Multistep Forecast Averaging with Stochastic and Deterministic Trends

Mohitosh Kejriwal (), Linh Nguyen () and Xuewen Yu
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Mohitosh Kejriwal: Daniels School of Business, Purdue University, 403 Mitch Daniels Blvd., West Lafayette, IN 47907, USA
Xuewen Yu: Department of Applied Economics, School of Management, Fudan University, 670 Guoshun Road, Shanghai 200433, China

Econometrics, 2023, vol. 11, issue 4, 1-44

Abstract: 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. 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 optimal, infeasible combination forecasts. Simulation experiments are used to demonstrate the finite sample efficacy of the proposed procedure relative to Mallows/Cross-Validation weighting that target the AMSE as well as underscore the importance of accounting for both persistence and lag order uncertainty. An application to forecasting US macroeconomic time series confirms the simulation findings and illustrates the benefits of employing the APE criterion for real as well as nominal variables at both short and long horizons. A practical implication of our analysis is that the degree of persistence can play an important role in the choice of combination weights.

Keywords: averaging; combination; cross-validation; Mallows; unit root; accumulated prediction errors (search for similar items in EconPapers)
JEL-codes: B23 C C00 C01 C1 C2 C3 C4 C5 C8 (search for similar items in EconPapers)
Date: 2023
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