Let X+ = a + bt, t = 1,...,n, where a and b are two constants and b + 0 (X4 is a pure deterministic time series).

(a) Compute Cou(X+, Xt+k) for k > 0. Can you conclude that Xt is weakly sta- tionary?

(b) Show that the sample autocovariance wk at lag k> 0 is 62 n-k fr E (e-n!!) t + 2 buk(n k) 2n n

(c) Show that for each fixed k > 1, the sample autocorrelation at lag k converges to 1, i.e., Pk +1 as n +0. Does this conflict any result in (a)?