1. An ARCH(m) example
S&P/TSX Capped Composite 4/26/2010 to 4/26/2013
Financials, energy, industries, materials
TSX listed stocks banks

2. rate log (ratio)
volatility
smo(y) lowess(y)
lowess(|y – smo(y)|
library(tseries) junk0<-scan("SPTXT.txt") p<-rev(junk0) y<-diff(log(p)) ny<-length(y) par(mfrow=c(2,1)) xaxis<-1:ny y<-ts(y,start=1,end=ny) plot(y,main="SPTXT 2010 to 2013",xlab="trading day",ylab="return") lunk<-lowess(xaxis,abs(y-mean(y)),f=.001) yabs<-ts(lunk$y,start=1,end=ny) plot(yabs,main="Smoothed abs(deviation)",xlab="trading day",ylab="")

4. acf, pacf
ARCH?
par(mfrow=c(2,1)) acf(y,main="ACF SPTXT returns",xlab="lag (days)") yy<-y-mean(y);yy<-yy^2 pacf(yy,main="PACF SPTXT returns^2",xlab="lag (days)")

7. Fitted conditional variance useful in forecasting plugin estimate of
library(tseries) P<-5 PP<-P+1 junk1<-garch(y,order=c(0,P),grad="analytic") summary(junk1) par(mfrow=c(2,1)) yvol<-ts(junk1$fit[,1],start=1,end=ny) plot(yvol,type="l",ylim=c(0,max(abs(y))),main=paste("Estimated volatility - ARCH",P),xlab="trading day",ylab="volatility")
Standardized residuals
yres<-ts(junk1$res,start=1,end=ny)

8. one step ahead cdl se
standardized

9. Standardized residuals
yres<-ts(junk1$res,start=1,end=ny) plot(yres,main="Residuals of ARCH(5)",type="l",xlab="trading day",ylab="return")

13. plot(junk1$coef[2:PP],type="l",las=1,main="Coefficients",ylim=c(0,max(junk1$coef[2:PP])),ylab="coef")
ave<-mean(junk1$coef[2:PP])
abline(h=ave)
junk1$asy<-sqrt(diag(junk1$vcov))
lines(ave+junk1$asy,lty=3)
lines(ave-junk1$asy,lty=3)

15. GARCH(m,r)