Prediction focussed model selection for autoregressive models bmodels

In order to make predictions of future values of a time series, one needs to specify a forecasting model. A popular choice is an autoregressive time series model, where the order of the model is chosen by an information criterion. We propose an extension of the Focussed Information Criterion (FIC) for model-order selection with focus on a high predictive accuracy (i.e. the mean squared forecast error is low). We obtain theoretical results and illustrate in a simulation study that this FIC can outperform classical order selection criteria in the setting with one series to predict and a different series for parameter estimation. We also demonstrate , via a simulation study and some real data examples, that in the practical setting of only one available time series, the performance of the FIC is comparable to the performance of other information criteria.