Suppose that ̵1, ̵2, ... is a i.i.d. Gaussian white noise process with mean 0 and variance 1, and a_t and u_t are stationary processes such that
a_t = ̱_t̵_t, where ̱^2_t = ̱_0 + ̱_1a^2_{t-1},
and
r_t = ̱ + ̱r_{t-1} + a_t.
(a) What type of process is a_t?
(b) What type of process is r_t?
(c) What type of process is a^2_t?
(d) Is the (unconditional) distribution of a_t Gaussian?
(e) (4 pts) Suppose ̱_0 = 2, ̱_1 = 0.3. Find the value of
Cov(a_{t-1}, a^2_{t+1}).