On selection of the order of the spectral density model for a stationary process

Let {X(t)} be a stationary process with mean zero and spectral density g(x). We shall use a kth order parametric spectral model f _τ(k) (x) for this process. Without Gaussianity we can obtain an estiamte of τ(k), say ĝt(k), by maximizing the quasi-Gaussian likelihood of this model. We can then construct the best linear predictor of X(t), which is computed on the basis of the estimated spectral density f _ĝt(k) (x). An asymptotic lower bound of the mean square error of the estimated predictor is obtained. The bound is attained if k is selected by Akaike's information criterion.