Suppose we have the linear process xt generated by xt = wt wt1, t = 0, 1, 2, . . ., where {wt} is

Suppose we have the linear process xt generated by xt = wt − θwt−1, t = 0, 1, 2, . . ., where {wt} is independent and identically distributed with characteristic function φw(·), and θ is a fixed constant. [Replace “characteristic function” with “moment generating function” if instructed to do so.]

(a) Express the joint characteristic function of x1, x2, . . . , xn, say,

φx1,x2,...,xn (λ1, λ2, . . . , λn), in terms of φw(·).

(b) Deduce from

(a) that xt is strictly stationary.