Use R to simulate and plot some data from simple ARIMA models. a. Use the following R code to generate data from an AR(1) model with ϕ 1 = 0.6 and σ 2 = 1. The process starts with y 1 = 0. 1 = 0.6 and...

Use R to simulate and plot some data from simple ARIMA models. a. Use the following R code to generate data from an AR(1) model with ϕ₁
= 0.6 and σ
²
= 1. The process starts with y₁
= 0.

₁
= 0.6 and σ²
= 1. σ 2 = 1 The process starts with y₁
= 0.

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(1) model with θ₁
= 0.6 and σ²
= 1.

d. Produce a time plot for the series. How does the plot change as you change θ₁
?

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

₁
= 0.6, θ₁
= 0.6 and σ²
= 1.

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

₁
= −0.8,

₂
= 0.3 and σ²
= 1. (Note that these parameters will give a non-stationary series.) g. Graph the latter two series and compare them.