Block Bootstrap data frame

gistfile1.txt

# Block Bootstrap Time Series 
# Andrew Bannerman 12.30.2017 

require(xts)
require(data.table)
require(ggplot2)
require(lubridate)
require(magrittr)
require(scales)
require(reshape2)
require(PerformanceAnalytics)
require(dplyr)
require(TTR)

######### Download ETF Data ###############
# Load Syntehtic and join to alpha vantage adjusted prices 
# Load synthetic VXX and XIV data 
library(readxl)
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 SPY data
# Note you need tyo place your API key...your_key_here
SPY <- fread("https://www.alphavantage.co/query?function=TIME_SERIES_DAILY_ADJUSTED&symbol=SPY&outputsize=full&apikey=your_api_key&datatype=csv") #fread() data.table for downloading directly to a data frame
SPY$timestamp <- ymd(SPY$timestamp)   #Lubridate to change character date to date format
SPY <- arrange(SPY,timestamp)   #dplyr to sort data frame by date ascending order
colnames(SPY)[1] <- "Date"
SPY$Date <- ymd(SPY$Date)
SPY <- as.data.frame(SPY)
SPY <- subset(SPY, Date >= as.POSIXct("2004-03-26") ) # synthetic data start
head(SPY)

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)
head(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)
head(XIV)
#XIV <- subset(XIV, Date >= as.POSIXct("2012-01-01"))

ZIV <- fread("https://www.alphavantage.co/query?function=TIME_SERIES_DAILY_ADJUSTED&symbol=ZIV&outputsize=full&apikey=your_api_key&datatype=csv") #fread() data.table for downloading directly to a data frame
ZIV$timestamp <- ymd(ZIV$timestamp)   #Lubridate to change character date to date format
ZIV <- arrange(ZIV,timestamp)   #dplyr to sort data frame by date ascending order
colnames(ZIV)[1] <- "Date"
ZIV$Date <- ymd(ZIV$Date)
ZIV <- as.data.frame(ZIV)
head(ZIV)

VXZ <- fread("https://www.alphavantage.co/query?function=TIME_SERIES_DAILY_ADJUSTED&symbol=VXZ&outputsize=full&apikey=your_api_key&datatype=csv") #fread() data.table for downloading directly to a data frame
VXZ$timestamp <- ymd(VXZ$timestamp)   #Lubridate to change character date to date format
VXZ <- arrange(VXZ,timestamp)   #dplyr to sort data frame by date ascending order
colnames(VXZ)[1] <- "Date"
VXZ$Date <- ymd(VXZ$Date)
VXZ <- as.data.frame(VXZ)
tail(VXZ)

# 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"))
ziv.synth <- subset(ziv.synth, Date <= as.POSIXct("2010-11-29"))
vxz.synth <- subset(vxz.synth, Date <= as.POSIXct("2009-02-19"))
# 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
ZIV <- ZIV[ -c(2:5, 7:9) ]  # subset adjusted close
VXZ <- VXZ[ -c(2:5, 7:9) ]  # subset adjusted close
SPY <- SPY[ -c(3:5, 7:9) ]  # subset adjusted close
colnames(VXX)[2] <- "vxx_close"
colnames(XIV)[2] <- "xiv_close"
colnames(ZIV)[2] <- "ziv_close"
colnames(VXZ)[2] <- "vxz_close"
colnames(SPY)[2] <- "spy_open"
colnames(SPY)[3] <- "spy_close"

# row bind 
VXX <- rbind(vxx.synth,VXX)
XIV <- rbind(xiv.synth,XIV)
ZIV <- rbind(ziv.synth,ZIV)
VXZ <- rbind(vxz.synth,VXZ)
df <- cbind(VXX,XIV,ZIV,VXZ,SPY)
tail(df)

# Download Spot VIX Price and VXV Price from CBOE website
VIX_cboe <- fread("http://www.cboe.com/publish/scheduledtask/mktdata/datahouse/vixcurrent.csv")
VIX_cboe <- as.data.frame(VIX_cboe)
VIX_cboe <- VIX_cboe[2:nrow(VIX_cboe), ]
colnames(VIX_cboe)[1] = "Date"
colnames(VIX_cboe)[2] = "vix_open"
colnames(VIX_cboe)[3] = "vix_high"
colnames(VIX_cboe)[4] = "vix_low"
colnames(VIX_cboe)[5] = "vix_close"
VIX_cboe$Date <- mdy(VIX_cboe$Date)
cols <-c(2:5)
VIX_cboe[,cols] %<>% lapply(function(x) as.numeric(as.character(x)))
VIX_cboe <- subset(VIX_cboe, Date >= as.POSIXct("2007-12-04") )
# Download VXZ 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")
tail(cboe.df)
df <- df[,c(-3,-5,-7,-9)] # Drop unused dates
df <- full_join(df, cboe.df, by = c("Date" = "Date"))

# Remove last rows
nrow <- NROW(df)-2
df <- head(df,nrow)
tail(df)

############################################
# Back Test VXV / VXMT Ratio 
# Find best params without bootstrapping
############################################
# 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"))

# VXV / VXMT Ratio
df$vxv.vxmt.ratio <- df$vxv_cboe_close / df$vxmt_cboe_close
df[is.na(df)] <- 0
head(df)

# Calculate SMA of ratio 
numdays <- 2:500
getSMA <- function(numdays) {
  function(df) {
    SMA(df[,"vxv.vxmt.ratio"], numdays)    # 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 numdays) {
  sma.matrix <- cbind(sma.matrix, getSMA(i)(df))
}

# Rename columns
colnames(sma.matrix) <- sapply(numdays, function(n)paste("ratio.sma.n", n, sep=""))

# Bind to existing dataframe
df <-  cbind(df, sma.matrix)
tail(df)

##############################################
# Optimize Strategy Params 
##############################################
num.days <- 2:300
i=3
# Initialize data frame
data_output_df <- data.frame() 
# Optimize #########
optIMIZE = function(x){
  #spx.sma <- df[,paste0("close.sma.n", sma[i])]
  names(df)
  # Enter buy / sell rules
  #df$vxx.signal <- ifelse(df$vxv.vxmt.ratio > 1 & df$vxv.vxmt.ratio > df$ratio.sma , 1,0)
  #df$xiv.signal <- ifelse(df$vxv.vxmt.ratio < 1 & df$vxv.vxmt.ratio < df$ratio.sma , 1,0)
  df$vxx.signal <- ifelse(df$vxv.vxmt.ratio > 1 & df$vxv.vxmt.ratio > df[,paste0("ratio.sma.n", num.days[i])], 1,0)
  df$xiv.signal <- ifelse(df$vxv.vxmt.ratio < 1 & df$vxv.vxmt.ratio < df[,paste0("ratio.sma.n", num.days[i])], 1,0)
  
  # lag signal by two forward days
  # CBOE data is available next day
  df$vxx.signal <- lag(df$vxx.signal,2) # Note k=1 implies a move *forward*
  df$xiv.signal <- lag(df$xiv.signal,2) # Note k=1 implies a move *forward*
  
  df[is.na(df)] <- 0  # Set NA to 0
  
  # Calculate equity curves
  df$vxx.signal.ret <-  df$vxx.signal * df$vxx.close.ret
  df$xiv.signal.ret <-  df$xiv.signal * df$xiv.close.ret
  
  # Combine signals 
  df$total.signal.ret <- df$vxx.signal.ret + df$xiv.signal.ret
  
  # Pull select columns from data frame to make XTS whilst retaining formats
  xts1 = xts(df$vxx.signal.ret, order.by=as.Date(df$Date, format="%m/%d/%Y"))
  xts2 = xts(df$xiv.signal.ret, order.by=as.Date(df$Date, format="%m/%d/%Y")) 
  xts3 = xts(df$total.signal.ret, order.by=as.Date(df$Date, format="%m/%d/%Y")) 
  tail(xts3)
  
  # 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)
  
  
  # Create data output of rep and close.diff columns rbind
  data_output_df <- data.frame("Annualized Return" = annualized,"Annualized Sharpe" = sharpe,"Cumulative Return" = cum.ret,"Maximum Draw Down" = dd)
  
}

for (i in 1:length(num.days)){    # Length of optimization
  tryCatch({
    temp <- optIMIZE(num.days[[i]])
    rownames(temp) <- paste0("",num.days[i])
    #cum_ret <- rbind.data.frame(cum_ret, temp)
    data_output_df <- rbind.data.frame(data_output_df,temp)
    ptm0 <- proc.time()
    Sys.sleep(0.1)  
    ptm1=proc.time() - ptm0
    time=as.numeric(ptm1[3])
    cat('\n','Iteration',i,'took', time, "seconds to complete")
  }, error = function(e) { print(paste("i =", i, "failed:")) })
}

# Join SMA number to data frame
data_output_df <- data.frame(data_output_df,num.days)

# Plot 
colnames(data_output_df)
library(ggplot2)
ggplot(data=data_output_df, aes(x=num.days,Annualized.Return))+
  geom_bar(stat="identity")+
  theme_classic()+
  scale_x_continuous(breaks = seq(min(data_output_df$num.days), max(data_output_df$num.days)))+
  theme(axis.text.x = element_text(angle = 90, hjust = 0.5,size=15))+
  ggtitle("VXV/VXMT Volatility Strategy - Optimized sma vzx/vxmt ratio",subtitle="2008 to present")+
  theme(plot.title = element_text(hjust=0.5),plot.subtitle =element_text(hjust=0.5))+
  geom_rect(aes(xmin=51,xmax=70,ymin=0,ymax=Inf),alpha=0.01,fill="#CC6666")+
  geom_rect(aes(xmin=117,xmax=161,ymin=0,ymax=Inf),alpha=0.01,fill="#CC6666")+
  annotate("text", label = "sma 51 to 70", x = 60, y = .65, color = "red")+
  annotate("text", label = "sma 117 to 161", x = 135, y = .65, color = "red")

###################################
# Perform autocorrelation test
###################################
acf(df$xiv.close.diff)

# First order differencing
# Removes auto correlation so each data point is not dependant on the other 
# XIV diff
df$xiv.close.diff <- c(rep(NA, 1), diff(df$xiv_close, lag = 1, differences = 1, arithmetic = TRUE, na.pad = TRUE))
plot(df$Date,df$xiv.close.diff, type="l",main="XIV Close Differencing")
mean(df$xiv.close.diff, na.rm = TRUE)
var(df$xiv.close.diff, na.rm = TRUE)
# VXX diff
df$vxx.close.diff <- c(rep(NA, 1), diff(df$vxx_close, lag = 1, differences = 1, arithmetic = TRUE, na.pad = TRUE))
df$vxx.close.diff <- c(rep(NA, 1), diff(df$vxx_close, lag = 1, differences = 1, arithmetic = TRUE, na.pad = TRUE))
plot(df$Date,df$vxx.close.diff, type="l")
mean(df$vxx.close.diff, na.rm = TRUE)
var(df$vxx.close.diff, na.rm = TRUE)
# VXV Diff
df$vxv.close.diff <- c(rep(NA, 1), diff(df$vxv_cboe_close, lag = 1, differences = 1, arithmetic = TRUE, na.pad = TRUE))
plot(df$Date,df$vxv.close.diff, type="l")
mean(df$vxv.close.diff, na.rm = TRUE)
var(df$vxv.close.diff, na.rm = TRUE)
#VXMT Diff
df$vxmt.close.diff <- c(rep(NA, 1), diff(df$vxmt_cboe_close, lag = 1, differences = 1, arithmetic = TRUE, na.pad = TRUE))
plot(df$Date,df$vxmt.close.diff, type="l")
mean(df$vxmt.close.diff, na.rm = TRUE)
var(df$vxmt.close.diff, na.rm = TRUE)

# Auto correlation on differences
# Auto correlation is removed by differencing
df[is.na(df)] <- 0
acf(df$xiv.close.diff)

###################################################
# Block Bootstrap
###################################################
df.sample <- df
df <- df.sample
# Create new data frame with differenced time series (staionary)
require(np)
#block.boot.df <- subset(df, Date >= as.POSIXct("2008-01-07") ) # subset at start of latest data set (VXMT)
block.boot.df <- data.frame(xiv.close.diff = df$xiv.close.diff, vxx.close.diff = df$vxx.close.diff, vxv.close.diff = df$vxv.close.diff, vxmt.close.diff = df$vxmt.close.diff)
# Find block size with package np 
np.block.size.xiv <- b.star(block.boot.df$xiv.close.diff,Kn = NULL,mmax= NULL,Bmax = NULL,c = NULL,round = TRUE)
xiv.block.size <- np.block.size.xiv[2]
np.block.size.vxx <- b.star(block.boot.df$vxx.close.diff,Kn = NULL,mmax= NULL,Bmax = NULL,c = NULL,round = TRUE)
vxx.block.size <- np.block.size.vxx[2]
np.block.size.vxv <- b.star(block.boot.df$vxv.close.diff,Kn = NULL,mmax= NULL,Bmax = NULL,c = NULL,round = TRUE)
vxv.block.size <- np.block.size.vxv[2]
np.block.size.vxmt <- b.star(block.boot.df$vxmt.close.diff,Kn = NULL,mmax= NULL,Bmax = NULL,c = NULL,round = TRUE)
vxmt.block.size <- np.block.size.vxmt[2]
block.size <- c(xiv.block.size,vxx.block.size,vxv.block.size,vxmt.block.size)
block <- max(block.size)

# Set block number to begin subsetting per NROW
reps <- NROW(block.boot.df)/block # Set block number
reps <-(round(reps))
id <- rep(1:reps,each=block) # each = 5 corresponds to number of blocks to bootstrap by (5 in this case)
# Check lengths of data and ID
NROW(block.boot.df)
length(id)
# If ID is longer than df NROW
if(length(id)>NROW(block.boot.df)){
  id.diff <- length(id) - NROW(block.boot.df)
  length.id <- length(id)-id.diff
  id  <- id[1:length.id]
} else {
  nrow.diff <- NROW(block.boot.df) - length(id)
  max.id <- max(id)
  add.value <- max.id+1
  pad.na <- rep(add.value,nrow.diff)  # pad nrow diff
  id <- c(id,pad.na)  # join added to vector
}

NROW(block.boot.df)
length(id)
tail(block.boot.df)

# Join ID and block.df
block.boot.df <- data.frame(block.boot.df,id) # place back in data frame
#block.boot.df$id.final[is.na(block.boot.df$id.final)] <- 693 # all NA to 1
tail(block.boot.df)
# Id data
IDs <- unique(block.boot.df$id)
temp <- list()
# Function for bootstrap 1x data frame
# subsets data by id number
i=1
bootSTRAP = function(x){
  for (i in 1:length(IDs)){ 
    temp[i] <- list(block.boot.df[block.boot.df$id==IDs[i],])
  }
  out <- sample(temp,replace = TRUE)
  boot.df.output <- do.call(rbind, out)
}

# Loop for running it a 1000 times
runs <- 1:100
run.output <- list()
i=1
for (i in 1:length(runs)){   
  tryCatch({
    temp.1 <- bootSTRAP(runs[i])
    #cum_ret <- rbind.data.frame(cum_ret, temp)
    run.output[[i]] <- cbind(temp.1)
    ptm0 <- proc.time()
    Sys.sleep(0.1)  
    ptm1=proc.time() - ptm0
    time=as.numeric(ptm1[3])
    cat('\n','Iteration',i,'took', time, "seconds to complete")
  }, error = function(e) { print(paste("i =", i, "failed:")) })
}

# cumsum staionary differenced series
for (i in 1:length(run.output)){
  run.output[[i]]$cumsum.diff.xiv.diff <- cumsum(run.output[[i]]$xiv.close.diff)
  run.output[[i]]$cumsum.diff.vxx.diff <- abs(cumsum(run.output[[i]]$vxx.close.diff))
  run.output[[i]]$cumsum.diff.vxv.diff <- cumsum(run.output[[i]]$vxv.close.diff)
  run.output[[i]]$cumsum.diff.vxmt.diff <- cumsum(run.output[[i]]$vxmt.close.diff)
}

# Reverse VXX down trending series
for (i in 1:length(run.output)){
  run.output[[i]]$cumsum.diff.vxx.diff <- rev(run.output[[i]]$cumsum.diff.vxx.diff )
}
# Add index for merging 
for (i in 1:length(run.output)){
  run.output[[i]]$index <- seq(1:NROW(run.output[[i]]))
}

# Merge all dfs 
L <- run.output[[1]]
for (i in 2:length(run.output)) L <- merge(L,  run.output[[i]], by=c("index"))

# cbinds 
replace.s <- cbind.data.frame(L)
replace.s <- replace.s[,-1]
NCOL(replace.s)
# Subset data frames for loop 
xiv.df <- replace.s[ , grepl("cumsum.diff.xiv.diff*", names(replace.s), perl=TRUE)]
vxx.df <- replace.s[ , grepl("cumsum.diff.vxx.diff*", names(replace.s), perl=TRUE)]
vxv.df <- replace.s[ , grepl("cumsum.diff.vxv.diff*", names(replace.s), perl=TRUE)]
vxmt.df <- replace.s[ , grepl("cumsum.diff.vxmt.diff*", names(replace.s), perl=TRUE)]
nrow(vxmt.df)
# Add Date to df's
# Note depending on block sized used, some of the data might be of different lengths, subsetting is necessary to make same lengths
df.date <- data.frame(Date = df$Date)
nrow(df.date)
diff <- nrow(df.date) - nrow(xiv.df)
df.date <- df.date[1:nrow(xiv.df),]
# Add Date to subsetted df 
xiv.ensemble.df <- data.frame(Date = df.date, xiv.df)
vxx.ensemble.df <- data.frame(Date = df.date, vxx.df)
vxv.ensemble.df <- data.frame(Date = df.date, vxv.df)
vxmt.ensemble.df <- data.frame(Date = df.date, vxmt.df)
tail(xiv.ensemble.df)

# Melt data frames for plotting 
xiv.plot.df <- melt(xiv.ensemble.df,id.vars = "Date")
vxx.plot.df <- melt(vxx.ensemble.df,id.vars = "Date")
vxv.plot.df <- melt(vxv.ensemble.df,id.vars = "Date")
vxmt.plot.df <- melt(vxmt.ensemble.df,id.vars = "Date")

# cbind output to data frame
#master <- cbind.data.frame(run.output)
# rename column names 
#cnames <- rep(c("xiv.close.diff","vxx.close.diff","vxv.close.diff","vxmt.close.diff","id","cumsum.diff.xiv.diff","cumsum.diff.vxx.diff","cumsum.diff.vxv.diff","cumsum.diff.vxmt.diff"), times=length(run.output))
#cindexes <- rep(c(1:length(run.output)),   each=length(run.output[[1]]))
#col.names   <- paste(cnames, cindexes, sep="")
#colnames(master) <- col.names
# Subset data frames for loop 
#xiv.df <- master[ , grepl("cumsum.diff.xiv.diff*", names(master), perl=TRUE)]
#vxx.df <- master[ , grepl("cumsum.diff.vxx.diff*", names(master), perl=TRUE)]
#vxv.df <- master[ , grepl("cumsum.diff.vxv.diff*", names(master), perl=TRUE)]
#vxmt.df <- master[ , grepl("cumsum.diff.vxmt.diff*", names(master), perl=TRUE)]

# Add Date to subsetted df 
#xiv.df <- data.frame(Date = df$Date, xiv.df)
#vxx.df <- data.frame(Date = df$Date, vxx.df)
#vxv.df <- data.frame(Date = df$Date, vxv.df)
#vxmt.df <- data.frame(Date = df$Date, vxmt.df)

# Melt data frames for plotting 
#xiv.plot.df <- melt(xiv.df,id.vars = "Date")
#vxx.plot.df <- melt(vxx.df,id.vars = "Date")
#vxv.plot.df <- melt(vxv.df,id.vars = "Date")
#vxmt.plot.df <- melt(vxmt.df,id.vars = "Date")

# Plot XIV Resampled series
ggplot(data = xiv.plot.df, aes(x=Date,y=value))+
  geom_line(aes(group = variable))+
  theme_classic()+
  theme(legend.position = "none")+
  geom_line(data=df,aes(x=Date,y=xiv_close,colour="red"))+
  theme(plot.title = element_text(hjust=0.5),plot.subtitle =element_text(hjust=0.5))+
  ggtitle("Resampled Time Series - XIV", subtitle="100 Iterations")

  # Plot VXX Resampled series
ggplot(data = vxx.plot.df, aes(x=Date,y=value))+
  geom_line(aes(group = variable))+
  theme_classic()+
  theme(legend.position = "none")+
  geom_line(data=df,aes(x=Date,y=vxx_close,colour="red"))+
  theme(plot.title = element_text(hjust=0.5),plot.subtitle =element_text(hjust=0.5))+
  ggtitle("Resampled Time Series - VXX", subtitle="100 Iterations")

# Plot VXV Resampled series
ggplot(data = vxv.plot.df, aes(x=Date,y=value))+
  geom_line(aes(group = variable))+
  theme_classic()+
  theme(legend.position = "none")+
  geom_line(data=df,aes(x=Date,y=vxv_cboe_close,colour="red"))+
  theme(plot.title = element_text(hjust=0.5),plot.subtitle =element_text(hjust=0.5))+
  ggtitle("Resampled Time Series - VXV", subtitle="100 Iterations")

# Plot VXMT Resampled series
ggplot(data = vxmt.plot.df, aes(x=Date,y=value))+
  geom_line(aes(group = variable))+
  theme_classic()+
  theme(legend.position = "none")+
  geom_line(data=df,aes(x=Date,y=vxmt_cboe_close,colour="red"))+
  theme(plot.title = element_text(hjust=0.5),plot.subtitle =element_text(hjust=0.5))+
  ggtitle("Resampled Time Series - VXMT", subtitle="100 Iterations")