Stationary Models and the Autocorrelation Function

Jeg skal vise følgende: Let xt = a+bt, a, b ≠ 0. Show that for each h ≥ 1, ρˆ(h) → 1 as n → ∞, where ρˆ(·) is the sample autocorrelation function: ρˆ(h)??γˆ(h), −n<h<n. γˆ ( 0 ). 

Håber, at nogle kan hjælpe. 

Anden tekst i min lærebog om autocorrelation function:

Remark 3. For h ≥ 0, γˆ (h) is approximately equal to the sample covariance of the n − h pairs of observations (x1, x1+h), (x2, x2+h), . . . , (xn−h, xn). The difference arises from use of the divisor n instead of n − h and the subtraction of the overall mean, x ¯, from each factor of the summands. Use of the divisor n ensures that the sample covariance matrix ??ˆ n :?? [γˆ (i − j )] ni, j ??1 is nonnegative definite.

Remark 4. Like the sample covariance matrix defined in Remark 3, the sample correlation matrix Rˆ n :?? [ρˆ (i − j )] ni, j 1 is nonnegative definite. Each of its diagonal elements is equal to 1, since ρˆ (0) ?? 1.