Multistep Forecast Averaging with Stochastic and Deterministic Trends

This paper presents a new approach to constructing multistep combination forecasts in a nonstationary framework with stochastic and deterministic trends. Existing forecast combination approaches in the stationary setup typically target the in-sample asymptotic mean squared error (AMSE) relying on its approximate equivalence with the asymptotic forecast risk (AFR). Such equivalence, however, breaks down in a nonstationary setup. To address this issue, this paper develops combination forecasts based on minimizing an Accumulated Prediction Errors (APE) criterion that directly targets the AFR and remains valid whether the time series is stationary or not. We show that the performance of APE-weighted forecasts is close to that of the infeasible combination forecasts which assume that the optimal (i.e., AFR minimizing) weights are known. Monte Carlo experiments are used to (i) demonstrate the finite sample efficacy of the proposed procedure relative to Mallows/Cross-Validation weighting that target the AMSE; (ii) underscore the importance of accounting for uncertainty about the stochastic trend and/or the lag order. When applied to forecasting US macroeconomic time series, we find strong evidence in favor of a version of the advocated approach that simultaneously addresses stochastic trend and lag order uncertainty