OPTIMAL MULTISTEP VAR FORECAST AVERAGING

This article proposes frequentist multiple-equation least-squares averaging approaches for multistep forecasting with vector autoregressive (VAR) models. The proposed VAR forecast averaging methods are based on the multivariate Mallows model averaging (MMMA) and multivariate leave-h-out cross-valida...

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Bibliographic Details
Published in:Econometric theory 2020-12, Vol.36 (6), p.1099-1126
Main Authors: Liao, Jen-Che, Tsay, Wen-Jen
Format: Article
Language:English
Subjects:
Econometrics
Economic theory
Forecasting
Multivariate analysis
Simulation
Validity
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Summary:This article proposes frequentist multiple-equation least-squares averaging approaches for multistep forecasting with vector autoregressive (VAR) models. The proposed VAR forecast averaging methods are based on the multivariate Mallows model averaging (MMMA) and multivariate leave-h-out cross-validation averaging (MCVAh) criteria (with h denoting the forecast horizon), which are valid for iterative and direct multistep forecast averaging, respectively. Under the framework of stationary VAR processes of infinite order, we provide theoretical justifications by establishing asymptotic unbiasedness and asymptotic optimality of the proposed forecast averaging approaches. Specifically, MMMA exhibits asymptotic optimality for one-step-ahead forecast averaging, whereas for direct multistep forecast averaging, the asymptotically optimal combination weights are determined separately for each forecast horizon based on the MCVAh procedure. To present our methodology, we investigate the finite-sample behavior of the proposed averaging procedures under model misspecification via simulation experiments.
ISSN:0266-4666
1469-4360
DOI:10.1017/S0266466619000434