FEASIBLE CROSS-VALIDATORY MODEL SELECTION FOR GENERAL STATIONARY-PROCESSES

Cross-validation is a method used to estimate the expected prediction error of a model. Such estimates may be of interest in themselves, but their use for model selection is more common. Unfortunately, cross-va lidation is viewed as being computationally expensive in many situatio ns. In this paper it is shown that the h-block cross-validation functi on for least-squares based estimators can be expressed in a form which can enormously impact on the amount of calculation required. The stan dard approach is of O(T-2) where T denotes the sample size, while the proposed approach is of O(T) and yields identical numerical results. T he proposed approach has widespread potential application ranging from the estimation of expected prediction error to least squares-based mo del specification to the selection of the series order for non-paramet ric series estimation. The technique is valid for general stationary o bservations. Simulation results and applications are considered. (C) 1 997 by John Wiley & Sons, Ltd.