library(tseries)
library(quantmod)
symbols = c("SP500")
getSymbols(symbols, src = "FRED")
head(SP500)
r = diff(log(SP500[,1]))

rlag1 = c(NA, r[1:(length(r)-1)])
summary(lm(r~rlag1))$coef

d = data.frame(r,rlag1)
d = na.omit(d)
d$tr = 1:nrow(d)
names(d)[1] = "r"
j = 1
t = NULL
while (j<=24) {
	subd = subset(d, tr>=(j-1)*100+1 & tr<=(j-1)*100+100)
	m = lm(r~rlag1,data=subd)
	t = c(t,summary(m)$coef[2,3])
	j = j + 1
}


plot(t,type="o",xlab="window",ylab="t value of rho",main="Rolling Windows AR(1)")
abline(h=-1.96,lty=2)
abline(h=1.96,lty=2)