Forecasting Time Series

Long Memory

Preamble

library("forecast")
library("fracdiff") # for fracdiff, fdGPH
library("tseries")  # for garch

Data Sets

# US CPI, Jan 1947 - Jan 2017, Monthly
cpi.data <- read.csv("http://ptrckprry.com/course/forecasting/data/cpi.csv")
cpi <- cpi.data$cpi
log.cpi <- log(cpi)

# US Unemployment Rate, Jan 1948 - Jan 2017, Montly, Seasonally adjusted
unemp.data <- read.csv("http://ptrckprry.com/course/forecasting/data/unemployment.csv")
unemp <- unemp.data$unemployment
log.unemp <- log(unemp)

# Russell 2000 Index, Sep 10, 1987 - Feb 10, 2017, Daily
russell.data <- read.csv("http://ptrckprry.com/course/forecasting/data/russell.csv")
russell <- russell.data$russell
log.russell <- log(russell)

# VIX Volatility Index, Jan 2, 2004 - Apr 20, 2017, Daily
vix.data <- read.csv("http://ptrckprry.com/course/forecasting/data/vix.csv")
vix <- vix.data$vix.adjclose
log.vix <- log(vix)
logrange.vix <- log(vix.data$vix.hi) - log(vix.data$vix.lo)

# SNP500 Daily Realized Volatility,  Feb 1, 1983 - June 29, 2000
snpvol.data <- read.csv("http://ptrckprry.com/course/forecasting/data/SNPVol.csv")
snpvol <- snpvol.data$SNPVol
log.snpvol <- log(snpvol)

make.plots <- function(x, main="", lag.max=100)
{
    ylab <- deparse(substitute(x))

    fit <- fdGPH(x)

    par(mfrow=c(1,2))
    plot(x, type="l", xlab="time", ylab=ylab, col=2, main=main)
    mtext(paste0("d = ", round(fit$d, 2), ", SE = ", round(fit$sd.reg, 2)))
    Acf(x, lag.max=lag.max, main=paste0("Series: ", ylab))
}

make.plots(log.russell, "Log(Russell 2000 Index), Sep 10, 1987 - Feb 10, 2017")

make.plots(log.cpi, "Log(US CPI), Jan 1947 - Jan 2017")