Compare-few-time-series-models.Rmd

---
title: "[Deriv.com](https://github.com/englianhu/binary.com-interview-question) - Intraday High Frequency Trading Models Comparison <span style='color:#4E79A7'>"
subtitle: "Introduce [`tidyverts`](https://github.com/tidyverts) for HFT"
author: "[®γσ, Lian Hu ξηg](https://englianhu.github.io/) <img src='www/quantitative trader 1.jpg' width='13'> <img src='www/xueba4.jpg' width='11'>®"
date: "`r lubridate::today('Asia/Tokyo')`"
output:
  html_document: 
    mathjax: https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js
    number_sections: yes
    toc: yes
    toc_depth: 4
    toc_float:
      collapsed: yes
      smooth_scroll: yes
    code_folding: hide
    css: CSSBackgrounds.css
---

<br>
<span style='color:green'>**Theme Song**</span>
<br>

<audio controls loop autoplay src="music/F4 - Can't Help Falling In Love With You (chorus).mp3" controls></audio>
<br>

------

# Setting

## SCSS Setup

<style>
pre {
  overflow-x: auto;
}
pre code {
  word-wrap: normal;
  white-space: pre;
}
.table-hover > tbody > tr:hover { 
  background-color: #8D918D;
}
</style>

```{r class.source='bg-success', class.output='bg-primary', message = FALSE, warning = FALSE}
# install.packages("remotes")
library('BBmisc', 'rmsfuns')
#remotes::install_github("rstudio/sass")
lib('sass')
```

```{scss class.source='bg-success', class.output='bg-primary'}
/* https://stackoverflow.com/a/66029010/3806250 */
h1 { color: #002C54; }
h2 { color: #2F496E; }
h3 { color: #375E97; }
h4 { color: #556DAC; }
h5 { color: #92AAC7; }

/* ----------------------------------------------------------------- */
/* https://gist.github.com/himynameisdave/c7a7ed14500d29e58149#file-broken-gradient-animation-less */
.hover01 {
  /* color: #FFD64D; */
  background: linear-gradient(155deg, #EDAE01 0%, #FFEB94 100%);
  transition: all 0.45s;
  &:hover{
    background: linear-gradient(155deg, #EDAE01 20%, #FFEB94 80%);
    }
  }

.hover02 {
  color: #FFD64D;
  background: linear-gradient(155deg, #002C54 0%, #4CB5F5 100%);
  transition: all 0.45s;
  &:hover{
    background: linear-gradient(155deg, #002C54 20%, #4CB5F5 80%);
    }
  }

.hover03 {
  color: #FFD64D;
  background: linear-gradient(155deg, #A10115 0%, #FF3C5C 100%);
  transition: all 0.45s;
  &:hover{
    background: linear-gradient(155deg, #A10115 20%, #FF3C5C 80%);
    }
  }
```

```{r global_options, class.source='hover01', class.output='hover02'}
## https://stackoverflow.com/a/36846793/3806250
options(width = 999)
knitr::opts_chunk$set(class.source = 'hover01', class.output = 'hover02', class.error = 'hover03')
```

<br><br>

## Setup

```{r warning=FALSE, message=FALSE}
if (!suppressPackageStartupMessages(require('BBmisc'))) {
  install.packages('BBmisc', dependencies = TRUE, INSTALL_opts = '--no-lock')
}
suppressPackageStartupMessages(require('BBmisc'))
# suppressPackageStartupMessages(require('rmsfuns'))

## load packages
pkgs <- c('knitr', 'kableExtra', 'tint', 'dygraphs', 
          'devtools','readr', 'lubridate', 'data.table', 'reprex', 
          'feather', 'purrr', 'quantmod', 'tidyquant', 'plotly', 
          'furrr', 'flyingfox', 'tidyr', 'jsonlite', 'MASS', 
          'timetk', 'plyr', 'dplyr', 'stringr', 'magrittr',
          'tdplyr', 'tidyverse', 'memoise', 'htmltools', 
          'formattable', 'rbokeh', 'dash', 'dashCoreComponents', 
          'dashHtmlComponents', 'dtplyr', 'viridis', 'hrbrthemes', 
          ##https://dashr.plotly.com
          'zoo', 'forecast', 'seasonal', 'seasonalview', 'rjson', 
          'rugarch', 'rmgarch', 'mfGARCH', 'sparklyr', 'jcolors', 
          'microbenchmark', 'dendextend', 'lhmetools', 'ggthemr', 
          'stringr', 'pacman', 'profmem', 'ggthemes', 'paletteer', 
          'htmltools', 'echarts4r', 'tsibble', 'fable', 
          'fabletools', 'tsibbledata', 'tibbletime', 'feasts', 
          'fpp3', 'prophet', 'fasster', 'fpp3', 'MASS', 
          'fable.prophet')

# remotes::install_github("robjhyndman/fpp3-package")
# https://tidyverts.github.io/tidy-forecasting-principles/tsibble.html
# https://facebook.github.io/prophet/docs/quick_start.html
# https://github.com/mpiktas/midasr
# https://github.com/onnokleen/mfGARCH
# devtools::install_github("business-science/tibbletime")
# devtools::install_github("DavisVaughan/furrr")

suppressAll(lib(pkgs))
# load_pkg(pkgs)

## Set the timezone but not change the datetime
Sys.setenv(TZ = 'Asia/Tokyo')
## options(knitr.table.format = 'html') will set all kableExtra tables to be 'html', otherwise need to set the parameter on every single table.
options(warn = -1, width = 999, knitr.table.format = 'html', 
        digits = 14, digits.secs = 6)

suppressAll(lib(pkgs))
# load_pkg(pkgs)

## Set the timezone but not change the datetime
Sys.setenv(TZ = 'Asia/Tokyo')
## options(knitr.table.format = 'html') will set all kableExtra tables to be 'html', otherwise need to set the parameter on every single table.
options(warn = -1, knitr.table.format = 'html')#, digits.secs = 6)

## https://stackoverflow.com/questions/39417003/long-vectors-not-supported-yet-abnor-in-rmd-but-not-in-r-script
knitr::opts_chunk$set(message = FALSE, warning = FALSE)#, 
                      #cache = TRUE, cache.lazy = FALSE)

## https://www.researchgate.net/post/How_to_solve_abnor_cannot_allocate_vector_of_size_12_Gb_in_R
#memory.size() ### Checking your memory size
#memory.limit() ## Checking the set limit
#memory.size(size=500000)
#memory.limit(size=56000) ### expanding your memory _ here it goes beyond to your actually memory. This 56000 is proposed for 64Bit.
rm(pkgs)
```

# Data

## Read Data

```{r error=TRUE}
## read files if not exists
if(!exists('dsmp')) {
  
  if(str_detect(Sys.info()[1], 'Linux')) {
    
    ## check if data path set
    if(!exists('.dtr')) {
      .dtr <- '/home/englianhu/Documents/GitHub/binary.com-interview-question-data/'}
    dsmp <- readRDS(paste0(.dtr, 'data/fx/USDJPY/dsmp.rds'))
    
    ## save files if not exists
    if(!file.exists(paste0(.dtr, 'data/fx/USDJPY/dsmp.rds'))) {
      saveRDS(dsmp, paste0(.dtr, 'data/fx/USDJPY/dsmp.rds'))}
    
  }
  
  if(str_detect(Sys.info()[1], 'Windows')) {
    
    ## check if data path set
    if(!exists('.dtr')) {
      .dtr <- 'C:/Users/User/Documents/GitHub/binary.com-interview-question-data/'}
    dsmp <- readRDS(paste0(.dtr, 'data/fx/USDJPY/dsmp.rds'))
    
    ## save files if not exists
    if(!file.exists(paste0(.dtr, 'data/fx/USDJPY/dsmp.rds'))) {
      saveRDS(dsmp, paste0(.dtr, 'data/fx/USDJPY/dsmp.rds'))}
    
  }
}

dsmp <- dsmp |> 
  ## as_tsibble() when needed since we can set number of keys
  #as_tsibble(key = c(close, quarter, month, week, wkdays), index = index) |> 
  arrange(index)
```

```{r error=TRUE, results='asis'}
## plot sample data
rbind(head(dsmp, 3), tail(dsmp, 3)) %>% 
  kbl(caption = '1 min Close Price Dataset', escape = FALSE) %>% 
  row_spec(0, background = 'DimGrey', color = 'gold', bold = TRUE) |> 
  column_spec(1, background = 'CornflowerBlue') |> 
  column_spec(2, background = 'Gray') |> 
  column_spec(3, background = 'DarkGrey') |> 
  column_spec(4, background = 'Gray') |> 
  column_spec(5, background = 'DarkGrey') |> 
  column_spec(6, background = '#4897D8') |> 
  column_spec(7, background = '#556DAC') |> 
  column_spec(8, background = '#92AAC7') |> 
  column_spec(9, background = '#556DAC') |> 
  column_spec(10, background = '#375E97') |> 
  column_spec(11, background = 'CornflowerBlue') |> 
  column_spec(12, background = 'LightGray', color = 'goldenrod') |> 
  kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive')) |> 
  kable_material(full_width = FALSE) %>% ##`full_width = FALSE` will auto adjust every single columns width to fit the table full width.
  scroll_box(width = '100%', fixed_thead = TRUE, height = '400px')
```

*source : `r paste0(dim(dsmp), collapse = ' x ')`*

## Filter Data

```{r error=TRUE, results='asis'}
## plot sample data
dp_df <- dsmp[dsmp$index %in% dsmp$index[duplicated(dsmp$index)],]
rbind(head(dp_df, 3), tail(dp_df, 3)) %>% 
  kbl(caption = 'NA and Duplicated Dataset', escape = FALSE) %>% 
  row_spec(0, background = 'DimGrey', color = 'gold', bold = TRUE) |> 
  column_spec(1, background = 'CornflowerBlue') |> 
  column_spec(2, background = 'Gray') |> 
  column_spec(3, background = 'DarkGrey') |> 
  column_spec(4, background = 'Gray') |> 
  column_spec(5, background = 'DarkGrey') |> 
  column_spec(6, background = '#4897D8') |> 
  column_spec(7, background = '#556DAC') |> 
  column_spec(8, background = '#92AAC7') |> 
  column_spec(9, background = '#556DAC') |> 
  column_spec(10, background = '#375E97') |> 
  column_spec(11, background = 'CornflowerBlue') |> 
  column_spec(12, background = 'LightGray', color = 'goldenrod') |> 
  kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive')) |> 
  kable_material(full_width = FALSE) %>% ##`full_width = FALSE` will auto adjust every single columns width to fit the table full width.
  scroll_box(width = '100%', fixed_thead = TRUE, height = '400px')
```

*source : `r paste0(dim(dp_df), collapse = ' x ')`*

from above table, we know there have same `index` and `NA` value, here we need to rearrange the `durations` an `sq` columns elements.

```{r error=TRUE}
ddsmp <- na.omit(dsmp) |> 
    {\(df) df |> 
         dplyr::mutate(
             sq = 1:n(), 
             date = as_date(index), 
             quarter = quarter(index), 
             month = month(index), 
             wkdays = weekdays(index), 
             wk_1m = rep(1:7200, nrow(df)/7200), 
             dy_1m = rep(1:1440, nrow(df)/1440), 
             hr_1m = rep(1:60, nrow(df)/60)) |> 
         dplyr::select(index, year, quarter, month, 
                       week, wkdays, wk_1m, dy_1m, hr_1m, 
                       sq, date, close)}()

## save files if not exists
if(!file.exists(paste0(.dtr, 'data/fx/USDJPY/ddsmp.rds'))) {
  saveRDS(ddsmp, paste0(.dtr, 'data/fx/USDJPY/ddsmp.rds'))}
```

*source : `r paste0(dim(ddsmp), collapse = ' x ')`*

```{r error=TRUE, results='asis'}
## plot sample data
rbind(head(ddsmp, 3), tail(ddsmp, 3)) %>% 
  kbl(caption = '1 min Close Price Dataset', escape = FALSE) %>% 
  row_spec(0, background = 'DimGrey', color = 'gold', bold = TRUE) |> 
  column_spec(1, background = 'CornflowerBlue') |> 
  column_spec(2, background = 'Gray') |> 
  column_spec(3, background = 'DarkGrey') |> 
  column_spec(4, background = 'Gray') |> 
  column_spec(5, background = 'DarkGrey') |> 
  column_spec(6, background = '#4897D8') |> 
  column_spec(7, background = '#556DAC') |> 
  column_spec(8, background = '#92AAC7') |> 
  column_spec(9, background = '#556DAC') |> 
  column_spec(10, background = '#375E97') |> 
  column_spec(11, background = 'CornflowerBlue') |> 
  column_spec(12, background = 'LightGray', color = 'goldenrod') |> 
  kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive')) |> 
  kable_material(full_width = FALSE) |> ##`full_width = FALSE` will auto adjust every single columns width to fit the table full width.
  scroll_box(width = '100%', fixed_thead = TRUE, height = '400px')
```

*source : `r paste0(dim(ddsmp), collapse = ' x ')`*

# Modeling

## Seasonal Modelling

```{r, error=TRUE, results='asis'}
## convert to time series tsibble
ts1_ddsmp <- as_tsibble(ddsmp, index = index)

ts2_ddsmp <- ddsmp |> 
  as_tsibble(key = c(close, quarter, month, week, wkdays), index = index)

timeID <- unique(ddsmp$date)
bse <- ddsmp[ddsmp$year == 2016,]$date[1] #"2016-01-04" #1st trading date in 2nd year
timeID %<>% .[. >= bse]
#timeID %<>% .[. >= as_date('2016-01-04')]
vrb <- 1200 #1200 observations
frb <- 1
i   <- 1
```

### Model 1

```{r, error=TRUE, results='asis'}
train1A <- ts1_ddsmp |> 
    filter(as_date(index) <= timeID[i]) |> 
    tail(vrb)

## https://stackoverflow.com/a/15031603/3806250
fit1A <- train1A |> 
    model(
        ets = ETS(close ~ error('M') + trend('N') + season('N')), 
        ets_bc = ETS(box_cox(close, 0.3) ~ error('A') + trend('N') + season('N')), 
        arima = ARIMA(close ~ 0 + pdq(0, 1, 0) + PDQ(0, 1, 0)), 
        theta = THETA(close), 
        theta_mul = THETA(close ~ season(method = 'multiplicative')), 
        rw = RW(close), 
        rw_df = RW(close ~ drift()), 
        naive = NAIVE(close), 
        snaive = SNAIVE(close), 
        prophet = prophet(close ~ season(period = 4, order = 2,
                                    type = 'multiplicative')))

fit1A |> 
     accuracy()
```

```{r, error=TRUE, results='asis'}
train_test <- ts1_ddsmp |> 
    filter(index >= train1A$index[1])

test <- train_test |> 
    filter(index > train1A$index[length(train1A$index)])

train_test |> 
  features(hr_1m, feat_acf)

fc1A <- fit1A |> 
  forecast(h = frb)

fc1A |> 
  accuracy(train_test)
```

```{r, error=TRUE, results='asis'}
fit1A |> 
    forecast(h = 365) %>%
    autoplot(train_test[1:1565,], level = NULL) +
    labs(y = 'USD/JPY',
         title = "Forecasts price") +
    guides(colour = guide_legend(title = 'Forecast'))
```

### Model 2

```{r, error=TRUE, results='asis'}
train1B <- ddsmp |> 
    {\(.) filter(., date < timeID[i]) |> 
            tail(vrb) |> 
            as_tsibble(key = c(close, quarter, month, week, wkdays), index = index)}()

fit1B <- train1B |> 
    model(
        ets = ETS(close ~ error('M') + trend('N') + season('N')), 
        ets_bc = ETS(box_cox(close, 0.3) ~ error('A') + trend('N') + season('N')), 
        arima = ARIMA(close ~ 0 + pdq(0, 1, 0) + PDQ(0, 1, 0)), 
        theta = THETA(close), 
        theta_mul = THETA(close ~ season(method = 'multiplicative')), 
        rw = RW(close), 
        rw_df = RW(close ~ drift()), 
        naive = NAIVE(close), 
        snaive = SNAIVE(close))

fc1B <- fit1B |> 
  forecast(h = frb)

fc1B |> 
  accuracy(ts1_ddsmp)
```

### Model 3

```{r, error=TRUE, results='asis'}
train1C <- ts2_ddsmp |> 
    {\(.) filter(., date < timeID[i]) |> 
            tail(vrb)}()

fit1C <- train1C |> 
    model(
        ets = ETS(close ~ error('M') + trend('N') + season('N')), 
        ets_bc = ETS(box_cox(close, 0.3) ~ error('A') + trend('N') + season('N')),
        arima = ARIMA(close ~ 0 + pdq(0, 1, 0) + PDQ(0, 1, 0)), 
        theta = THETA(close), 
        rw = RW(close), 
        rw_df = RW(close ~ drift()), 
        naive = NAIVE(close), 
        snaive = SNAIVE(close))

fc1C <- fit1C |> 
  forecast(h = frb)

fc1C |> 
  accuracy(ts2_ddsmp)
```

### Model 4

```{r, error=TRUE, results='asis'}
train1D <- ts2_ddsmp |> 
    {\(.) filter(., date < timeID[i]) |> 
            tail(vrb) |> 
            as_tsibble(key = c(close, quarter, month, week, wkdays), index = index)}()

fit1D <- train1D |> 
    model(
        ets = ETS(close ~ error('M') + trend('N') + season('N')), 
        ets_bc = ETS(box_cox(close, 0.3) ~ error('A') + trend('N') + season('N')),
        arima = ARIMA(close ~ 0 + pdq(0, 1, 0) + PDQ(0, 1, 0)), 
        theta = THETA(close), 
        rw = RW(close), 
        rw_df = RW(close ~ drift()), 
        naive = NAIVE(close), 
        snaive = SNAIVE(close))

fc1D <- fit1D |> 
  forecast(h = frb)

fc1D |> 
  accuracy(ts2_ddsmp)
```

```{r, error=TRUE, results='asis'}
## filter data by date
timeID <- unique(dsmp$date)
bse <- dsmp[year == 2016]$date[1] #"2016-01-04" #1st trading date in 2nd year
timeID %<>% .[. >= bse]
#timeID %<>% .[. >= as_date('2016-01-04')]
vrb <- 7200 #last 7200 observations DT[(.N - (vrb - 1)):.N]
frb <- 1440

i = 1

train <- dsmp[date < timeID[i]][(.N - (vrb - 1)):.N]
ctr <- (train[,(sq)][1]):(train[.N,(sq)] + frb)

## convert to tsibble data
train %<>% 
  as_tsibble(key = close, index = index)

train_test <- dsmp[sq %in% ctr] |> 
  as_tsibble(key = close, index = index)

## modeling
fit <- train |> 
  model(
    ets = ETS(close), 
    #ets_bc = ETS(box_cox(close, 0.3)),
    arima = ARIMA(close), 
    rw = RW(close), 
    rw_df = RW(close ~ drift()), 
    naive = NAIVE(close), 
    snaive = SNAIVE(close)
    )

## forecast
fc <- fit |> 
  forecast(h = frb)

## accuracy
fc |> 
  accuracy(train_test)
```

## `timetk::tk_ts()`

[Chapter 12 Advanced forecasting methods in **Forecasting: Principles and Practice (3rd Edt)**](https://otexts.com/fpp3/advanced.html)

```{r, error=TRUE, results='asis'}
my_dcmp_spec <- decomposition_model(
  STL(close ~ season(period = 1440), robust = TRUE),
  ETS(season_adjust ~ season('N')))

fit <- smp1 |> 
  as_tsibble(index = index) |> 
  model(
    ets = ETS(close ~ trend('A')), 
    ets_bc = ETS(box_cox(close, 0.3)), #https://stackoverflow.com/questions/26617587/finding-optimal-lambda-for-box-cox-transform-in-r
    #ets_lg = ETS(my_scaled_logit(mdeaths, 750, 3000) ~ error('A') + trend('N') + season('A')), #http://fable.tidyverts.org/articles/transformations.html
    arima = ARIMA(close), 
    rw = RW(close), 
    rw_df = RW(close ~ drift()), 
    naive = NAIVE(close), 
    snaive = SNAIVE(close), 
    snaive_ = SNAIVE(close ~ lag('year'))#,
    #dcmp = my_dcmp_spec
    )
```

```{r, error=TRUE, results='asis'}
fit |>
  forecast(h = 1440) |> 
  autoplot()
```

```{r, error=TRUE, results='asis'}
#dsmp |> as_tsibble(key = c(qrt, mon, wek, wkdays, sq_1m), index = index)
```

```{r, error=TRUE, results='asis'}

```

```{r, error=TRUE, results='asis'}

```

```{r, error=TRUE, results='asis'}

```

# Conclusion

## Summary

## Final Conclude

```{r opt, echo = FALSE}
## Set options back to original options
options(warn = 0)
```

# Appendix

## Blooper

## Documenting File Creation 

- File creation date: 2018-08-28
- File latest updated date: `r today('Asia/Tokyo')`
- `r R.version.string`
- R version (short form): `r getRversion()`
- [**rmarkdown** package](https://github.com/rstudio/rmarkdown) version: `r packageVersion('rmarkdown')`
- File version: 1.0.1
- Author Profile: [®γσ, Eng Lian Hu](https://beta.rstudioconnect.com/content/4352/)
- GitHub: [Source Code](https://github.com/englianhu/binary.com-interview-question)
- Additional session information:

```{r info, warning=FALSE, results='asis'}
suppressMessages(require('dplyr', quietly = TRUE))
suppressMessages(require('magrittr', quietly = TRUE))
suppressMessages(require('formattable', quietly = TRUE))
suppressMessages(require('knitr', quietly = TRUE))
suppressMessages(require('kableExtra', quietly = TRUE))

sys1 <- devtools::session_info()$platform %>% 
    unlist() %>% 
    (function(df) data.frame(Category = names(df), session_info = df))()
rownames(sys1) <- NULL

sys2 <- data.frame(Sys.info()) |> 
    (function(df) df |> 
         dplyr::mutate(Category = rownames(df)) |> 
         dplyr::select(2,1) |> 
         dplyr::rename('Sys.info' = 'Sys.info..'))()
rownames(sys2) <- NULL

if (nrow(sys1) == 9 & nrow(sys2) == 8) {
  sys2 %<>% rbind(., data.frame(
  Category = 'Current time', 
  Sys.info = paste(as.character(lubridate::now('Asia/Tokyo')), 'JST🗾')))
} else {
  sys1 %<>% rbind(., data.frame(
  Category = 'Current time', 
  session_info = paste(as.character(lubridate::now('Asia/Tokyo')), 'JST🗾')))
}

sys <- cbind(sys1, sys2) |> 
  kbl(caption = 'Additional session information:') |> 
  kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive')) |> 
  row_spec(0, background = 'DimGrey', color = 'yellow') |> 
  column_spec(1, background = 'CornflowerBlue', color = 'red') |> 
  column_spec(2, background = 'grey', color = 'black') |> 
  column_spec(3, background = 'CornflowerBlue', color = 'blue') |> 
  column_spec(4, background = 'grey', color = 'white') |> 
  row_spec(9, bold = T, color = 'yellow', background = '#D7261E')

rm(sys1, sys2)
sys
```

## Reference

01. [High-Performance Time Series Forecasting in R & Python](https://www.youtube.com/watch?v=elQb4VzRINg)
02. [Forecasting: Principles and Practice (3rd ed)](https://otexts.com/fpp3)
03. [A Guide to Time Series Forecasting in R You Should Know](https://www.simplilearn.com/tutorials/data-science-tutorial/time-series-forecasting-in-r)

---

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