8.5 Use R to simulate and plot some data from simple ARIMA models.

(a) Use the following R code to generate data from an AR(l) model with 1 = 0.6 and a 2

= 1. The process starts with y1 = 0.

-------- R code y <- ts(numeric(100))

e <- rnorm(100)

for(i in 2:100)

y[i] <- 0.6*y[i-1] + e[i]

(b) Produce a time plot for the series. How does the plot change as you change 1?

(c) Write your own code to generate data from an MA(l) model with 01 = 0.6 and a 2

= 1.

(d) Produce a time plot for the series. How does the plot change as you change 01?

(e) Generate data from an ARMA(l,1) model with

1 = 0.6 and 01 = 0.6 and a 2

= 1.

(f) Generate data from an AR(2) model with

1 = -0.8 and 2 = 0.3 and a 2

= 1. (Note that these parameters will give a non-stationary series.)

(g) Graph the latter two series and compare them.