Suppose that ̵1, ̵2, ... is a i.i.d. Gaussian white noise process with mean 0 and variance 1, and at and ut are stationary processes such that
at = ̵t̵t, where ̵t^2 = ̱0 + ̱1at-1^2,
and
rt = ̱ + ̱rt-1 + at.
(a) What type of process is at?
(b) What type of process is rt?
(c) What type of process is at^2?
(d) Is the (unconditional) distribution of at Gaussian?
(e) Suppose ̱0 = 2, ̱1 = 0.3. Find the value of Cov(at-1, at+1^2).