Consider the following MA(2) process

(6.21)

where ut is a zero mean white noise process with variance σ

2

.

(1) Calculate the mean and variance of yt

.

(2) Derive the autocorrelation function for this process (i.e., express the autocorrelations, τ1

, τ2

, … as functions of the parameters θ1 and θ2

).

(3) If θ1 = −0.5 and θ2 = 0.25, sketch the acf of yt

.