Misspecification-Robust Shrinkage and Selection for VAR Forecasts and IRFs

Oriol Gonzalez-Casasus () and Frank Schorfheide ()
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Oriol Gonzalez-Casasus: University of Pennsylvania
Frank Schorfheide: University of Pennsylvania CEPR, PIER, NBER

PIER Working Paper Archive from Penn Institute for Economic Research, Department of Economics, University of Pennsylvania

Abstract: VARs are often estimated with Bayesian techniques to cope with model dimensionality. The posterior means define a class of shrinkage estimators, indexed by hyperparameters that determine the relative weight on maximum likelihood estimates and prior means. In a Bayesian setting, it is natural to choose these hyperparameters by maximizing the marginal data density. However, this is undesirable if the VAR is misspecified. In this paper, we derive asymptotically unbiased estimates of the multi-step forecasting risk and the impulse response estimation risk to determine hyperparameters in settings where the VAR is (potentially) misspecified. The proposed criteria can be used to jointly select the optimal shrinkage hyperparameter, VAR lag length, and to choose among different types of multi-step-ahead predictors; or among IRF estimates based on VARs and local projections. The selection approach is illustrated in a Monte Carlo study and an empirical application.

Keywords: Forecasting; Hyperparameter Selection; Local Projections; Misspecification; Multi-step Estimation; Shrinkage Estimators; Vector Autoregressions (search for similar items in EconPapers)
JEL-codes: C11 C32 C52 C53 (search for similar items in EconPapers)
Pages: 70 pages
Date: 2025-02-05
New Economics Papers: this item is included in nep-ecm and nep-ets
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