Question

1) Consider the MA(2) process, where all the {et} values are independent white noise with variance  2 e:

Yt = et – 0.5 et – 1 – 0.3 et – 2

a) Find cov(Yt, Yt) = var(Yt).

b) Find cov(Yt, Yt – 1) and, from this, find the lag-1 autocorrelation corr(Yt, Yt – 1).

c) Find cov(Yt, Yt – 2) and, from this, find the lag-2 autocorrelation corr(Yt, Yt – 2).

d) Argue that cov(Yt, Yt – k) = 0 for all k ≥ 3.

3) Consider the AR(1) process: Yt = Yt – 1 + et

Show that if || = 1, the process cannot be stationary. [Hint: Take variances of both sides.]

Answer 1