Use Property 6.6 to complete the following exercises. (a) Write a univariate AR(1) model, yt = yt1 + vt, in state-space form. Verify your answer

Use Property 6.6 to complete the following exercises.

(a) Write a univariate AR(1) model, yt = φyt−1 + vt, in state-space form.

Verify your answer is indeed an AR(1).

(b) Repeat

(a) for an MA(1) model, yt = vt + θvt−1.

(c) Write an IMA(1,1) model, yt = yt−1 + vt + θvt−1, in state-space form.