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binary-Q1Inter-HFT-NEW.Rmd
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binary-Q1Inter-HFT-NEW.Rmd
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---
title: "<img src='www/deriv.jpg' width='240'>"
subtitle: "[Deriv.com](https://github.com/englianhu/binary.com-interview-question) - Interday High Frequency Trading Models Comparison <span style='color:#4E79A7'>**Review**</span>"
author: "[®γσ, Lian Hu](https://englianhu.github.io/) <img src='www/quantitative trader 1.jpg' width='24'> <img src='www/RYU.jpg' width='24'> <img src='www/ENG.jpg' width='24'>® <img src='www/xueba1.jpg' width='24'>"
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
---
# Abstract
Due to below isseus from [<span style='color:goldenrod'>*Deriv.com - Interday High Frequency Trading Models Comparison</span> <span style='color:red'>**Blooper**</span>](https://rpubs.com/englianhu/binary-Q1Inter-HFT), here I review the researh by using same dataset.
- Weekly dataset `7200` mins forecast in advanced despite `Saturday` and `Sunday`.
- Use the dataset `data_m1` from `2015-01-05` to `2017-12-31`.
- Use `Close Price` to ease the workload and some errors (ex: OHLC abnor, NA price).
<span style='color:red'>**Load Packages**</span>
```{r, warning = FALSE, message = FALSE}
if(!suppressPackageStartupMessages(require('BBmisc'))) {
utils::install.packages('BBmisc', dependencies = TRUE, INSTALL_opts = '--no-lock')
}
suppressPackageStartupMessages(require('BBmisc'))
# suppressPackageStartupMessages(require('rmsfuns'))
pkgs <- c('devtools', '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',
##https://dashr.plotly.com
'zoo', 'forecast', 'seasonal', 'seasonalview', 'rjson',
'rugarch', 'rmgarch', 'mfGARCH', 'sparklyr', 'jcolors',
'microbenchmark', 'dendextend', 'lhmetools', 'ggthemr',
'stringr', 'pacman', 'profmem', 'ggthemes',
'htmltools', 'echarts4r', 'viridis', 'hrbrthemes', 'tsibble',
'fable', 'fabletools', 'tsibbledata', 'tibbletime', 'feasts',
'fpp3', 'prophet', 'fasster')
# 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)
funs <- c('uv_fx.R', 'opt_arma.R', 'multi_seasons.R',
'filterFX.R', 'filter_spec.R', 'mv_fx.R',
'task_progress.R', 'read_umodels.R', 'convertOHLC.R')
l_ply(funs, function(x) source(paste0('./function/', x)))
#l_ply(pkgs, function(x) {
# if(!suppressPackageStartupMessages(require(x))) {
# install.packages(x, dependencies = TRUE, INSTALL_opts = '--no-lock')
# }
# suppressPackageStartupMessages(require(x))
#})
# spark_install()
# if(FALSE) {
# Not run due to side-effects
# spark_home_set()
# }
# sc <- spark_connect(master = 'local')
#spark_install()
#sc <- spark_connect(master = 'local')
.cl = FALSE
## 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$set(cache = TRUE, warning = FALSE,
message = FALSE, cache.lazy = FALSE)
## https://www.researchgate.net/post/How_to_solve_abnor_cannot_allocate_vector_of_size_12_Gb_in_R
#memory.size() ### Checking your memory size
#memory.limit() ## Checking the set limit
#memory.size(size=500000)
#memory.limit(size=56000) ### expanding your memory _ here it goes beyond to your actually memory. This 56000 is proposed for 64Bit.
rm(pkgs, funs)
```
There has few tools :
- [<span style='color:goldenrod'>Introduction to `fable` packages</span>](https://tidyverts.github.io/tidy-forecasting-principles)
- [<span style='color:goldenrod'>Introduction to `prophet` packages</span>](https://facebook.github.io/prophet/docs/installation.html)
- [<span style='color:goldenrod'>Introduction to `fasster` packages</span>](https://github.com/tidyverts/fasster)
Kindly read through [<span style='color:goldenrod'>**Forecasting: Principles and Practice (3rd Edt)**</span>](https://otexts.com/fpp3) to learn time series data modeling and forecasting.
<span style='color:red'>**Progress Function**</span>
```{r}
task_progress <- function(mbase, timeID0 = NULL, scs = 60, .pattern = '^mts|^sets', .loops = TRUE) {
## ------------- 定时查询进度 ----------------------
## 每分钟自动查询与更新以上模拟预测汇价进度（储存文件量）。
require('magrittr')
require('tibble')
if(!is.data.frame(class(mbase))) {
mbase %<>% data.frame
}
if (.loops == TRUE) {
while(1) {
cat('Current Tokyo Time :', as.character(now('Asia/Tokyo')), '\n\n')
y = as_date(mbase$index) %>%
unique
y <- y[weekdays(y) != 'Saturday'] #filter and omit the weekly last price which is 12:00am on saturday
datee = y
if(is.null(timeID0)) {
timeID0 = y[1]
} else if (is.Date(timeID0)) {
timeID0 = as_date(timeID0)
} else {
timeID0 = as_date(mbase$index) %>%
unique
}
y = y[y >= timeID0]
x = list.files(paste0('C:/Users/User/Documents/GitHub/binary.com-interview-question-data/data/fx/USDJPY/'), pattern = .pattern) %>%
str_replace_all('.rds', '') %>%
str_replace_all('.201', '_201') %>%
str_split_fixed('_', '2') %>%
as_tibble %>%
dplyr::rename('Model' = 'V1', 'Date' = 'V2') %>%
dplyr::mutate(Model = factor(Model), Date = as_date(Date))
x = join(tibble(Date = datee), x) %>%
as_tibble
x %<>% na.omit
x %<>% dplyr::mutate(binary = if_else(is.na(Model), 0, 1)) %>%
spread(Model, binary)
z <- ldply(x[,-1], function(zz) {
na.omit(zz) %>% length }) %>%
dplyr::rename(x = V1) %>%
dplyr::mutate(n = length(y), progress = percent(x/n))
print(z)
prg = sum(z$x)/sum(z$n)
cat('\n================', as.character(percent(prg)), '================\n\n')
if (prg == 1) break #倘若进度达到100%就停止更新。
Sys.sleep(scs) #以上ldply()耗时3~5秒，而休息时间60秒。
}
} else {
cat('Current Tokyo Time :', as.character(now('Asia/Tokyo')), '\n\n')
y = as_date(mbase$index) %>%
unique
datee = y
if(is.null(timeID0)) {
timeID0 = y[1]
} else if (is.Date(timeID0)) {
timeID0 = as_date(timeID0)
} else {
timeID0 = as_date(mbase$index) %>%
unique
}
y = y[y >= timeID0]
x = list.files(paste0('C:/Users/User/Documents/GitHub/binary.com-interview-question-data/data/fx/USDJPY/'), pattern = .pattern) %>%
str_replace_all('.rds', '') %>%
str_replace_all('.201', '_201') %>%
str_split_fixed('_', '2') %>%
as_tibble %>%
dplyr::rename('Model' = 'V1', 'Date' = 'V2') %>%
dplyr::mutate(Model = factor(Model), Date = as_date(Date))
x = join(tibble(Date = datee), x) %>%
as_tibble
x %<>% na.omit
x %<>% dplyr::mutate(binary = if_else(is.na(Model), 0, 1)) %>%
spread(Model, binary)
z <- ldply(x[,-1], function(zz) {
na.omit(zz) %>% length }) %>%
dplyr::rename(x = V1) %>%
dplyr::mutate(n = length(y), progress = percent(x/n))
print(z)
prg = sum(z$x)/sum(z$n)
cat('\n================', as.character(percent(prg)), '================\n\n')
}
}
```
# Introduction
Review the [<span style='color:goldenrod'>*Deriv.com - Interday High Frequency Trading Models Comparison</span> <span style='color:red'>**Blooper**</span>](https://rpubs.com/englianhu/binary-Q1Inter-HFT).
# Data
## Read Data
### Raw Data
```{r, warning = FALSE, message = FALSE, results = 'asis'}
data_m1 <- read_rds('C:/Users/User/Documents/GitHub/real-time-fxcm/data/USDJPY/data_m1.rds') %>%
data.table
data_m1 %<>% .[order(index)]
## plot sample data
data_m1[c(1:3, (nrow(data_m1)-3):nrow(data_m1)),] %>%
kbl('html', caption = '1 min Raw Dataset', escape = FALSE) %>%
## https://www.w3schools.com/cssref/css_colors.asp
row_spec(0, background = 'DimGrey') %>%
column_spec(1, background = 'CornflowerBlue') %>%
column_spec(2, background = 'DarkGrey') %>%
column_spec(3, background = 'LightSlateGrey') %>%
column_spec(4, background = 'LightGray', color = 'goldenrod') %>%
column_spec(5, background = 'Gainsboro', color = 'goldenrod') %>%
column_spec(6, background = 'LightGray', color = 'goldenrod') %>%
column_spec(7, background = 'Gainsboro', color = 'goldenrod') %>%
column_spec(8, background = 'LightGray', color = 'goldenrod') %>%
column_spec(9, background = 'Gainsboro', color = 'goldenrod') %>%
column_spec(10, background = 'LightGray', color = 'goldenrod') %>%
column_spec(11, background = 'Gainsboro', 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(data_m1), collapse = ' x ')`*
As we can know there has few errors from [<span style='color:goldenrod'>*Deriv.com - Interday High Frequency Trading Models Comparison</span> <span style='color:red'>**Blooper**</span>](https://rpubs.com/englianhu/binary-Q1Inter-HFT):
- open price higher than highest price
- open price lower than lowest price
- close price higher than highest price
- close price lower than lowest price
### OHLC Data
Convert to OHLC data as we know from [<span style='color:goldenrod'>*Deriv.com - Interday High Frequency Trading Models Comparison</span> <span style='color:red'>**Blooper**</span>](https://rpubs.com/englianhu/binary-Q1Inter-HFT).
```{r, warning = FALSE, message = FALSE, results = 'asis'}
if(names(data_m1) %>% str_detect('Bid|Ask') %>% any()) {
dsmp <- data_m1[,{
open = (BidOpen + AskOpen)/2
high = (BidHigh + AskHigh)/2
low = (BidLow + AskLow)/2
close = (BidClose + AskClose)/2
.SD[,.(index = index, year = year, week = week,
open = open, high = high, low = low, close = close), ]}, ]
}
## plot sample data
dsmp[c(1:3, (nrow(dsmp)-3):nrow(dsmp)),] %>%
kbl('html', caption = '1 min OHLC Dataset', escape = FALSE) %>%
## https://www.w3schools.com/cssref/css_colors.asp
row_spec(0, background = 'DimGrey') %>%
column_spec(1, background = 'CornflowerBlue') %>%
column_spec(2, background = 'DarkGrey') %>%
column_spec(3, background = 'LightSlateGrey') %>%
column_spec(4, background = 'LightGray', color = 'goldenrod') %>%
column_spec(5, background = 'Gainsboro', color = 'goldenrod') %>%
column_spec(6, background = 'LightGray', color = 'goldenrod') %>%
column_spec(7, background = 'Gainsboro', 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 ')`*
## Data Cleaning
```{r, warning = FALSE, message = FALSE, results = 'asis'}
dsmp <- dsmp[,{
quarter = quarter(index)
month = month(index)
wkdays = weekdays(index)
wk_1m = 1:7200
dy_1m = 1:1440
hr_1m = 1:60
date = as_date(index)
.SD[,.(index = index, year = year, quarter = quarter,
month = month, week = week, wkdays = wkdays,
wk_1m = wk_1m, dy_1m = dy_1m, hr_1m = hr_1m,
sq = 1:.N, date = date, close = close), ]}, ]
```
```{r, warning = FALSE, message = FALSE, results = 'asis'}
## plot sample data
dsmp[c(1:3, (nrow(dsmp)-3):nrow(dsmp)),] %>%
kbl('html', caption = '1 min Close Price Dataset', escape = FALSE) %>%
## https://www.w3schools.com/cssref/css_colors.asp
## https://public.tableau.com/en-us/gallery/100-color-palettes?gallery=votd
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 ')`*
```{r, warning = FALSE, message = FALSE, results = 'asis'}
## Below codes list out all Tuesday to Sunday data details.
# data_abn <- dsmp[wkdays %chin% 'Saturday' & !str_detect(index, '00:00:00') | wkdays %chin% 'Sunday']$date_1m
# date_abn2 <- date_abn[1:length(date_abn) %% 2 == 0]
## --------------------------------------------
date_abn <- dsmp[wkdays %chin% 'Sunday']$date_1m %>%
unique
date_abn_seq <- llply(date_abn, function(dte)
as.character(seq(dte - days(6), dte, by = 'day'))) %>%
unlist %>%
as_date
rm(date_abn, date_abn2)
data_abn <- dsmp[date_1m %in% date_abn_seq]
## plot sample data
data_abn[c(1:3, (nrow(data_abn)-3):nrow(data_abn)),] %>%
kbl('html', caption = '1 min Close Price Dataset (abnor : Tuesday - Sunday)', escape = FALSE) %>%
## https://www.w3schools.com/cssref/css_colors.asp
row_spec(0, background = 'DimGrey') %>%
column_spec(1, background = 'CornflowerBlue') %>%
column_spec(2, background = 'DarkGrey') %>%
column_spec(3, background = 'LightSlateGrey') %>%
column_spec(4, background = '#4E79A7') %>%
column_spec(5, background = 'LightSlateGrey') %>%
column_spec(6, background = 'CornflowerBlue') %>%
column_spec(7, background = '#4E79A7') %>%
column_spec(8, background = 'LightGray', color = 'goldenrod') %>%
kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive')) %>%
kable_material(full_width = FALSE) %>% ##`full_width = FALSE` will auto adjust every single columns width to fit the table full width.
scroll_box(width = '100%', fixed_thead = TRUE, height = '400px')
```
There has transactions in from *Tuesday (12:01AM)* to *Sunday (12:00AM)* as we can know from above and below.
```{r, eval = FALSE, warning = FALSE, message = FALSE}
## -------------------- eval = FALSE --------------------
matrix(weekdays(unique(as_date(dsmp$index))), ncol = 6, byrow = TRUE)
[104,] "Tuesday" "Wednesday" "Thursday" "Friday" "Saturday" "Sunday"
[105,] "Tuesday" "Wednesday" "Thursday" "Friday" "Saturday" "Sunday"
...
[156,] "Tuesday" "Wednesday" "Thursday" "Friday" "Saturday" "Sunday"
[157,] "Tuesday" "Wednesday" "Thursday" "Friday" "Saturday" "Sunday"
```
There has 2 weeks abnormal data (`r paste(date_abn_seq[c(1,(length(date_abn_seq)/2))], collapse = ' to ')` and `r paste(date_abn_seq[c(((length(date_abn_seq)/2)+1),length(date_abn_seq))], collapse = ' to ')`).
There might probably because of Christmas to postpone 1 day, here I forecast `7200` trading datetime in advanced despite the date and weekdays. Every forecast price will base on the out of sample date. There will no any effects .
```{r, warning = FALSE, message = FALSE}
## save files if not exists
if(!file.exists('C:/Users/User/Documents/GitHub/binary.com-interview-question-data/data/fx/USDJPY/dsmp.rds') & exists('dsmp')) {
saveRDS(dsmp, 'C:/Users/User/Documents/GitHub/binary.com-interview-question-data/data/fx/USDJPY/dsmp.rds')}
## read files if not exists
if(!exists('dsmp')) {
dsmp <- readRDS('C:/Users/User/Documents/GitHub/binary.com-interview-question-data/data/fx/USDJPY/dsmp.rds')}
```
# Modelling
## Due to I have annually length dataset, here I start my 1st forecast date from 1st trading datetime of 2016 (`r dsmp)[year == 2016]$date_1m[1]` which is 2nd year in dataset).
## Seasonal `ts()`
### Wk >> Dy
I set the length of data as weekly (`7200` minutes which is 5 trading days) and frequency set as `1440` minutes (`1440` minutes is a trading day).
```{r, eval=FALSE}
# --------- eval=FALSE ---------
timeID <- unique(dsmp$date)
bse <- dsmp[year == 2016]$date[1] #"2016-01-04" #1st trading date in 2nd year
timeID %<>% .[. >= bse]
#timeID %<>% .[. >= as_date('2016-01-04')]
vrb <- 7200 #last 7200 observations DT[(.N - (vrb - 1)):.N]
frb <- 1440
for (i in 1:length(timeID)) {
smp <- dsmp[date < timeID[i]][(.N - (vrb - 1)):.N]
frc <- dsmp[date >= timeID[i]][1:frb]
smp1 <- smp[, .(index, close)] %>% lazy_dt
frc1 <- smp[, .(index, close)] %>% lazy_dt
sets <- smp1 %>%
tk_ts(frequency = 1440) %>%
forecast(h = 1440) %>%
llply(tk_tbl)
if(is.double(sets$forecast$index[1])){
sq <- smp %>%
tail(1) %>%
index
if(weekdays(sq) == '土曜日'|weekdays(sq) == 'Saturday') sq <- sq + days(2)
sq <- seq(from = sq + minutes(1), sq + days(1), by = 'min')
sets$forecast$index <- sq
} else {
sets$forecast$index <- data_m1$index[
(which(data_m1$index == smp %>%
index %>%
xts::last()) + 1):(
which(data_m1$index == smp %>%
index %>%
xts::last()) + 1440)]
}
if (!dir.exists(paste0('data/fx/USDJPY')))
dir.create(paste0('data/fx/USDJPY'))
saveRDS(sets, paste0('data/fx/USDJPY/sets.wk.1440.',
as_date(sets$forecast$index[1]), '.rds'))
cat(paste0(
'data/fx/USDJPY/sets.wk.1440.',
as_date(sets$forecast$index[1]), '.rds saved!\n'))
}
```
### Monthly >> Daily
I set the length of dataset as monthly but the frequency set as 1440 minutes (per day). Initial forecast will be based on weekly dataset and then accumulated date-by-date until a monthly dataset.
```{r, eval=FALSE}
# --------- eval=FALSE ---------
#sq <- seq(1 , length(data_m1$index), by = 1440)
#sets <- list()
timeID <- data_m1$index %>%
as_date %>%
unique %>%
sort
timeID %<>% .[. > as_date('2015-01-11')]
for (dt in timeID) {
smp <- data_m1 %>%
tk_xts(silent = TRUE)
dt %<>% as_date
smp <- smp[paste0(dt %m-% months(1) + seconds(59), '/', dt + seconds(59))]
sets <- smp %>%
tk_ts(frequency = 1440) %>%
forecast(h=1440) %>%
llply(tk_tbl)
if(is.double(sets$forecast$index[1])){
sq <- smp %>%
tail(1) %>%
index
if(weekdays(sq) == '土曜日'|weekdays(sq) == 'Saturday') sq <- sq + days(2)
sq <- seq(from = sq + minutes(1), sq + days(1), by = 'min')
sets$forecast$index <- sq
} else {
sets$forecast$index <- data_m1$index[
(which(data_m1$index == smp %>%
index %>%
xts::last()) + 1):(
which(data_m1$index == smp %>%
index %>%
xts::last()) + 1440)]
}
if (!dir.exists(paste0('data/fx/USDJPY')))
dir.create(paste0('data/fx/USDJPY'))
saveRDS(sets, paste0('data/fx/USDJPY/sets.mo.1440.',
as_date(sets$forecast$index[1]), '.rds'))
cat(paste0(
'data/fx/USDJPY/sets.mo.1440.',
as_date(sets$forecast$index[1]), '.rds saved!\n'))
}
```
### Quarterly >> Daily
I set the length of dataset as quarterly but the frequency set as 1440 minutes (per day). Initial forecast will be based on weekly dataset and then accumulated date-by-date until a quarterly dataset.
```{r, eval=FALSE}
# --------- eval=FALSE ---------
#sq <- seq(1 , length(data_m1$index), by = 1440)
#sets <- list()
timeID <- data_m1$index %>%
as_date %>%
unique %>%
sort
timeID %<>% .[. > as_date('2015-01-11')]
for (dt in timeID) {
smp <- data_m1 %>%
tk_xts(silent = TRUE)
dt %<>% as_date
smp <- smp[paste0(dt %m-% months(3) + seconds(59), '/', dt + seconds(59))]
sets <- smp %>%
tk_ts(frequency = 1440) %>%
forecast(h=1440) %>%
llply(tk_tbl)
if(is.double(sets$forecast$index[1])){
sq <- smp %>%
tail(1) %>%
index
if(weekdays(sq) == '土曜日'|weekdays(sq) == 'Saturday') sq <- sq + days(2)
sq <- seq(from = sq + minutes(1), sq + days(1), by = 'min')
sets$forecast$index <- sq
} else {
sets$forecast$index <- data_m1$index[
(which(data_m1$index == smp %>%
index %>%
xts::last()) + 1):(
which(data_m1$index == smp %>%
index %>%
xts::last()) + 1440)]
}
if (!dir.exists(paste0('data/fx/USDJPY')))
dir.create(paste0('data/fx/USDJPY'))
saveRDS(sets, paste0('data/fx/USDJPY/sets.qt.1440.',
as_date(sets$forecast$index[1]), '.rds'))
cat(paste0(
'data/fx/USDJPY/sets.qt.1440.',
as_date(sets$forecast$index[1]), '.rds saved!\n'))
}
```
### Yearly >> Daily
I set the length of dataset as yearly but the frequency set as 1440 minutes (per day). Initial forecast will be based on weekly dataset and then accumulated date-by-date until a yearly dataset.
```{r, eval=FALSE}
# --------- eval=FALSE ---------
#sq <- seq(1 , length(data_m1$index), by = 1440)
#sets <- list()
timeID <- data_m1$index %>%
as_date %>%
unique %>%
sort
timeID %<>% .[. > as_date('2015-01-11')]
for (dt in timeID) {
smp <- data_m1 %>% tk_xts(silent = TRUE)
dt %<>% as_date
smp <- smp[paste0(dt %m-% years(1) + seconds(59), '/', dt + seconds(59))]
sets <- smp %>%
tk_ts(frequency = 1440) %>%
forecast(h=1440) %>%
llply(tk_tbl)
if(is.double(sets$forecast$index[1])){
sq <- smp %>%
tail(1) %>%
index
if(weekdays(sq) == '土曜日'|weekdays(sq) == 'Saturday') sq <- sq + days(2)
sq <- seq(from = sq + minutes(1), sq + days(1), by = 'min')
sets$forecast$index <- sq
} else {
sets$forecast$index <- data_m1$index[
(which(data_m1$index == smp %>%
index %>%
xts::last()) + 1):(
which(data_m1$index == smp %>%
index %>%
xts::last()) + 1440)]
}
if (!dir.exists(paste0('data/fx/USDJPY')))
dir.create(paste0('data/fx/USDJPY'))
saveRDS(sets, paste0('data/fx/USDJPY/sets.yr.1440.',
as_date(sets$forecast$index[1]), '.rds'))
cat(paste0(
'data/fx/USDJPY/sets.yr.1440.',
as_date(sets$forecast$index[1]), '.rds saved!\n'))
}
```
### Weekly >> Weekly
I set the length of dataset as weekly but the frequency set as 7200 minutes (per week).
```{r, eval=FALSE}
# --------- eval=FALSE ---------
#sq <- seq(1 , length(data_m1$index), by = 7200)
#sets <- list()
timeID <- data_m1$index %>%
as_date %>%
unique %>%
sort
timeID %<>% .[. > as_date('2015-01-05')] #2015-01-11
for (dt in timeID) {
smp <- data_m1 %>%
tk_xts(silent = TRUE)
dt %<>% as_date
smp <- smp[paste0(dt %m-% weeks(1) + seconds(59), '/', dt + seconds(59))]
sets <- smp %>%
tk_ts(frequency = 7200) %>%
forecast(h = 7200) %>%
llply(tk_tbl)
if(is.double(sets$forecast$index[1])){
sq <- smp %>%
tail(1) %>%
index
if(weekdays(sq) == '土曜日'|weekdays(sq) == 'Saturday') sq <- sq + days(2)
sq <- seq(from = sq + minutes(1), sq + days(5), by = 'min')
##sqe[regexpr('Saturday|Sunday', weekdays(sqe)) == -1]
sets$forecast$index <- sq
} else {
sets$forecast$index <- data_m1$index[
(which(data_m1$index == smp %>%
index %>%
xts::last()) + 1):(
which(data_m1$index == smp %>%
index %>%
xts::last()) + 7200)]
}
if (!dir.exists(paste0('data/fx/USDJPY')))
dir.create(paste0('data/fx/USDJPY'))
saveRDS(sets, paste0('data/fx/USDJPY/sets.wk.7200.',
as_date(sets$forecast$index[1]), '.rds'))
cat(paste0(
'data/fx/USDJPY/sets.wk.7200.',
as_date(sets$forecast$index[1]), '.rds saved!\n'))
}
```
### Monthly >> Weekly
I set the length of dataset as monthly but the frequency set as 7200 minutes (per week).
```{r, eval=FALSE}
# --------- eval=FALSE ---------
#sq <- seq(1 , length(data_m1$index), by = 7200)
#sets <- list()
timeID <- data_m1$index %>%
as_date %>%
unique %>%
sort
timeID %<>% .[. > as_date('2015-01-05')] #2015-01-11
for (dt in timeID) {
smp <- data_m1 %>%
tk_xts(silent = TRUE)
dt %<>% as_date
smp <- smp[paste0(dt %m-% months(1) + seconds(59), '/', dt + seconds(59))]
sets <- smp %>%
tk_ts(frequency = 7200) %>%
forecast(h = 7200) %>%
llply(tk_tbl)
if(is.double(sets$forecast$index[1])){
sq <- smp %>%
tail(1) %>%
index
if(weekdays(sq) == '土曜日'|weekdays(sq) == 'Saturday') sq <- sq + days(2)
sq <- seq(from = sq + minutes(1), sq + days(5), by = 'min')
sets$forecast$index <- sq
} else {
sets$forecast$index <- data_m1$index[
(which(data_m1$index == smp %>%
index %>%
xts::last()) + 1):(
which(data_m1$index == smp %>%
index %>%
xts::last()) + 7200)]
}
if (!dir.exists(paste0('data/fx/USDJPY')))
dir.create(paste0('data/fx/USDJPY'))
saveRDS(sets, paste0('data/fx/USDJPY/sets.mo.7200.',
as_date(sets$forecast$index[1]), '.rds'))
cat(paste0(
'data/fx/USDJPY/sets.mo.7200.',
as_date(sets$forecast$index[1]), '.rds saved!\n'))
}
```
### Quarterly >> Weekly
I set the length of dataset as quarterly but the frequency set as 7200 minutes (per week).
```{r, eval=FALSE}
# --------- eval=FALSE ---------
#sq <- seq(1 , length(data_m1$index), by = 7200)
#sets <- list()
timeID <- data_m1$index %>%
as_date %>%
unique %>%
sort
timeID %<>% .[. > as_date('2015-01-05')] #2015-01-11
for (dt in timeID) {
smp <- data_m1 %>%
tk_xts(silent = TRUE)
dt %<>% as_date
smp <- smp[paste0(dt %m-% months(3) + days(5), '/', dt + seconds(59))]
sets <- smp %>%
tk_ts(frequency = 7200) %>%
forecast(h = 7200) %>%
llply(tk_tbl)
if(is.double(sets$forecast$index[1])){
sq <- smp %>%
tail(1) %>%
index
if(weekdays(sq) == '土曜日'|weekdays(sq) == 'Saturday') sq <- sq + days(2)
sq <- seq(from = sq + minutes(1), sq + weeks(1), by = 'min')
sets$forecast$index <- sq
} else {
sets$forecast$index <- data_m1$index[
(which(data_m1$index == smp %>%
index %>%
xts::last()) + 1):(
which(data_m1$index == smp %>%
index %>%
xts::last()) + 7200)]
}
if (!dir.exists(paste0('data/fx/USDJPY')))
dir.create(paste0('data/fx/USDJPY'))
saveRDS(sets, paste0('data/fx/USDJPY/sets.qt.7200.',
as_date(sets$forecast$index[1]), '.rds'))
cat(paste0(
'data/fx/USDJPY/sets.qt.7200.',
as_date(sets$forecast$index[1]), '.rds saved!\n'))
}
```
### Yearly >> Weekly
I set the length of dataset as yearly but the frequency set as 7200 minutes (per week).
```{r, eval=FALSE}
# --------- eval=FALSE ---------
#sq <- seq(1 , length(data_m1$index), by = 7200)
#sets <- list()
timeID <- data_m1$index %>%
as_date %>%
unique %>%
sort
timeID %<>% .[. > as_date('2015-01-05')] #2015-01-11
for (dt in timeID) {
smp <- data_m1 %>%
tk_xts(silent = TRUE)
dt %<>% as_date
smp <- smp[paste0(dt %m-% years(1) + seconds(59), '/', dt + seconds(59))]
sets <- smp %>%
tk_ts(frequency = 7200) %>%
forecast(h = 7200) %>%
llply(tk_tbl)
if(is.double(sets$forecast$index[1])){
sq <- smp %>%
tail(1) %>%
index
if(weekdays(sq) == '土曜日'|weekdays(sq) == 'Saturday') sq <- sq + days(2)
sq <- seq(from = sq + minutes(1), sq + days(5), by = 'min')
sets$forecast$index <- sq
} else {
sets$forecast$index <- data_m1$index[
(which(data_m1$index == smp %>%
index %>%
xts::last()) + 1):(
which(data_m1$index == smp %>%
index %>%
xts::last()) + 7200)]
}
if (!dir.exists(paste0('data/fx/USDJPY')))
dir.create(paste0('data/fx/USDJPY'))
saveRDS(sets, paste0('data/fx/USDJPY/sets.yr.7200.',
as_date(sets$forecast$index[1]), '.rds'))
cat(paste0(
'data/fx/USDJPY/sets.yr.7200.',
as_date(sets$forecast$index[1]), '.rds saved!\n'))
}
```
## Seasonal ARIMA
### Introduce SARIMA
- [Seasonal model with auto.arima](https://stats.stackexchange.com/questions/355839/seasonal-model-with-auto-arima)
- [Seasonality not taken account of in `auto.arima()`](https://stats.stackexchange.com/questions/213201/seasonality-not-taken-account-of-in-auto-arima) ask about why there has no
- [8.5 Non-seasonal ARIMA models](https://otexts.org/fpp2/non-seasonal-arima.html) introduce a non-seasonal ARIMA model.
- [8.9 Seasonal ARIMA models](https://otexts.org/fpp2/seasonal-arima.html) introduce the arima and also sarima models, teach we how to get the `P,D,Q`.
- [Seasonality in `auto.arima()` from forecast package](https://stackoverflow.com/questions/37400062/seasonality-in-auto-arima-from-forecast-package) ask the question which is what I am trying to know (normal arima model only get `(p,d,q)` but not `(P,D,Q)`). The answer is do NOT set both `approximation` and `stepwise` to `FALSE`.
- [Is there a way to force seasonality from `auto.arima`](https://stackoverflow.com/questions/37046275/is-there-a-way-to-force-seasonality-from-auto-arima) ask about how to model a force-seasonal-ARIMA. The topic talk about the `D` parameter in `auto.arima` which governs seasonal differencing. The example shows that `D=1` will get a smaller AIC/BIC figures than default `D=NULL`.
- [Why does `auto.arima` drop my seasonality component when `stepwise=FALSE` and `approximation=FALSE`](https://stackoverflow.com/questions/24390859/why-does-auto-arima-drop-my-seasonality-component-when-stepwise-false-and-approx) ask about why the `stepwise=FALSE` and `approximation=FALSE` got the better AIC than default model. The answer describe that normally `max.order=5` where we can get a better truly seasonal model, just increase the `max.order=10`. There is not too much gained using `approximation=FALSE`. What that does is force it to evaluate the likelihood more accurately for each model, but the approximation is quite good and much faster, so is usually acceptable.
- [How to read p,d and q of `auto.arima()`?](https://stats.stackexchange.com/questions/178577/how-to-read-p-d-and-q-of-auto-arima) ask about what is the meaning of `a$arma` and somebody answer the help page in `auto.arima()` has descibe that `a$arma` is `(p, q, P, Q, s, d, D)`.
- [In R, `auto.arima` fails to capture seasonality](https://stackoverflow.com/questions/43600827/in-r-auto.arima-fails-to-capture-seasonality) simulate an annual dataset with set `trace=TRUE`, `stepwise=FALSE` and `D=1` but didn't provides the answer to get optimal `P,D,Q`.
- [How I can get best arima model in R (closed)](https://stats.stackexchange.com/questions/160343/how-i-can-get-best-arima-model-in-r) only say the `auto.arima()` able get the best model, however does not provides the answer how to get the optimal `P,D,Q` instead of only `p,d,q`.
- [how to extract integration order (d) from auto.arima](https://stackoverflow.com/questions/19483952/how-to-extract-integration-order-d-from-auto-arima) ask that the `ndiffs()` sometimes give the different resukt than best model, describe the `a$arma`. More generally, the order `(d)` is the next to last element; the seasonal order `(D)` is the last. So `a$arma[length(a$arma)-1]` is the order d and `a$arma[length(a$arma)]` is the seasonal order.
- [How to read p,d and q of `auto.arima()`?](https://stats.stackexchange.com/questions/178577/how-to-read-p-d-and-q-of-auto-arima) describe the help page in `auto.arima()` has descibe that `a$arma` is `(p, q, P, Q, d, D)`.
- [How to interpret the second part of an auto arima result in R?](https://stackoverflow.com/questions/47119765/how-to-interpret-the-second-part-of-an-auto-arima-result-in-r) interpret the seasonal arima model.
- [extract ARIMA specificaiton](https://stackoverflow.com/questions/23617662/extract-arima-specificaiton) provides a function how to extract the `a$arma[c(1, 6, 2, 3, 7, 4, 5)]` from an `auto.arima()`.
- [How to include seasonality in auto arima with regressors in R?](https://stats.stackexchange.com/questions/295004/how-to-include-seasonality-in-auto-arima-with-regressors-in-r) use a `xreg` for seasonal model.
- [Step-by-Step Graphic Guide to Forecasting through ARIMA Modeling using R – Manufacturing Case Study Example (Part 4)](http://ucanalytics.com/blogs/step-by-step-graphic-guide-to-forecasting-through-arima-modeling-in-r-manufacturing-case-study-example/) forecast seasonal sales by using `auto.arima()`.
- [Frequency parameter and its impact on auto.arima results](https://stats.stackexchange.com/questions/187304/frequency-parameter-and-its-impact-on-auto-arima-results)^[[Seasonal periods](https://robjhyndman.com/hyndsight/seasonal-periods/) describe very details on the `seasonal period` parameters determination.] ask about the determination of frequency parameter for `seasonal period` where the author of `forecast` package provides a details and concise answer.
- [`auto.arima` Warns `NaNs` Produced on Std abnor](https://stats.stackexchange.com/questions/26999/auto-arima-warns-nans-produced-on-std-abnor) suggested set `stepwise=FALSE` and `approximation=FALSE` is better model.
> If you look at the help file of auto.arima and navigate to the section "Value", you are directed to the help file of arima function and there you find the following (under the section "Value") regarding the arma slot:
A compact form of the specification, as a vector giving the number of AR, MA, seasonal AR and seasonal MA coefficients, plus the period and the number of non-seasonal and seasonal differences.
That is what the seven elements you reported correspond to. In your case, you have a non-seasonal `ARIMA(1,2,0)`.
*Source : How to read p,d and q of `auto.arima()`? (which is 1 among the reference link above.)*
> So far, we have restricted our attention to non-seasonal data and non-seasonal ARIMA models. However, ARIMA models are also capable of modelling a wide range of seasonal data.
A seasonal ARIMA model is formed by including additional seasonal terms in the ARIMA models we have seen so far. It is written as follows:
| ARIMA | $\underbrace{(p, d, q)}$ | $\underbrace{(P, D, Q)_{m}}$ |
|:-------:|:------------------------------:|:-----------------------------:|
| | ↑ | ↑ |
| | Non-seasonal part of the model | Seasonal part of the model |
where `m = number of observations per year`. We use uppercase notation for the seasonal parts of the model, and lowercase notation for the non-seasonal parts of the model.
The seasonal part of the model consists of terms that are similar to the non-seasonal components of the model, but involve backshifts of the seasonal period. For example, an $ARIMA(1,1,1)(1,1,1)_{4}$ model (without a constant) is for quarterly data (m = 4), and can be written as
$$(1 - {\color{Red}\phi_{1}}B)~(1 - {\color{Red}\Phi_{1}}B^{4}) (1 - B) (1 - B^{4})y_{t} = (1 + {\color{Red}\theta_{1}}B)~ (1 + {\color{Red}\Theta_{1}}B^{4})\varepsilon_{t}$$
The additional seasonal terms are simply multiplied by the non-seasonal terms.
`auto.arima(euretail, stepwise=FALSE, approximation=FALSE)` is better than `auto.arima(euretail)`.
> The `auto.arima()` function uses `nsdiffs()` to determine D (the number of seasonal differences to use), and `ndiffs()` to determine d (the number of ordinary differences to use). The selection of the other model parameters `(p, q, P and Q)` are all determined by minimizing the AICc, as with non-seasonal ARIMA models.
*Source : 8.9 Seasonal ARIMA models (which is 1 among the reference link above.)*
Above *8.5 Non-seasonal ARIMA models* reference link describe the `auto.arima()` and the default setting is `seasonal=TRUE` where it will automatically model^[help of `auto.arima()` describe the `seasonal : If FALSE, restricts search to non-seasonal models.`] .
> The default arguments are designed for rapid estimation of models for many time series. If you are analysing just one time series, and can afford to take some more time, it is recommended that you set stepwise=FALSE and approximation=FALSE.
Non-stepwise selection can be slow, especially for seasonal data. The stepwise algorithm outlined in Hyndman & Khandakar (2008) is used except that the default method for selecting seasonal differences is now based on an estimate of seasonal strength (Wang, Smith & Hyndman, 2006) rather than the Canova-Hansen test. There are also some other minor variations to the algorithm described in Hyndman and Khandakar (2008).
*Source : help section of `auto.arima()`.*
>`ARIMA(2,1,1)(1,0,0)[12]` is seasonal ARIMA. `[12]` stands for number of periods in season, i.e. months in year in this case. `(1,0,0)` stands for seasonal part of model. Take a look at [this](https://onlinecourses.science.psu.edu/stat510/node/67).
*Source : extract ARIMA specificaiton (which is 1 among the reference link above.)*
> You can force a seasonal model by setting `D=1`, although `auto.arima()` runs for quite some time with forced seasonality. (Note that the information criteria are not comparable between the original and the differenced series.)
$$
\begin{array}{l,l,l}
&\text{Training} & \text{Test}\\
\mathrm{ARIMA}(2,1,1) & 5.729 & 7.657\\
\mathrm{SARIMA}(1,1,0)_{52}\text{ with drift} & 6.481 & 7.390\\
\text{3 harmonics, }\mathrm{ARIMA}(2,1,0) & 5.578 & 5.151\\
\text{4 harmonics, }\mathrm{ARIMA}(2,1,1) & 5.219 & 5.188
\end{array}
$$
*Source : Seasonality not taken account of in `auto.arima()` (which is 1 among the reference link above.)*
> The problem with fitting seasonal ARIMA to daily data is that the "seasonal component" may only operate on the weekends or maybe just the weekdays thus overall there is a non-significnat "seasonal component". Now what you have to do is to augment your data set with 6 dummies representing the days of the week and perhaps monthly indicators to represent annual effects. Now consider incorporating events such as holidays and include any lead, contemoraneous or lag effect around these known variables. No there may be unusual values (pulses) or level shifts or local time trends in the data. Furthermore the day-of-the-week effects may have changed over time e.g. there was no Saturday effect for the first 20 weeks but a Saturday effect for the last 50 weeks.If you wish to post tour daily data I will give it a try and maybe other readers of the list might also contribute their analysis to help guide you through this.
*Source : Auto.arima with daily data: how to capture seasonality/periodicity?*
### Modelling SARIMA
#### Seasonal Data
- [*Seasonality not taken account of in `auto.arima()`*](https://stats.stackexchange.com/a/213455/68357) compares few models and concludes that the harmonics ARIMA is the best fit model.
- Non-stepwise model will slow down the seasonal model.
- `a$arma[c(1, 6, 2, 3, 7, 4, 5)]` is $(p,d,q)(P,D,Q)_{s}$.
- [How does R's auto.arima() function determine the order of differencing when estimating a regression with seasonal ARIMA abnors?](https://stats.stackexchange.com/questions/30220/how-does-rs-auto-arima-function-determine-the-order-of-differencing-when-esti?answertab=votes#tab-top) talk about the OCSB test where [Major changes to the forecast package](https://robjhyndman.com/hyndsight/forecast3/) describe the improvement in `forecast` package.
- [Frequency parameter and its impact on auto.arima results](https://stats.stackexchange.com/questions/187304/frequency-parameter-and-its-impact-on-auto-arima-results) talk about the frequency parameter for `seasonal period` while the author of `forecast` package provides [Seasonal periods](https://robjhyndman.com/hyndsight/seasonal-periods/) where describe very details on the `seasonal period` parameters determination.
- [Auto.arima with daily data: how to capture seasonality/periodicity?](https://stats.stackexchange.com/questions/14742/auto-arima-with-daily-data-how-to-capture-seasonality-periodicity), the author of `forecast` package answered `salests <- ts(data,start=2010,frequency=7)` and `modArima <- auto.arima(salests)` for weekly seasonality determination.
- [Why is this xts frequency always 1?](https://stackoverflow.com/questions/34454947/why-is-this-xts-frequency-always-1)
>**Improved auto.arima()**
The `auto.arima()` function is widely used for automatically selecting ARIMA models. It works quite well, except that selection of $D$, the order of seasonal differencing, has always been poor. Up until now, the default has been to use the Canova-Hansen test to select $D$. Because the CH test has a null hypothesis of deterministic seasonality based on dummy variables, the function will often select $D=0$. So I’ve now switched to using the OCSB test for selecting $D$ which has a null hypothesis involving a seasonal difference, so it is much more likely to choose $D=1$ than previously. I’ve done extensive testing of the forecasts obtained under the two methods, and the OCSB test leads to better forecasts. Hence it is now the default. This means that the function may return a different ARIMA model than previously when the data are seasonal.
A separate function for selecting the seasonal order has also been made visible. So you can now call `nsdiffs()` to find the recommended number of seasonal differences without calling auto.arima(). There is also a `ndiffs()` function for selecting the number of first differences. Within `auto.arima()`, `nsdiffs()` is called first to select $D$, and then `ndiffs()` is applied to `diff(x,D)` if $D > 0$ or to $x$ if $D=0$.
> **Double-seasonal Holt-Winters**
The new dshw() function implements *Taylor’s (2003)* double-seasonal Holt-Winters method. This allows for two levels of seasonality. For example, with hourly data, there is often a daily period of 24 and a weekly period of 168. These are modelled separately in the `dshw()` function.
> I am planning some major new functionality to extend this to the various types of complex seasonality discussed in my recent JASA paper. Hopefully that will be ready in the next few weeks – I have a research assistant working on the new code.
*Source : Major changes to the forecast package*
- [Forecasting Daily Data with Multiple Seasonality in R](http://www.dbenson.co.uk/Rparts/subpages/forecastR/) provides the example for seasonal modelling. Now we start modelling harmonics model (which is using `xreg`).
- [R/msts.R](https://rdrr.io/cran/forecast/src/R/msts.R) introduced a multi seasonal time series objects, intended to be used for models that support multiple seasonal periods. The msts class inherits from the ts class and has an additional "msts" attribute which contains the vector of seasonal periods. All methods that work on a ts class, should also work on a msts class.
- [Multiseasonal models for multivariate time series](https://stats.stackexchange.com/questions/355746/multiseasonal-models-for-multivariate-time-series) and [Forecast double seasonal time series with multiple linear regression in R](https://petolau.github.io/Forecast-double-seasonal-time-series-with-multiple-linear-regression-in-R/) provides example for multi-seasonal modelling.
- [How to setup `xreg` argument in `auto.arima()` in R? [closed]](https://stats.stackexchange.com/questions/41070/how-to-setup-xreg-argument-in-auto-arima-in-r) using `xreg` for multivariate modelling.
- [Find Arima equation using auto.arima, daily long-term data (msts), 3 seasonal regressors, and calculating K in fourier](https://stats.stackexchange.com/questions/135521/find-arima-equation-using-auto-arima-daily-long-term-data-msts-3-seasonal-re) introduced 3 seasonal modelling.
- [R - Putting time series with frequency of 20 min into the function `stl()`](https://stackoverflow.com/questions/17738746/r-putting-time-series-with-frequency-of-20-min-into-the-function-stl)
- ["Frequency" value for seconds/minutes intervals data in R](https://stats.stackexchange.com/questions/120806/frequency-value-for-seconds-minutes-intervals-data-in-r)
- [Time Series and Forecasting using R](http://manishbarnwal.com/blog/2017/05/03/time_series_and_forecasting_using_R/)
```
library(forecast)
# create some artifical data
modelfitsample <- data.frame(Customer_Visit=rpois(49,3000),Weekday=rep(1:7,7),
Christmas=c(rep(0,40),1,rep(0,8)),Day=1:49)
# Create matrix of numeric predictors
xreg <- cbind(Weekday=model.matrix(~as.factor(modelfitsample$Weekday)),
Day=modelfitsample$Day,
Christmas=modelfitsample$Christmas)
# Remove intercept
xreg <- xreg[,-1]
# Rename columns
colnames(xreg) <- c("Mon","Tue","Wed","Thu","Fri","Sat","Day","Christmas")
# Variable to be modelled
visits <- ts(modelfitsample$Customer_Visit, frequency=7)
# Find ARIMAX model
modArima <- auto.arima(visits, xreg=xreg)
```
*Source : [How to setup `xreg` argument in `auto.arima()` in R? [closed]](https://stats.stackexchange.com/questions/41070/how-to-setup-xreg-argument-in-auto-arima-in-r)*
```
library(forecast)
ts_ <- ts(PaulsData$Temperature, frequency = 1)
msts_ <- msts(ts_, c(7,30,365))
fit <- auto.arima(ts_, seasonal=F, xreg=fourier(msts_, K=c(3,5,10))) # i,j,k
```
*Source : [Find Arima equation using auto.arima, daily long-term data (msts), 3 seasonal regressors, and calculating K in fourier](https://stats.stackexchange.com/questions/135521/find-arima-equation-using-auto-arima-daily-long-term-data-msts-3-seasonal-re)*
```{r, eval=FALSE}
ts_ <- data_m1$close %>%
ts()
mts_ <- data_m1 %>%
msts(seasonal.periods = c(1440, 7200), start = index(.)[1])
fit1 <- auto.arima(ts_, seasonal = FALSE, xreg=fourier(mts_, K=c(3,5,10)))