R Prep
#rm(list=ls())
#install.packages("quantmod")
#install.packages("psych")
library(quantmod)
## Loading required package: xts
## Loading required package: zoo
##
## Attaching package: 'zoo'
## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric
## Loading required package: TTR
## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoo
library(psych)
Data Acquisition
getSymbols(c("AAPL", "TSLA", "MSFT", "WMT"))
## [1] "AAPL" "TSLA" "MSFT" "WMT"
r.aapl <- dailyReturn(AAPL[,6])
r.tsla <- dailyReturn(TSLA[,6])
r.msft <- dailyReturn(MSFT[,6])
r.wmt <- dailyReturn(WMT[,6])
r.all <- merge(r.aapl, r.tsla)
r.all <- merge(r.all, r.msft)
r.all <- merge(r.all, r.wmt)
r.all <- na.omit(r.all)
colnames(r.all) <- c("AAPL", "TSLA", "MSFT", "WMT")
Exploratory Data Analysis
TT <- dim(r.all)[1]
CVD <- 2395
describe(r.all)
## vars n mean sd median trimmed mad min max range skew kurtosis se
## AAPL 1 3517 0 0.02 0 0 0.01 -0.13 0.12 0.25 -0.05 5.34 0
## TSLA 2 3517 0 0.04 0 0 0.03 -0.21 0.24 0.45 0.33 4.91 0
## MSFT 3 3517 0 0.02 0 0 0.01 -0.15 0.14 0.29 0.05 7.79 0
## WMT 4 3517 0 0.01 0 0 0.01 -0.11 0.12 0.23 0.09 16.46 0
describe(r.all[1:CVD-1,])
## vars n mean sd median trimmed mad min max range skew kurtosis se
## AAPL 1 2394 0 0.02 0 0 0.01 -0.12 0.09 0.21 -0.22 4.62 0
## TSLA 2 2394 0 0.03 0 0 0.02 -0.19 0.24 0.44 0.51 6.29 0
## MSFT 3 2394 0 0.01 0 0 0.01 -0.11 0.10 0.22 0.08 6.57 0
## WMT 4 2394 0 0.01 0 0 0.01 -0.10 0.11 0.21 0.16 16.11 0
describe(r.all[CVD:TT,])
## vars n mean sd median trimmed mad min max range skew kurtosis se
## AAPL 1 1123 0 0.02 0 0 0.02 -0.13 0.12 0.25 0.12 4.99 0
## TSLA 2 1123 0 0.04 0 0 0.03 -0.21 0.20 0.41 0.13 2.97 0
## MSFT 3 1123 0 0.02 0 0 0.01 -0.15 0.14 0.29 0.01 6.78 0
## WMT 4 1123 0 0.01 0 0 0.01 -0.11 0.12 0.23 0.02 14.21 0
cor(r.all)
## AAPL TSLA MSFT WMT
## AAPL 1.0000000 0.3564952 0.5883106 0.2907337
## TSLA 0.3564952 1.0000000 0.3455202 0.1396734
## MSFT 0.5883106 0.3455202 1.0000000 0.3414911
## WMT 0.2907337 0.1396734 0.3414911 1.0000000
c1 <- cor(r.all[1:CVD-1,])
c2 <- cor(r.all[CVD:TT,])
Rolling Correlation Matrix Plots
# Assuming df is your data frame with N time series
# N is the number of time series, T is the length of each time series
# Parameters
H <- 100 # Number of days for rolling correlation
T <- dim(r.all)[1]
num_series <- ncol(r.all) # Number of time series
# Calculate rolling correlations
correlations <- matrix(NA, nrow = T, ncol = choose(num_series, 2))
col_counter <- 1
for (i in 1:(num_series - 1)) {
for (j in (i + 1):num_series) {
ts1 <- r.all[, i]
ts2 <- r.all[, j]
rolling_cor <- rollapplyr(cbind(ts1, ts2), width = H, FUN = function(x) cor(x[,1], x[,2]), by.column = FALSE, align = "right")
correlations[, col_counter] <- rolling_cor
col_counter <- col_counter + 1
}
}
# Plotting
plot_titles <- combn(colnames(r.all), 2, paste, collapse = " vs ")
plot_colors <- rainbow(choose(num_series, 2))
par(mfrow = c(3, 2)) # Adjust rows and columns as needed for your number of time series
for (k in 1:ncol(correlations)) {
plot(correlations[, k], type = 'l', col = plot_colors[k], xlab = 'Time', ylab = 'Correlation', main = paste("Rolling correlation:", plot_titles[k]))
legend("bottomright", legend = plot_titles[k], col = plot_colors[k], lty = 1)
}
# Reset plotting parameters
par(mfrow = c(1, 1)) # Reset to default plotting layout
Multivariate GARCH (Assume Independent Errors)
Constant Conditional Correlation Modelling
Dynamic Conditional Correlation Modelling
Applications