Let Z_t, t = ..., -2, -1, 0, 1, 2, ..., be a strictly stationary white noise process and let a, b, c be constants. Which of the following processes are stationary? For each stationary process specify whether it is strongly or weakly stationary:
a). X_t = a + b Z_t + c Z_(t-1)
b). X_t = a + b Z_0
c). X_t = cos(ct) Z_1 + sin(ct) Z_2
d). X_t = cos(ct) Z_0
e). X_t = cos(ct) Z_t + sin(ct) Z_(t-1)
f). X_t = Z_t Z_(t-1)
I understand that in order to show that a process is stationary (and hence weakly stationary) I need to show that the mean is a constant and that the autocovariance function does not depend on t. However, how can I show that a stationary process is strongly stationary? I think that it is necessary to show that it is Gaussian, but I do not know how it is possible to show that a stationary process is Gaussian in a simple yet acceptable way. Please pick any process from the list above and show me how it is possible to prove that it is strongly stationary. I would appreciate your help and hints!