Efficient Multistep Forecast Procedures for Multivariate Time Series

Upon the evidence that infinite‐order vector autoregression setting is more realistic in time series models, we propose new model selection procedures for producing efficient multistep forecasts. They consist of order selection criteria involving the sample analog of the asymptotic approximation of the h‐step‐ahead forecast mean squared error matrix, where h is the forecast horizon. These criteria are minimized over a truncation order n_T under the assumption that an infinite‐order vector autoregression can be approximated, under suitable conditions, with a sequence of truncated models, where n_T is increasing with sample size. Using finite‐order vector autoregressive models with various persistent levels and realistic sample sizes, Monte Carlo simulations show that, overall, our criteria outperform conventional competitors. Specifically, they tend to yield better small‐sample distribution of the lag‐order estimates around the true value, while estimating it with relatively satisfactory probabilities. They also produce more efficient multistep (and even stepwise) forecasts since they yield the lowest h‐step‐ahead forecast mean squared errors for the individual components of the holding pseudo‐data to forecast. Thus estimating the actual autoregressive order as well as the best forecasting model can be achieved with the same selection procedure. Such results stand in sharp contrast to the belief that parsimony is a virtue in itself, and state that the relative accuracy of strongly consistent criteria such as the Schwarz information criterion, as claimed in the literature, is overstated. Our criteria are new tools extending those previously existing in the literature and hence can suitably be used for various practical situations when necessary. Copyright © 2015 John Wiley & Sons, Ltd.