Consider the series xt = sin(2U t), t = 1, 2, . . ., where U has a uniform distribution on the interval (0, 1).

Consider the series xt = sin(2πU t), t = 1, 2, . . ., where U has a uniform distribution on the interval (0, 1).

(a) Prove xt is weakly stationary.

(b) Prove xt is not strictly stationary. [Hint: consider the joint bivariate cdf

(1.18) at the points t = 1, s = 2 with h = 1, and find values of ct, cs where strict stationarity does not hold.]