Question

I also need an R code for this problem

Problem 3 Explore the correlation structure of the following models, by simulating their realizations of 500 observations and computing ACFs and PACFs. Comment on how these cut off.

Answer 1

Run the code below in R:

rm(list = ls())
set.seed(1001)
nn <- 500
z <- rnorm(nn+2)
x <- numeric(nn+2)
for(i in 3:(nn+2)){
x[i] <- 0.7*x[i-1] - 0.5*x[i-2] + z[i]
}
x <- x[-c(1:2)]
acf(x)
pacf(x)

z <- rnorm(nn+2)
x <- numeric(nn+2)
for(i in 3:(nn+2)){
x[i] <- -0.3*z[i-2] + 0.7*x[i-1] + z[i]
}
x <- x[-c(1:2)]
acf(x)
pacf(x)