Consider the two series xt = wt yt = wt wt1 + ut, where wt and ut are independent white noise series with variances

Consider the two series xt = wt yt = wt − θwt−1 + ut, where wt and ut are independent white noise series with variances σ2 w and σ2 u, respectively, and θ is an unspecified constant.

(a) Express the ACF, ρy(h), for h = 0, ±1, ±2, . . . of the series yt as a function of σ2 w, σ2 u, and θ.

(b) Determine the CCF, ρxy(h) relating xt and yt.

(c) Show that xt and yt are jointly stationary.