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Time Series Cross Validation
# Train / Test Set VXV / VXMT Strategy
# Andrew Bannerman
################################################
# Procedure
# 1. Split data into train / test sets
# 2. Select 1 year look back for each train set (252 days)
# 3. Select 6 months test set (126)
# 4. Re-calibrate on a moving window through entire time series
#################################################
# Required Packages
library(readxl)
require(xts)
require(data.table)
require(ggplot2)
require(RColorBrewer)
require(lubridate)
require(magrittr)
require(scales)
require(reshape2)
require(PerformanceAnalytics)
require(dplyr)
require(TTR)
#################################################
# 1. Load Data
#################################################
# Load Syntehtic and join to alpha vantage adjusted prices
# Load synthetic VXX and XIV data
synth <- read_excel("D:/R Projects/Final Scripts/VIX_term_structure/vix-funds-models-no-formulas.xls", col_names = TRUE)
synth1 <- read_excel("D:/R Projects/Final Scripts/VIX_term_structure/vix-mt-funds-models-no-formulas.xls", col_names = TRUE)
synth <- as.data.frame(synth)
synth1 <- as.data.frame(synth1)
# Extract synthetic series
vxx.synth <- data.frame(synth$Date, synth$'VXX calc')
xiv.synth <- data.frame(synth$Date, synth$'XIV calc')
ziv.synth <- data.frame(synth1$Date, synth1$'ZIV calc')
vxz.synth <- data.frame(synth1$Date, synth1$'VXZ calc')
colnames(vxx.synth)[1] <- "Date"
colnames(vxx.synth)[2] <- "vxx_close"
colnames(xiv.synth)[1] <- "Date"
colnames(xiv.synth)[2] <- "xiv_close"
colnames(ziv.synth)[1] <- "Date"
colnames(ziv.synth)[2] <- "ziv_close"
colnames(vxz.synth)[1] <- "Date"
colnames(vxz.synth)[2] <- "vxz_close"
vxx.synth$Date <- ymd(vxx.synth$Date)
xiv.synth$Date <- ymd(xiv.synth$Date)
ziv.synth$Date <- ymd(ziv.synth$Date)
vxz.synth$Date <- ymd(vxz.synth$Date)
# Download data from alphavantage
VXX <- fread("https://www.alphavantage.co/query?function=TIME_SERIES_DAILY_ADJUSTED&symbol=VXX&outputsize=full&apikey=your_api_key&datatype=csv") #fread() data.table for downloading directly to a data frame
VXX$timestamp <- ymd(VXX$timestamp) #Lubridate to change character date to date format
VXX <- arrange(VXX,timestamp) #dplyr to sort data frame by date ascending order
colnames(VXX)[1] <- "Date"
VXX$Date <- ymd(VXX$Date)
VXX <- as.data.frame(VXX)
XIV <- fread("https://www.alphavantage.co/query?function=TIME_SERIES_DAILY_ADJUSTED&symbol=XIV&outputsize=full&apikey=your_api_key&datatype=csv") #fread() data.table for downloading directly to a data frame
XIV$timestamp <- ymd(XIV$timestamp) #Lubridate to change character date to date format
XIV <- arrange(XIV,timestamp) #dplyr to sort data frame by date ascending order
colnames(XIV)[1] <- "Date"
XIV$Date <- ymd(XIV$Date)
XIV <- as.data.frame(XIV)
# Join sythentic data to alpha vantage
vxx.synth <- subset(vxx.synth, Date <= as.POSIXct("2009-01-29"))
xiv.synth <- subset(xiv.synth, Date <= as.POSIXct("2010-11-29"))
# Subset only date and close from alpha vantage data
VXX <- VXX[ -c(2:5, 7:9) ] # subset adjusted close
XIV <- XIV[ -c(2:5, 7:9) ] # subset adjusted close
colnames(VXX)[2] <- "vxx_close"
colnames(XIV)[2] <- "xiv_close"
# row bind
VXX <- rbind(vxx.synth,VXX)
XIV <- rbind(xiv.synth,XIV)
df <- cbind(VXX,XIV)
# Download VXV and VXMT data from CBOE website
# Download VXV Data From CBOE website
VXV_cboe <- fread("http://www.cboe.com/publish/scheduledtask/mktdata/datahouse/vix3mdailyprices.csv")
VXV_cboe <- as.data.frame(VXV_cboe)
VXV_cboe <- VXV_cboe[3:nrow(VXV_cboe), ]
colnames(VXV_cboe)[1] = "Date"
colnames(VXV_cboe)[2] = "vxv_cboe_open"
colnames(VXV_cboe)[3] = "vxv_cboe_high"
colnames(VXV_cboe)[4] = "vxv_cboe_low"
colnames(VXV_cboe)[5] = "vxv_cboe_close"
VXV_cboe$Date <- mdy(VXV_cboe$Date)
cols <-c(2:5)
VXV_cboe[,cols] %<>% lapply(function(x) as.numeric(as.character(x)))
# Download VXMT Data from CBOE website
VXMT_cboe <- fread("http://www.cboe.com/publish/scheduledtask/mktdata/datahouse/vxmtdailyprices.csv")
VXMT_cboe <- as.data.frame(VXMT_cboe)
VXMT_cboe <- VXMT_cboe[3:nrow(VXMT_cboe), ]
colnames(VXMT_cboe)[1] = "Date"
colnames(VXMT_cboe)[2] = "vxmt_cboe_open"
colnames(VXMT_cboe)[3] = "vxmt_cboe_high"
colnames(VXMT_cboe)[4] = "vxmt_cboe_low"
colnames(VXMT_cboe)[5] = "vxmt_cboe_close"
VXMT_cboe$Date <- mdy(VXMT_cboe$Date)
cols <-c(2:5)
VXMT_cboe[,cols] %<>% lapply(function(x) as.numeric(as.character(x)))
# Join VIX, VIX3m (VXV) and VXMT CBOE data to ETF df
cboe.df <- merge(VIX_cboe,VXV_cboe, by="Date")
cboe.df <- merge(cboe.df,VXMT_cboe, by="Date")
start_date <- cboe.df$Date[1]
# Subset Strategy To Start At VXMT Date
df <- subset(df, Date >= as.POSIXct(start_date) )
df <- df[,c(-3)] # Drop unused dates
df <- full_join(df, cboe.df, by = c("Date" = "Date"))
####################################################################
# Create VXV VXMT Ratio and ratio SMA
###################################################################
# VXV / VXMT Ratio
df$vxv.vxmt.ratio <- df$vxv_cboe_close / df$vxmt_cboe_close
# Calculate Close-to-Close returns
df$vxx.close.ret <- ROC(df$vxx_close, type = c("discrete"))
df$xiv.close.ret <- ROC(df$xiv_close, type = c("discrete"))
# Calculate SMA of VXV , VXMT ratio
sma.lookback <- 2:170
getSMA <- function(y) {
function(x) {
SMA(df[,"vxv.vxmt.ratio"], sma.lookback[i]) # Calls TTR package to create SMA
}
}
# Create a matrix to put the SMAs in
sma.matrix <- matrix(nrow=nrow(df), ncol=0)
# Loop for filling it
for (i in 1:length(sma.lookback)) {
sma.matrix <- cbind(sma.matrix, getSMA(i)(x))
}
# Rename columns
colnames(sma.matrix) <- sapply(sma.lookback, function(n)paste("ratio.sma.n", n, sep=""))
# Bind to existing dataframe
df <- cbind(df, sma.matrix)
####################################################################
# Split Data Into Train and Test Sets
# 252 days train , 126 days test
##################################################################
# Set row numbers for splitting to train and test sets
total.row <- nrow(df) # total rows
train.length <- 252
test.length <- 125
train.list <- list()
test.list <- list()
# Set start and ending rows for subsetting by row
train_num_set <- seq(1, nrow(df), by=test.length+1)
test_num_set <- seq(train.length+1, nrow(df), by=test.length+1)
train.list<- lapply(train_num_set, function(i) df[c(i:(i+train.length)),])
test.list<- lapply(test_num_set, function(i) df[c(i:(i+test.length)),])
####################################################################
# Run Optimizations over all training windows
# Select optimal sharpe ratio
####################################################################
train.set.results <- data.frame()
i=1
train.loop.length[i]
train.loop.length <- rep(1:length(train.list),each=length(sma.lookback)) # run through the dfs the same length as the number of smas
sma.loop.length <- rep(2:length(sma.lookback),length(train.list)) # run each sma over every df
train.xts <- list()
# Loop for running all smas through all train sets, note need to wrap train.loop.length and sma.loop.lenght in [[i]]
for (i in 1:length(train.loop.length)) {
tryCatch({
df.num <- train.loop.length[[i]]
# Enter buy / sell rules
train.temp.df <- data.frame(Date=train.list[[df.num]]$Date)
train.temp.df$vxx.signal <- ifelse(train.list[[df.num]]$vxv.vxmt.ratio > 1 & train.list[[df.num]]$vxv.vxmt.ratio > train.list[[df.num]][,paste0("ratio.sma.n", sma.loop.length[[i]])], 1,0)
train.temp.df$xiv.signal <- ifelse(train.list[[df.num]]$vxv.vxmt.ratio < 1 & train.list[[df.num]]$vxv.vxmt.ratio < train.list[[df.num]][,paste0("ratio.sma.n", sma.loop.length[[i]])], 1,0)
# lag signal by two forward days
# CBOE data is available next day
train.temp.df$vxx.signal <- lag(train.temp.df$vxx.signal,2) # Note k=1 implies a move *forward*
train.temp.df$xiv.signal <- lag(train.temp.df$xiv.signal,2) # Note k=1 implies a move *forward*
train.temp.df[is.na(train.temp.df)] <- as.Date(0) # Set NA to 0
# Calculate equity curves
train.temp.df$vxx.signal.ret <- train.temp.df$vxx.signal * train.list[[df.num]]$vxx.close.ret
train.temp.df$xiv.signal.ret <- train.temp.df$xiv.signal * train.list[[df.num]]$xiv.close.ret
# Combine signals
train.temp.df$total.signal.ret <- train.temp.df$vxx.signal.ret + train.temp.df$xiv.signal.ret
# Pull select columns from data frame to make XTS whilst retaining formats
xts1 = xts(train.temp.df$vxx.signal.ret, order.by=as.Date(train.temp.df$Date, format="%y-%m-%d"))
xts2 = xts(train.temp.df$xiv.signal.ret, order.by=as.Date(train.temp.df$Date, format="%y/%m/%d"))
xts3 = xts(train.temp.df$total.signal.ret, order.by=as.Date(train.temp.df$Date, format="%y/%m/%d"))
# Join XTS together
compare <- cbind(xts1,xts2,xts3)
# Use the PerformanceAnalytics package for trade statistics
require(PerformanceAnalytics)
colnames(compare) <- c("vxx","xiv","combined")
#charts.PerformanceSummary(compare,main="Long when current month is higher than previous 12 month", wealth.index=TRUE, colorset=rainbow12equal)
#performance.table <- rbind(table.AnnualizedReturns(compare),maxDrawdown(compare), CalmarRatio(compare),table.DownsideRisk(compare))
#drawdown.table <- rbind(table.Drawdowns(xts3))
#dev.off()
# logRets <- log(cumprod(1+compare))
# chart.TimeSeries(logRets, legend.loc='topleft', colorset=rainbow12equal,main="Log Returns")
#print(performance.table)
#print(drawdown.table)
cum.ret <- Return.cumulative(xts3, geometric = TRUE)
annualized <- Return.annualized(xts3, scale = NA, geometric = TRUE)
dd <- maxDrawdown(xts3)
sharpe <- SharpeRatio.annualized(xts3, Rf = 0, scale = NA, geometric = TRUE)
# Output data
temp <- data.frame("Annualized Return" = annualized,"Annualized Sharpe" = sharpe,"Cumulative Return" = cum.ret,"Maximum Draw Down" =dd, ID=as.numeric(sma.loop.length[[i]]))
rownames(temp) <- paste0("train.set.",train.loop.length[[i]],"_sma_",sma.loop.length[[i]])
train.set.results <- rbind.data.frame(train.set.results,temp)
compare <- data.frame(compare)
compare <- data.frame(date=index(compare), coredata(compare))
train.xts[[i]] <- cbind.data.frame(compare)
ptm0 <- proc.time()
Sys.sleep(0.1)
ptm1=proc.time() - ptm0
time=as.numeric(ptm1[3])
cat('\n','Iteration Train Set',train.loop.length[i],'sma',sma.loop.length[i],'took', time, "seconds to complete")
}, error = function(e) { print(paste("i =", i, "failed:")) })
}
# Seperate train set results from data frame output
train.set.results <- setDT(train.set.results, keep.rownames = TRUE)[] # Set row names
train.set.results$ID <- as.numeric(train.set.results$ID)
# Subset test set results
l <- nrow(train.set.results)
train.result.list <- list()
output_num <- seq(1, l, by=length(sma.lookback))
train.result.list<- lapply(output_num, function(i) train.set.results[c(i:(i+length(sma.lookback)-1)),])
# Extract highest performance metric from each data frame within list
# Sharpe Ratio in this case
highest.sharpe <- list()
i=1
for (i in 1:length(train.result.list)) { # for every data frame inside results list
temp <- train.result.list[[i]][order(train.result.list[[i]]$Annualized.Sharpe),]
highest.sharpe[[i]] <- as.data.frame(tail(temp[,6],1))
}
# Save performance metric
sharpe.df <- do.call(cbind,highest.sharpe)
sharpe.vec <- paste(sharpe.df)
sharpe.vec <- as.numeric(sharpe.vec)
cat("Optimal In-Sample Train Set Parameters:SMA of VXV/VXMT Ratio - Optimal SMAs =",sharpe.vec)
###### Sharpe Optimization Complete ##########
#################################################################
# Run Optimal Parameters over all train sets
#################################################################
test.set.results <- data.frame()
test.xts <- list()
test.loop.length <- rep(1:length(test.list),1) # run through the all df's 1x
optimal.sma <- sharpe.vec # run each sma over every df
i=1
################### Manual Intervention ############################
# Remove nas on last test data frame inside list (Note this willl change adjust as needed)
#######################################################################
length.test.set <- length(test.list)
tail(test.list[[length.test.set]])
nrow.test.list <- NROW(test.list[[length.test.set]])
test.list[[length.test.set]] <- test.list[[length.test.set]][1:((nrow.test.list)-5),]
# Loop for running all smas through all train sets, note need to wrap train.loop.length and sma.loop.lenght in [[i]]
for (i in 1:length(test.loop.length )) {
tryCatch({
df.num <- test.loop.length[i]
# Enter buy / sell rules
test.temp.df <- data.frame(Date=test.list[[df.num]]$Date)
test.temp.df$vxx.signal <- ifelse(test.list[[df.num]]$vxv.vxmt.ratio > 1 & test.list[[df.num]]$vxv.vxmt.ratio > test.list[[df.num]][,paste0("ratio.sma.n", optimal.sma[[i]])], 1,0)
test.temp.df$xiv.signal <- ifelse(test.list[[df.num]]$vxv.vxmt.ratio < 1 & test.list[[df.num]]$vxv.vxmt.ratio < test.list[[df.num]][,paste0("ratio.sma.n", optimal.sma[[i]])], 1,0)
# lag signal by two forward days
# CBOE data is available next day
test.temp.df$vxx.signal <- lag(test.temp.df$vxx.signal,2) # Note k=1 implies a move *forward*
test.temp.df$xiv.signal <- lag(test.temp.df$xiv.signal,2) # Note k=1 implies a move *forward*
test.temp.df[is.na(test.temp.df)] <- as.Date(0) # Set NA to 0
# Calculate equity curves
test.temp.df$vxx.signal.ret <- test.temp.df$vxx.signal * test.list[[df.num]]$vxx.close.ret
test.temp.df$xiv.signal.ret <- test.temp.df$xiv.signal * test.list[[df.num]]$xiv.close.ret
# Combine signals
test.temp.df$total.signal.ret <- test.temp.df$vxx.signal.ret + test.temp.df$xiv.signal.ret
# Pull select columns from data frame to make XTS whilst retaining formats
xts1 = xts(test.temp.df$vxx.signal.ret, order.by=as.Date(test.temp.df$Date, format="%y-%m-%d"))
xts2 = xts(test.temp.df$xiv.signal.ret, order.by=as.Date(test.temp.df$Date, format="%y/%m/%d"))
xts3 = xts(test.temp.df$total.signal.ret, order.by=as.Date(test.temp.df$Date, format="%y/%m/%d"))
# Join XTS together
compare <- cbind(xts1,xts2,xts3)
# Use the PerformanceAnalytics package for trade statistics
require(PerformanceAnalytics)
colnames(compare) <- c("vxx","xiv","combined")
charts.PerformanceSummary(compare,main="Long when current month is higher than previous 12 month", wealth.index=TRUE, colorset=rainbow12equal)
#performance.table <- rbind(table.AnnualizedReturns(compare),maxDrawdown(compare), CalmarRatio(compare),table.DownsideRisk(compare))
#drawdown.table <- rbind(table.Drawdowns(xts3))
#dev.off()
# logRets <- log(cumprod(1+compare))
# chart.TimeSeries(logRets, legend.loc='topleft', colorset=rainbow12equal,main="Log Returns")
#print(performance.table)
#print(drawdown.table)
cum.ret <- Return.cumulative(xts3, geometric = TRUE)
annualized <- Return.annualized(xts3, scale = NA, geometric = TRUE)
dd <- maxDrawdown(xts3)
sharpe <- SharpeRatio.annualized(xts3, Rf = 0, scale = NA, geometric = TRUE)
# Save test set results
temp <- data.frame("Annualized Return" = annualized,"Annualized Sharpe" = sharpe,"Cumulative Return" = cum.ret,"Maximum Draw Down" =dd, ID=as.numeric(optimal.sma[[i]]))
test.set.results <- rbind.data.frame(test.set.results)
test.xts[[i]] <- cbind.data.frame(compare)
ptm0 <- proc.time()
Sys.sleep(0.1)
ptm1=proc.time() - ptm0
time=as.numeric(ptm1[3])
cat('\n','Iteration Test Set',test.loop.length[i],'optimal.sma',optimal.sma[i],'took', time, "seconds to complete")
}, error = function(e) { print(paste("i =", i, "failed:")) })
}
# Extract xts3 cumulative returns
cum.rets <- do.call(rbind,test.xts)
cum.rets <- setDT(cum.rets, keep.rownames = TRUE)[] # Set row names
colnames(cum.rets)[1] <- "Date"
cum.rets[is.na(cum.rets)] <- 0
cum.rets$Date <- ymd(cum.rets$Date)
cum.rets.xts <- xts(cum.rets$combined, order.by=as.Date(cum.rets$Date, format="%y-%m-%d"))
# Summary Statistic on final walk forward curve
charts.PerformanceSummary(cum.rets,main="Long when current month is higher than previous 12 month", wealth.index=TRUE, colorset=rainbow12equal)
table.AnnualizedReturns(cum.rets.xts)
maxDrawdown(cum.rets.xts)
CalmarRatio(cum.rets.xts)
table.DownsideRisk(cum.rets.xts)
drawdown.table <- rbind(table.Drawdowns(cum.rets.xts))
drawdown.table
# Extract train and test dates for plotting
# Train Dates
train.dateslist <- list()
train.dates.loop.length <- rep(1:length(train.list),each=1)
temp <- data.frame()
i=1
for (i in 1:length(train.dates.loop.length)) {
temp <- data.frame("ID"=paste("train.id",train.dates.loop.length[[i]]))
date <- train.list[[i]]$Date
train.dateslist[[i]] <- cbind("Date" = date,ID=temp)
# Test Dates
test.dateslist <- list()
test.dates.loop.length <- rep(1:length(test.list),each=1)
i=1
for (i in 1:length(test.dates.loop.length)) {
temp <- data.frame("ID"=paste("test.id",test.dates.loop.length[[i]]))
date <- test.list[[i]]$Date
test.dateslist[[i]] <- cbind("Date" = date,ID=temp)
}
# Loop to extract start and end dates of each train / test segment
train.dates.start <- list()
train.dates.end <- list()
for (i in 1:length(train.dateslist)) {
train.dates.start[[i]] <- train.dateslist[[i]]$Date[1]
train.dates.end[[i]] <- tail(train.dateslist[[i]]$Date,1)
}
test.dates.start <- list()
test.dates.end <- list()
for (i in 1:length(test.dateslist)) {
test.dates.start[[i]] <- test.dateslist[[i]]$Date[1]
test.dates.end[[i]] <- tail(test.dateslist[[i]]$Date,1)
}
# Plot train and test starting / ending periods
ggplot()+
theme_bw()+
scale_y_continuous(expand = c(0, 0),breaks = round(seq(min(1), max(length(test.dateslist)), by = 1)))+ # set y axis to same amount as total train / test sample periosd
theme(legend.position = "none")+
theme(plot.title = element_text(hjust=0.5),plot.subtitle =element_text(hjust=0.5))+
ggtitle("Train And Test Windows",subtitle=paste("Train Width =",train.length,"Days, Test Width =",test.length,"Days"))+
geom_rect(aes(xmin=as.Date(train.dates.start[[1]]),xmax=as.Date(train.dates.end[[1]]),ymin=1, ymax=2),fill="#0072B2",alpha=.8)+
geom_rect(aes(xmin=as.Date(train.dates.start[[2]]),xmax=as.Date(train.dates.end[[2]]),ymin=2, ymax=3),fill="#0072B2",alpha=.8)+
geom_rect(aes(xmin=as.Date(train.dates.start[[3]]),xmax=as.Date(train.dates.end[[3]]),ymin=3, ymax=4),fill="#0072B2",alpha=.8)+
geom_rect(aes(xmin=as.Date(train.dates.start[[4]]),xmax=as.Date(train.dates.end[[4]]),ymin=4, ymax=5),fill="#0072B2",alpha=.8)+
geom_rect(aes(xmin=as.Date(train.dates.start[[5]]),xmax=as.Date(train.dates.end[[5]]),ymin=5, ymax=6),fill="#0072B2",alpha=.8)+
geom_rect(aes(xmin=as.Date(train.dates.start[[6]]),xmax=as.Date(train.dates.end[[6]]),ymin=6, ymax=7),fill="#0072B2",alpha=.8)+
geom_rect(aes(xmin=as.Date(train.dates.start[[7]]),xmax=as.Date(train.dates.end[[7]]),ymin=7, ymax=8),fill="#0072B2",alpha=.8)+
geom_rect(aes(xmin=as.Date(train.dates.start[[8]]),xmax=as.Date(train.dates.end[[8]]),ymin=8, ymax=9),fill="#0072B2",alpha=.8)+
geom_rect(aes(xmin=as.Date(train.dates.start[[9]]),xmax=as.Date(train.dates.end[[9]]),ymin=9, ymax=10),fill="#0072B2",alpha=.8)+
geom_rect(aes(xmin=as.Date(train.dates.start[[10]]),xmax=as.Date(train.dates.end[[10]]),ymin=10, ymax=11),fill="#0072B2",alpha=.8)+
geom_rect(aes(xmin=as.Date(train.dates.start[[11]]),xmax=as.Date(train.dates.end[[11]]),ymin=11, ymax=12),fill="#0072B2",alpha=.8)+
geom_rect(aes(xmin=as.Date(train.dates.start[[12]]),xmax=as.Date(train.dates.end[[12]]),ymin=12, ymax=13),fill="#0072B2",alpha=.8)+
geom_rect(aes(xmin=as.Date(train.dates.start[[13]]),xmax=as.Date(train.dates.end[[13]]),ymin=13, ymax=14),fill="#0072B2",alpha=.8)+
geom_rect(aes(xmin=as.Date(train.dates.start[[14]]),xmax=as.Date(train.dates.end[[14]]),ymin=14, ymax=15),fill="#0072B2",alpha=.8)+
geom_rect(aes(xmin=as.Date(train.dates.start[[15]]),xmax=as.Date(train.dates.end[[15]]),ymin=15, ymax=16),fill="#0072B2",alpha=.8)+
geom_rect(aes(xmin=as.Date(train.dates.start[[16]]),xmax=as.Date(train.dates.end[[16]]),ymin=16, ymax=17),fill="#0072B2",alpha=.8)+
geom_rect(aes(xmin=as.Date(train.dates.start[[17]]),xmax=as.Date(train.dates.end[[17]]),ymin=17, ymax=18),fill="#0072B2",alpha=.8)+
geom_rect(aes(xmin=as.Date(train.dates.start[[18]]),xmax=as.Date(train.dates.end[[18]]),ymin=18, ymax=19),fill="#0072B2",alpha=.8)+
geom_rect(aes(xmin=as.Date(test.dates.start[[1]]),xmax=as.Date(test.dates.end[[1]]),ymin=1, ymax=2),fill="#D55E00",alpha=.8)+
geom_rect(aes(xmin=as.Date(test.dates.start[[2]]),xmax=as.Date(test.dates.end[[2]]),ymin=2, ymax=3),fill="#D55E00",alpha=.8)+
geom_rect(aes(xmin=as.Date(test.dates.start[[3]]),xmax=as.Date(test.dates.end[[3]]),ymin=3, ymax=4),fill="#D55E00",alpha=.8)+
geom_rect(aes(xmin=as.Date(test.dates.start[[4]]),xmax=as.Date(test.dates.end[[4]]),ymin=4, ymax=5),fill="#D55E00",alpha=.8)+
geom_rect(aes(xmin=as.Date(test.dates.start[[5]]),xmax=as.Date(test.dates.end[[5]]),ymin=5, ymax=6),fill="#D55E00",alpha=.8)+
geom_rect(aes(xmin=as.Date(test.dates.start[[6]]),xmax=as.Date(test.dates.end[[6]]),ymin=6, ymax=7),fill="#D55E00",alpha=.8)+
geom_rect(aes(xmin=as.Date(test.dates.start[[7]]),xmax=as.Date(test.dates.end[[7]]),ymin=7, ymax=8),fill="#D55E00",alpha=.8)+
geom_rect(aes(xmin=as.Date(test.dates.start[[8]]),xmax=as.Date(test.dates.end[[8]]),ymin=8, ymax=9),fill="#D55E00",alpha=.8)+
geom_rect(aes(xmin=as.Date(test.dates.start[[9]]),xmax=as.Date(test.dates.end[[9]]),ymin=9, ymax=10),fill="#D55E00",alpha=.8)+
geom_rect(aes(xmin=as.Date(test.dates.start[[10]]),xmax=as.Date(test.dates.end[[10]]),ymin=10, ymax=11),fill="#D55E00",alpha=.8)+
geom_rect(aes(xmin=as.Date(test.dates.start[[11]]),xmax=as.Date(test.dates.end[[11]]),ymin=11, ymax=12),fill="#D55E00",alpha=.8)+
geom_rect(aes(xmin=as.Date(test.dates.start[[12]]),xmax=as.Date(test.dates.end[[12]]),ymin=12, ymax=13),fill="#D55E00",alpha=.8)+
geom_rect(aes(xmin=as.Date(test.dates.start[[13]]),xmax=as.Date(test.dates.end[[13]]),ymin=13, ymax=14),fill="#D55E00",alpha=.8)+
geom_rect(aes(xmin=as.Date(test.dates.start[[14]]),xmax=as.Date(test.dates.end[[14]]),ymin=14, ymax=15),fill="#D55E00",alpha=.8)+
geom_rect(aes(xmin=as.Date(test.dates.start[[15]]),xmax=as.Date(test.dates.end[[15]]),ymin=15, ymax=16),fill="#D55E00",alpha=.8)+
geom_rect(aes(xmin=as.Date(test.dates.start[[16]]),xmax=as.Date(test.dates.end[[16]]),ymin=16, ymax=17),fill="#D55E00",alpha=.8)+
geom_rect(aes(xmin=as.Date(test.dates.start[[17]]),xmax=as.Date(test.dates.end[[17]]),ymin=17, ymax=18),fill="#D55E00",alpha=.8)+
geom_rect(aes(xmin=as.Date(test.dates.start[[18]]),xmax=as.Date(test.dates.end[[18]]),ymin=18, ymax=19),fill="#D55E00",alpha=.8)+
labs(x="Date",y="Train / Test Set No.")
# Extract final equity curve from test set
final.plot <- list()
i=1
for (i in 1:length(test.xts)) {
to.sum <- data.frame("to.sum"=test.xts[[i]]$combined)
dates <- test.list[[i]]$Date
final.plot[[i]] <- data.frame("Date"=dates,to.sum)
}
# Make df of output
final.df <- do.call(rbind,final.plot)
# Cumsum equity curve
final.df$equity <- cumprod(final.df$to.sum + 1) -1
final.df <- final.df[c(1,3) ]
# Melt df
final.plot.df <- melt(data = final.df,id.vars = 'Date') # melt df for plotting with ggplot2
# Create ID
final.plot.df$final_num <- as.numeric(rep(1:test.length+1, each=test.length+1, length.out=nrow(final.plot.df)))
# Subset plots to plot each test period a different colour
subset.plots <- list()
test.width <- 125
subset.plots<- lapply(test_num_set, function(i) final.plot.df[c(i:(i+test.length)),])
# Create plot
# Create colour scheme
myPalette <- colorRampPalette(rev(brewer.pal(11, "Paired")))
sc <- scale_colour_gradientn(colours = myPalette(100), limits=c(1, 18))
# Plot out of sample test results equity curve
ggplot(data = subset.plots[[1]], aes(x =Date, y = value,colour=final_num))+
geom_line(data = subset.plots[[2]], aes(x =Date, y = value))+
geom_line(data = subset.plots[[3]], aes(x =Date, y = value,colour=final_num))+
geom_line(data = subset.plots[[4]], aes(x =Date, y = value,colour=final_num))+
geom_line(data = subset.plots[[5]], aes(x =Date, y = value,colour=final_num))+
geom_line(data = subset.plots[[6]], aes(x =Date, y = value,colour=final_num))+
geom_line(data = subset.plots[[7]], aes(x =Date, y = value,colour=final_num))+
geom_line(data = subset.plots[[8]], aes(x =Date, y = value,colour=final_num))+
geom_line(data = subset.plots[[9]], aes(x =Date, y = value,colour=final_num))+
geom_line(data = subset.plots[[10]], aes(x =Date, y = value,colour=final_num))+
geom_line(data = subset.plots[[11]], aes(x =Date, y = value,colour=final_num))+
geom_line(data = subset.plots[[12]], aes(x =Date, y = value,colour=final_num))+
geom_line(data = subset.plots[[13]], aes(x =Date, y = value,colour=final_num))+
geom_line(data = subset.plots[[14]], aes(x =Date, y = value,colour=final_num))+
geom_line(data = subset.plots[[15]], aes(x =Date, y = value,colour=final_num))+
geom_line(data = subset.plots[[16]], aes(x =Date, y = value,colour=final_num))+
geom_line(data = subset.plots[[17]], aes(x =Date, y = value,colour=final_num))+
geom_line(data = subset.plots[[18]], aes(x =Date, y = value,colour=final_num))+
sc+
theme_bw()+
theme(legend.position = "none")+
scale_y_continuous(breaks = seq(1, 110, by = 5))+
ggtitle("Test Set Results", subtitle =paste("Test Set Lengths =",test.length," rows")) +
labs(x="Date",y="Cumulative Return")+
theme(plot.title = element_text(hjust=0.5),plot.subtitle =element_text(hjust=0.5))
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