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-validation is viewed as being computationally expensive in many situations. In this paper it is shown that the h-block cross-validation function for least-squares based estimators can be expressed in a form which enormously impact on the amount of calculation required. The standard approach is of O(T[superscript 2]) where T denotes the sample size, while the proposed approach is of O(T) and yields identical numerical results The proposed approach has widespread potential application ranging from the estimation of expected prediction error to least squares-based model specification to the selection of the series order for non-parametric series estimation. The technique is valid for general stationary observations. Simulation results and applications are considered.