Model Averaging for Time–varying Vector Autoregressions

This paper proposes a novel time-varying model averaging (TVMA) approach to enhancing forecast accuracy for multivariate time series subject to structural changes. The TVMA method averages predictions from a set of time-varying vector autoregressive models using optimal time-varying combination weights selected by minimizing a penalized local criterion. This allows the relative importance of different models to adaptively evolve over time in response to structural shifts. We establish an asymptotic optimality for the proposed TVMA approach in achieving the lowest possible quadratic forecast errors. The convergence rate of the selected time-varying weights to the optimal weights minimizing expected quadratic errors is derived. Moreover, we show that when one or more correctly specified models exist, our method consistently assigns full weight to them, and an asymptotic normality for the TVMA estimators under some regularity conditions can be established. Furthermore, the proposed approach encompasses special cases including time-varying VAR models with exogenous predictors, as well as time-varying factor augmented VAR (FAVAR) models. Simulations and empirical applications illustrate the proposed TVMA method outperforms some commonly used model averaging and selection methods in the presence of structural changes.