Let {Zt} be a sequence of independent normal random variables, each with mean 0 and variance σ2, and let a, b, and c be constants. Which, if any, of the following processes are stationary? For each stationary process specify the mean and autocovariance function.
a. Xt = a + bZt + cZt−2
b. Xt = Z1 cos(ct) + Z2 sin(ct)
c. Xt = Zt cos(ct) + Zt−1 sin(ct)
d. Xt = a + bZ0
e. Xt = Z0 cos(ct)
f. Xt = ZtZt−1