Consider two time series

Xt = Wt Wt1 , Yt = .5(Wt + Wt1) ,

formed from white noise Wt with variance 2 = 1.

• Are Xt and Yt jointly stationary? Recall the cross-covariance function must depend only on the lag h and cannot depend on time.
• Compute the power spectrum fY () and fX(), and comment on the difference between the two results.