Cross Validation of Prediction Models for Seasonal Time Series by Parametric Bootstrapping

Out-of-sample prediction for the final portion of a sample is a popular tool for model selection in model-based forecasting. We suggest to add a simulation step to this exercise, where pseudo-samples are generated (parametrically bootstrapped), conditional on the observed data and on any of the candidate models, and these pseudo-samples are predicted using any of the candidate models. The technique is demonstrated by an artificial univariate time-series specification that highlights the main features, and also by a real-life multivariate application to agricultural price data. In the exemplary data set on quarterly European barley prices, strong seasonal variation is obvious and represents a crucial feature in constructing good models for short-run prediction. Following some preliminary statistical testing, we restrict focus to vector autoregressions with deterministic seasonal cycles. We also consider a restricted specification that imposes a common seasonal cycle on all countries. While the restriction is formally rejected by hypothesis tests, it assists in reducing prediction errors. The parametric bootstrap experiments show that this improvement by using an invalid restriction is systematic.