9.211774 0 0 0 0 10009.21 0.000000 10018.42
2016-02-12 0 9.211774 9.211774 0 0 0 0 10009.21 0.000000 10018.42
2016-02-12 0 9.211774 9.211774 0 0 0 0 10009.21 0.000000 10018.42
2016-02-15 0 9.211774 9.211774 0 0 0 0 10009.21 0.000000 10018.42
2016-02-15 0 9.211774 9.211774 0 0 0 0 10009.21 0.000000 10018.42
2016-02-16 0 9.211774 9.211774 0 0 0 0 10009.21 0.000000 10018.42
2016-02-16 0 9.211774 9.211774 0 0 0 0 10009.21 0.000000 10018.42
2016-02-17 0 9.211774 9.211774 0 0 0 0 10009.21 0.000000 10018.42
2016-02-17 0 9.211774 9.211774 0 0 0 0 10009.21 0.000000 10018.42
2016-02-18 0 9.211774 9.211774 0 0 0 0 10009.21 0.000000 10018.42
2016-02-18 0 9.211774 9.211774 0 0 0 0 10009.21 0.000000 10018.42
2016-02-22 0 9.211774 9.211774 0 0 0 0 10009.21 0.000000 10018.42
2016-02-22 0 9.211774 9.211774 0 0 0 0 10009.21 0.000000 10018.42
2016-02-23 0 9.211774 9.211774 0 0 0 0 10009.21 0.000000 10018.42
2016-02-23 0 9.211774 9.211774 0 0 0 0 10009.21 0.000000 10018.42
2016-02-24 0 9.211774 9.211774 0 0 0 sell 10009.21 0.000000 10018.42
2016-02-24 0 9.211774 9.211774 0 0 0 close 10009.21 0.000000 10018.42
2016-02-25 0 9.211774 9.211774 0 0 0 0 10009.21 0.000000 10018.42
2016-02-25 0 9.211774 9.211774 0 0 0 0 10009.21 0.000000 10018.42
2016-02-26 0 9.211774 9.211774 0 0 0 0 10009.21 0.000000 10018.42
2016-02-26 0 9.211774 9.211774 0 0 0 0 10009.21 0.000000 10018.42
2016-02-29 0 9.211774 9.211774 0 0 0 0 10009.21 0.000000 10018.42
2016-02-29 0 9.211774 9.211774 0 0 0 0 10009.21 0.000000 10018.42
2016-03-01 0 9.211774 9.211774 0 0 0 0 10009.21 0.000000 10018.42
2016-03-01 0 9.211774 9.211774 0 0 0 0 10009.21 0.000000 10018.42
2016-03-02 0 9.211774 9.211774 0 0 1 sell 10009.21 9.211774 10027.63
2016-03-02 0 9.212694 9.212694 0 0 0 close 10018.42 0.000000 10036.84
2016-03-03 0 9.212694 9.212694 0 0 0 sell 10018.42 0.000000 10036.84
2016-03-03 0 9.212694 9.212694 0 0 0 close 10018.42 0.000000 10036.84
2016-03-04 0 9.212694 9.212694 0 0 0 0 10018.42 0.000000 10036.84
2016-03-04 0 9.212694 9.212694 0 0 0 0 10018.42 0.000000 10036.84
2016-03-07 0 9.212694 9.212694 0 0 0 0 10018.42 0.000000 10036.84
2016-03-07 0 9.212694 9.212694 0 0 0 0 10018.42 0.000000 10036.84
2016-03-08 0 9.212694 9.212694 0 0 0 0 10018.42 0.000000 10036.84
2016-03-08 0 9.212694 9.212694 0 0 0 0 10018.42 0.000000 10036.84
2016-03-09 0 9.212694 9.212694 0 0 0 0 10018.42 0.000000 10036.84
2016-03-09 0 9.212694 9.212694 0 0 0 0 10018.42 0.000000 10036.84
2016-03-10 0 9.212694 9.212694 0 0 0 0 10018.42 0.000000 10036.84
2016-03-10 0 9.212694 9.212694 0 0 0 0 10018.42 0.000000 10036.84
2016-03-11 0 9.212694 9.212694 0 1 0 buy 10018.42 0.000000 10036.84
2016-03-11 0 9.212694 9.212694 0 0 0 close 10018.42 0.000000 10036.84
2016-03-14 0 9.212694 9.212694 0 0 0 0 10018.42 0.000000 10036.84
2016-03-14 0 9.212694 9.212694 0 0 0 0 10018.42 0.000000 10036.84
2016-03-15 0 9.212694 9.212694 0 0 0 sell 10018.42 0.000000 10036.84
2016-03-15 0 9.212694 9.212694 0 0 0 close 10018.42 0.000000 10036.84
2016-03-16 0 9.212694 9.212694 0 0 0 0 10018.42 0.000000 10036.84
2016-03-16 0 9.212694 9.212694 0 0 0 0 10018.42 0.000000 10036.84
2016-03-17 0 9.212694 9.212694 0 0 0 0 10018.42 0.000000 10036.84
2016-03-17 0 9.212694 9.212694 0 0 0 0 10018.42 0.000000 10036.84
2016-03-18 0 9.212694 9.212694 0 0 0 0 10018.42 0.000000 10036.84
2016-03-18 0 9.212694 9.212694 0 0 0 0 10018.42 0.000000 10036.84
2016-03-21 0 9.212694 9.212694 0 0 0 0 10018.42 0.000000 10036.84
2016-03-21 0 9.212694 9.212694 0 0 0 0 10018.42 0.000000 10036.84
2016-03-22 0 9.212694 9.212694 0 1 0 buy 10018.42 0.000000 10036.84
2016-03-22 0 9.212694 9.212694 0 0 0 close 10018.42 0.000000 10036.84
2016-03-23 0 9.212694 9.212694 0 0 0 0 10018.42 0.000000 10036.84
2016-03-23 0 9.212694 9.212694 0 0 0 0 10018.42 0.000000 10036.84
2016-03-24 0 9.212694 9.212694 0 0 0 0 10018.42 0.000000 10036.84
2016-03-24 0 9.212694 9.212694 0 0 0 0 10018.42 0.000000 10036.84
2016-03-25 0 9.212694 9.212694 0 0 0 0 10018.42 0.000000 10036.84
2016-03-25 0 9.212694 9.212694 0 0 0 0 10018.42 0.000000 10036.84
2016-03-27 0 9.212694 9.212694 0 0 0 0 10018.42 0.000000 10036.84
2016-03-27 0 9.212694 9.212694 0 0 0 0 10018.42 0.000000 10036.84
2016-03-28 0 9.212694 9.212694 0 0 0 0 10018.42 0.000000 10036.84
2016-03-28 0 9.212694 9.212694 0 0 0 0 10018.42 0.000000 10036.84
2016-03-29 0 9.212694 9.212694 0 0 0 0 10018.42 0.000000 10036.84
2016-03-29 0 9.212694 9.212694 0 0 0 0 10018.42 0.000000 10036.84
2016-03-30 0 9.212694 9.212694 0 0 0 0 10018.42 0.000000 10036.84
2016-03-30 0 9.212694 9.212694 0 0 0 0 10018.42 0.000000 10036.84
2016-03-31 0 9.212694 9.212694 0 0 0 0 10018.42 0.000000 10036.84
2016-03-31 0 9.212694 9.212694 0 0 0 0 10018.42 0.000000 10036.84
2016-04-03 0 9.212694 9.212694 0 0 0 0 10018.42 0.000000 10036.84
2016-04-03 0 9.212694 9.212694 0 0 0 0 10018.42 0.000000 10036.84
2016-04-04 0 9.212694 9.212694 0 0 0 0 10018.42 0.000000 10036.84
2016-04-04 0 9.212694 9.212694 0 0 0 0 10018.42 0.000000 10036.84
2016-04-05 0 9.212694 9.212694 0 0 0 0 10018.42 0.000000 10036.84
2016-04-05 0 9.212694 9.212694 0 0 0 0 10018.42 0.000000 10036.84
2016-04-06 0 9.212694 9.212694 0 0 0 0 10018.42 0.000000 10036.84
2016-04-06 0 9.212694 9.212694 0 0 0 0 10018.42 0.000000 10036.84
2016-04-07 0 9.212694 9.212694 0 0 0 0 10018.42 0.000000 10036.84
2016-04-07 0 9.212694 9.212694 0 0 0 0 10018.42 0.000000 10036.84
2016-04-10 0 9.212694 9.212694 0 0 0 0 10018.42 0.000000 10036.84
2016-04-10 0 9.212694 9.212694 0 0 0 0 10018.42 0.000000 10036.84
2016-04-11 0 9.212694 9.212694 0 0 0 0 10018.42 0.000000 10036.84
2016-04-11 0 9.212694 9.212694 0 0 0 0 10018.42 0.000000 10036.84
2016-04-12 0 9.212694 9.212694 0 0 0 buy 10018.42 0.000000 10036.84
2016-04-12 0 9.212694 9.212694 0 0 0 close 10018.42 0.000000 10036.84
2016-04-13 0 9.212694 9.212694 0 0 0 0 10018.42 0.000000 10036.84
2016-04-13 0 9.212694 9.212694 0 0 0 0 10018.42 0.000000 10036.84
2016-04-14 0 9.212694 9.212694 0 0 0 0 10018.42 0.000000 10036.84
2016-04-14 0 9.212694 9.212694 0 0 0 0 10018.42 0.000000 10036.84
2016-04-17 0 9.212694 9.212694 0 0 0 0 10018.42 0.000000 10036.84
2016-04-17 0 9.212694 9.212694 0 0 0 0 10018.42 0.000000 10036.84
2016-04-18 0 9.212694 9.212694 0 0 0 0 10018.42 0.000000 10036.84
2016-04-18 0 9.212694 9.212694 0 0 0 0 10018.42 0.000000 10036.84
2016-04-19 0 9.212694 9.212694 0 0 0 0 10018.42 0.000000 10036.84
2016-04-19 0 9.212694 9.212694 0 0 0 0 10018.42 0.000000 10036.84
2016-04-24 0 9.212694 9.212694 0 0 0 0 10018.42 0.000000 10036.84
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2018-05-13 0 9.226390 9.226390 0 0 0 0 10156.58 0.000000 10313.29
2018-05-13 0 9.226390 9.226390 0 0 0 0 10156.58 0.000000 10313.29
2018-05-14 0 9.226390 9.226390 0 0 0 0 10156.58 0.000000 10313.29
2018-05-14 0 9.226390 9.226390 0 0 0 0 10156.58 0.000000 10313.29
2018-05-15 0 9.226390 9.226390 0 0 0 0 10156.58 0.000000 10313.29
2018-05-15 0 9.226390 9.226390 0 0 0 0 10156.58 0.000000 10313.29
2018-05-16 0 9.226390 9.226390 0 0 0 0 10156.58 0.000000 10313.29
2018-05-16 0 9.226390 9.226390 0 0 0 0 10156.58 0.000000 10313.29
2018-05-17 0 9.226390 9.226390 0 0 0 0 10156.58 0.000000 10313.29
2018-05-17 0 9.226390 9.226390 0 0 0 0 10156.58 0.000000 10313.29
2018-05-20 0 9.226390 9.226390 0 0 0 0 10156.58 0.000000 10313.29
2018-05-20 0 9.226390 9.226390 0 0 0 0 10156.58 0.000000 10313.29
2018-05-21 0 9.226390 9.226390 0 1 0 buy 10156.58 0.000000 10313.29
2018-05-21 0 9.226390 9.226390 0 0 0 close 10156.58 0.000000 10313.29
2018-05-22 0 9.226390 9.226390 0 0 0 0 10156.58 0.000000 10313.29
2018-05-22 0 9.226390 9.226390 0 0 0 0 10156.58 0.000000 10313.29
2018-05-23 0 9.226390 9.226390 0 0 0 sell 10156.58 0.000000 10313.29
2018-05-23 0 9.226390 9.226390 0 0 0 close 10156.58 0.000000 10313.29
2018-05-24 0 9.226390 9.226390 0 0 0 0 10156.58 0.000000 10313.29
2018-05-24 0 9.226390 9.226390 0 0 0 0 10156.58 0.000000 10313.29
2018-05-27 0 9.226390 9.226390 0 0 0 0 10156.58 0.000000 10313.29
2018-05-27 0 9.226390 9.226390 0 0 0 0 10156.58 0.000000 10313.29
2018-05-28 0 9.226390 9.226390 0 0 0 0 10156.58 0.000000 10313.29
2018-05-28 0 9.226390 9.226390 0 0 0 0 10156.58 0.000000 10313.29
2018-05-29 0 9.226390 9.226390 0 0 0 sell 10156.58 0.000000 10313.29
2018-05-29 0 9.226390 9.226390 0 0 0 close 10156.58 0.000000 10313.29
2018-05-30 0 9.226390 9.226390 0 0 0 0 10156.58 0.000000 10313.29
2018-05-30 0 9.226390 9.226390 0 0 0 0 10156.58 0.000000 10313.29
2018-05-31 0 9.226390 9.226390 0 0 0 0 10156.58 0.000000 10313.29
2018-05-31 0 9.226390 9.226390 0 0 0 0 10156.58 0.000000 10313.29
2018-06-03 0 9.226390 9.226390 0 0 0 0 10156.58 0.000000 10313.29
2018-06-03 0 9.226390 9.226390 0 0 0 0 10156.58 0.000000 10313.29
2018-06-04 0 9.226390 9.226390 0 0 0 0 10156.58 0.000000 10313.29
2018-06-04 0 9.226390 9.226390 0 0 0 0 10156.58 0.000000 10313.29
2018-06-05 0 9.226390 9.226390 0 0 0 0 10156.58 0.000000 10313.29
2018-06-05 0 9.226390 9.226390 0 0 0 0 10156.58 0.000000 10313.29
2018-06-06 0 9.226390 9.226390 0 0 0 0 10156.58 0.000000 10313.29
2018-06-06 0 9.226390 9.226390 0 0 0 0 10156.58 0.000000 10313.29
2018-06-07 0 9.226390 9.226390 0 0 0 0 10156.58 0.000000 10313.29
2018-06-07 0 9.226390 9.226390 0 0 0 0 10156.58 0.000000 10313.29
2018-06-10 0 9.226390 9.226390 0 0 0 0 10156.58 0.000000 10313.29
2018-06-10 0 9.226390 9.226390 0 0 0 0 10156.58 0.000000 10313.29
2018-06-11 0 9.226390 9.226390 0 0 0 0 10156.58 0.000000 10313.29
2018-06-11 0 9.226390 9.226390 0 0 0 0 10156.58 0.000000 10313.29
2018-06-12 0 9.226390 9.226390 0 0 0 0 10156.58 0.000000 10313.29
2018-06-12 0 9.226390 9.226390 0 0 0 0 10156.58 0.000000 10313.29
2018-06-13 0 9.226390 9.226390 0 0 0 0 10156.58 0.000000 10313.29
2018-06-13 0 9.226390 9.226390 0 0 0 0 10156.58 0.000000 10313.29
2018-06-14 0 9.226390 9.226390 0 0 0 0 10156.58 0.000000 10313.29
2018-06-14 0 9.226390 9.226390 0 0 0 0 10156.58 0.000000 10313.29
2018-06-17 0 9.226390 9.226390 0 0 0 0 10156.58 0.000000 10313.29
2018-06-17 0 9.226390 9.226390 0 0 0 0 10156.58 0.000000 10313.29
2018-06-18 0 9.226390 9.226390 0 0 0 sell 10156.58 0.000000 10313.29
2018-06-18 0 9.226390 9.226390 0 0 0 close 10156.58 0.000000 10313.29
2018-06-19 0 9.226390 9.226390 0 0 1 sell 10156.58 9.226390 10322.52
2018-06-19 0 9.227297 9.227297 0 0 0 close 10165.80 0.000000 10331.73
2018-06-20 0 9.227297 9.227297 0 0 0 0 10165.80 0.000000 10331.73
2018-06-20 0 9.227297 9.227297 0 0 0 0 10165.80 0.000000 10331.73
2018-06-21 0 9.227297 9.227297 0 0 0 0 10165.80 0.000000 10331.73
2018-06-21 0 9.227297 9.227297 0 0 0 0 10165.80 0.000000 10331.73
2018-06-24 0 9.227297 9.227297 0 0 0 0 10165.80 0.000000 10331.73
2018-06-24 0 9.227297 9.227297 0 0 0 0 10165.80 0.000000 10331.73
2018-06-25 0 9.227297 9.227297 0 0 0 0 10165.80 0.000000 10331.73
2018-06-25 0 9.227297 9.227297 0 0 0 0 10165.80 0.000000 10331.73
2018-06-26 0 9.227297 9.227297 0 0 0 0 10165.80 0.000000 10331.73
2018-06-26 0 9.227297 9.227297 0 0 0 0 10165.80 0.000000 10331.73
2018-06-27 0 9.227297 9.227297 0 0 0 0 10165.80 0.000000 10331.73
2018-06-27 0 9.227297 9.227297 0 0 0 0 10165.80 0.000000 10331.73
2018-06-28 0 9.227297 9.227297 0 0 0 0 10165.80 0.000000 10331.73
2018-06-28 0 9.227297 9.227297 0 0 0 0 10165.80 0.000000 10331.73
2018-07-01 0 9.227297 9.227297 0 0 0 0 10165.80 0.000000 10331.73
2018-07-01 0 9.227297 9.227297 0 0 0 0 10165.80 0.000000 10331.73
2018-07-02 0 9.227297 9.227297 0 0 0 0 10165.80 0.000000 10331.73
2018-07-02 0 9.227297 9.227297 0 0 0 0 10165.80 0.000000 10331.73
2018-07-03 0 9.227297 9.227297 0 0 0 0 10165.80 0.000000 10331.73
2018-07-03 0 9.227297 9.227297 0 0 0 0 10165.80 0.000000 10331.73
2018-07-04 0 9.227297 9.227297 0 0 0 0 10165.80 0.000000 10331.73
2018-07-04 0 9.227297 9.227297 0 0 0 0 10165.80 0.000000 10331.73
2018-07-05 0 9.227297 9.227297 0 0 0 0 10165.80 0.000000 10331.73
2018-07-05 0 9.227297 9.227297 0 0 0 0 10165.80 0.000000 10331.73

Table 5.2.1 : ROI for financial betting market.

Graph 5.2.1A : ROI for financial betting market. (Normal Kelly model)

Graph 5.2.1B : ROI for financial betting market. (Adjusted Kelly model 1)

Graph 5.2.1C : ROI for financial betting market. (Adjusted Kelly model 2)

Graph 5.2.1D : ROI for financial betting market. (Adjusted Kelly model 3)

Graph 5.2.1E : ROI for financial betting market. (Adjusted Kelly model 4)

Graph 5.2.1F : ROI for financial betting market. (Adjusted Kelly model 5)

Graph 5.2.1G : ROI for financial betting market. (Adjusted Kelly model 6)

6 Conclusion

6.1 Conclusion and Future Works

I can use tick-data from FXCMTickData for this paper while it is weekly and not up-to-date, the getSymbols() able to get near real-time (15 minutes late) where suite for daily trading in Real Time Trading System (Trial) but there are a lot of trading date is not available.

Due to I had almost completed this paper and only noticed that I am using calC() but not calc_fx() for simulation. Therefore I wrote another paper to compare the accuacy of the arma ordered GARCH models via GARCH模型中的ARMA(p,d,q)参数最优化. There will be another paper for multivariate GARCH model upon completion of Q1App2 web application.

Therefore High Frequency Trading in another research Real Time FXCM where all data price gathered from real-time will be accurate.

6.2 Correction in Next Paper

\[\begin{equation} \varepsilon = h(x)_{1} - h(x)_{2} \ \cdots Equation\ 4.2.3 \end{equation}\]

where \(tp = abs(h(x)_{1} - h(x)_{2})\) and \(tp\) is take-profit pips. As mentioned, my previous paper using pnorm() without weighted the most recent price, here I try to use ppois() to overcame the weighted data issue10. However, there has a question for stop-loss in order to make the \(Equation\ 4.1.1\) stand. B = 20 pips / 40 pips = 0.5 where 20 pips take-profit and 40 pips stop-loss in Source quote 4.1.2 also provides an example for mentioned equation.

Here I compare both \(\sigma^2\) and VaR retrived from GARCH model to set as stop-loss pips.

## Both calC() and calc_fx() added new return value.
##   paper binary-Q1-FiGJRGARCH.Rmd already completed. All 
##   dataset need to re-simulate in order to get the VaR 
##   and sigma^2 values to set as stop-loss pips. Only 
##   based on the odds price we can calculate the staking 
##   amount.

calC <- function(..){
  ...
  ...
  ...
  tmp = list(latestPrice = latestPrice, forecastPrice = res, 
             fit = fit, AIC = infocriteria(fit))
  return(tmp)
}

calc_fx <- function(..){
  ...
  ...
  ...
  tmp = list(latestPrice = latestPrice, forecastPrice = res, 
             fit = fit, AIC = infocriteria(fit))
  return(tmp)
}

Here I forced to changed this paper to be blooper due to :

  • Existing saved simulated model files does not use most accurate Fi-gjrGARCH model.
  • Existing saved simulated model files does not include VaR and \(\sigma\) value in order to set as a stop-loss pips.
  • When I reviewd the coding, there are statistical error occured in univariate forecasting. Although it will not affect whole staking model by filter before placed order, the multivariate models might be test the accuracy at first in order to modify the staking model.
  • Existing staking model is wrong since loss bets count as 0 as shows in Table 5.1.1 and Table 5.2.1, it just a small error which can be corrected but the biggest problem is that whole predictive simulation need to do gain due to lack of stop-loss pips to correct the odds price in order to make Kelly criterion model stand.
  • Only know highest bid or lowest ask time in daily trading is not enough due to the stop-loss point might probably hit and close a transaction if based on the daily High-Low data.
  • I want to model a dynamic fractional Kelly criterion \(0.5 <= f <= 1\), and compare with optimalf(), normal Kelly models and also modified Kelly model11 in section 2 Application of Kelly Criterion model in Sportsbook Investment to test the best fit betting strategy. It will occupied a long section in Optimal Edge but will test it in next paper.
dfm <- xts(tibble(bid = round(rnorm(100, mean = 1, sd = 0.1), 5)) %>% 
               mutate(ask = bid + 0.00003), order.by = now('Asia/Tokyo') - seconds(1:100))
ggplot(dfm, aes(index(dfm))) + 
    geom_line(aes(y = bid, colour = 'bid')) + 
    geom_line(aes(y = ask, colour = 'ask')) + 
    xlab('Time [Seconds]') + ylab('Currency X / Currency Y')

Graph 6.2.1 : Demo real-time bid ask price moving.

Above graph shows an example for open transaction, take-profit and stop-loss point. The Hi-Lo bid/ask price without whole course of price flutuation will not be able to know the exact ROI.

subset(dfm, bid == max(bid)|ask == min(ask))
##                         bid     ask
## 2018-08-11 00:12:59 0.75354 0.75357
## 2018-08-11 00:14:00 1.26085 1.26088
## randomly set as example
Hi <- dfm$bid %>% as.vector %>% sort(decreasing = TRUE) %>% .[2]
Lo <- dfm$ask %>% as.vector %>% sort %>% .[2]

## forecast highest and lowest price.  
s.fct.Hi <- dfm$bid %>% as.vector %>% sort(decreasing = TRUE) %>% .[3]
s.fct.Lo <- dfm$ask %>% as.vector %>% sort %>% .[3]

##odds price for buy transaction, tk = take-profit and sl = stop-loss.
buy.tk <- s.fct.Hi - s.fct.Lo #provided the univariate Hi > Lo
buy.sl <- s.fct.Lo - 0.1 #given that 0.01 is a calculated value.

##odds price for sell transaction, tk = take-profit and sl = stop-loss.
sell.tk <- s.fct.Hi - s.fct.Lo #provided the univariate Hi > Lo 
sell.sl <- s.fct.Hi + 0.1 #given that 0.01 is a calculated value.

The limit order of buy on 0.79947 or sell on 1.21656 will open transaction, and then :

  1. If first ask price hit 0.79947, buy order limit open transaction.
  • If bid price first hit 0.69947, closed transaction and loss 0.1.
  • If bid price first hit 1.21656, closed transaction and gain 0.41709.
  • If bid price does not appear within the day, then the closing price will be the settled price.
  1. If first bid price hit 1.21656, sell order limit open transaction.
  • If ask price first hit 1.31656, closed transaction and loss 0.1.
  • If ask price first hit 0.79947, closed transaction and gain 0.41709.
  • If ask price does not appear within the day, then the closing price will be the settled price.

From the example above, The daily highest price is 1.23547 and daily lowest price is 0.76519. The highest bid/ask price is not neccesary daily Hi-Lo price. We unable know if we buy first or sell first solely based on the Hi-Lo tick data and also the daily OHLCV dataset but a completed tick-data required.12

Here I also publish this paper in order to let other quantitative traders or enthursiasters know the ROI of previous paper is not accurate based on mentioned equations in Staking Model and the table Table 5.1.1 and Table 5.1.1.

7 Appendix

7.1 Documenting File Creation

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

  • File creation date: 2018-07-13
  • File latest updated date: 2018-08-11
  • 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
[1] “2018-08-11 00:14:39 JST”
Category session_info
version R version 3.5.1 (2018-07-02)
system x86_64, mingw32
ui RTerm
language en
collate English_United States.1252
tz Asia/Tokyo
date 2018-08-11
Category Sys.info
sysname Windows
release 8.1 x64
version build 9600
nodename AUTOBVT-TPMV8DU
machine x86-64
login Owner
user Owner
effective_user Owner

  1. You are feel feel to get the data via FXCMTickData

  2. Kindly refer to GJR-GARCH 模型 for more information

  3. You can read the paper by search inside section Reference

  4. armaSearch() error on method = ‘ML’

  5. You may feel free to read the comment onto the article Q&A on Kelly criterion, stop-loss, take-profit and also leverage ratio as well.

  6. Publised book Data Science: Theories, Models, Algorithms, and Analytics - Sanjiv Ranjan Das (2017-03-24).

  7. The pips difference for USD/JPY different with others. Thereore there will need to compare among currencies.

  8. Here I will conducting another research for financial betting.

  9. The odds price offered by operators do not same with the probabilities of the result, similar with the exchange rate offered by different operators will be difference as well.

  10. As the GARCH model has already forecast the most recent price.

  11. The paper named Modified Kelly Criteria in Reference

  12. I initially think only use filted Hi-Lo tick-data to wrote this paper and also states completed tick-data will be in project Real Time FXCM in section Conclusion and Future Works. However due to noticed a lot of ommit and careless and new idea upon studied couples reference at the same time.