Auto-Regression (2) in R

Question

I need help generating an AR(2) model in R and I am new to the software.

I have the following AR(2) process:

y[t] = phi_1 * y[t-1] + phi_2 * y[t-2] + e[t] where e[t] ~ N(0,2)

How can I generate a series of y[t]?

Thanks for the help, much appreciated!

Answer 1

You could do:

set.seed(123)
n <- 200
phi_1 <- 0.9
phi_2 <- 0.7
e <- rnorm(n, 0, 2)
y <- vector("numeric", n)
y[1:2] <- c(0, 1)
for (t in 3:n) {
  y[t] <- phi_1 * y[t - 1] + phi_2 * y[t - 2] + e[t]
}

plot(seq(n), y, type = "l")