Accumulative prediction error and the selection of time series models

This article reviews the rationale for using accumulative one-step-ahead prediction error (APE) as a data-driven method for model selection. Theoretically, APE is closely related to Bayesian model selection and the method of minimum description length (MDL). The sole requirement for using APE is that the models under consideration are capable of generating a prediction for the next, unseen data point. This means that APE may be readily applied to selection problems involving very complex models. APE automatically takes the functional form of parameters into account, and the ‘plug-in’ version of APE does not require the specification of priors. APE is particularly easy to compute for data that have a natural ordering, such as time series. Here, we explore the possibility of using APE to discriminate the short-range ARMA(1,1) model from the long-range ARFIMAð0; d ; 0Þ model. We also illustrate how APE may be used for model meta-selection, allowing one to choose between different model selection methods. r 2006 Elsevier Inc. All rights reserved.