CROSS‐VALIDATORY CHOICE OF A SPECTRUM ESTIMATE AND ITS CONNECTIONS WITH AIC

Clifford Hurvich and Kaizô I. Beltrato

Journal of Time Series Analysis, 1990, vol. 11, issue 2, 121-137

Abstract: Abstract. This paper concerns the use of a generalized version of the cross‐validated log likelihood criterion (CVLL) for selecting a spectrum estimator from an arbitrary class of candidate estimators. It is shown that CVLL is asymptotically equivalent to the expected Kullback‐Leibler information of the candidate estimator. The Akaike information criterion (AIC) is also asymptotically equivalent to Kullback‐Leibler information, but the applicability of AIC is limited to parametric estimators. Thus CVLL can be viewed as a cross‐validatory generalization of AIC. Monte Carlo results show that CVLL is able to provide an effective choice from a class of candidates which simultaneously includes autoregressive and classical smoothed periodogram estimators. To save computation time, CVLL can be evaluated only for the classical estimators while the computationally more efficient AIC is evaluated for the parametric estimators. The criterion values are all directly comparable in this case. As an additional computation‐saving device, a non‐cross‐validatory version of CVLL for classical estimators is proposed and studied.

Date: 1990
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