Misspecification-Robust Shrinkage and Selection for VAR Forecasts and IRFs

TL;DR

This paper develops a robust method for selecting hyperparameters in Bayesian VAR models that accounts for potential model misspecification, improving forecast and impulse response estimation accuracy.

Contribution

It introduces asymptotically unbiased risk estimates for hyperparameter selection in misspecified VARs, enhancing model robustness and predictive performance.

Findings

Improved forecast accuracy under misspecification.

Effective joint selection of hyperparameters and lag length.

Better impulse response estimates compared to traditional methods.

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.