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

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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.

Original languageEnglish
Pages (from-to)401-419
Number of pages19
JournalAnnals of the Institute of Statistical Mathematics
Issue number1
Publication statusPublished - 1980 Dec 1


ASJC Scopus subject areas

  • Statistics and Probability

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