Model averaging for time–varying vector autoregressions
本文提出一种时变模型平均方法，用于提高存在结构变化的多元时间序列预测精度，通过惩罚局部准则选取最优时变权重，并从理论上证明了最优性与一致性，对研究预测建模的学者有参考价值。
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 regular conditions can be established. Furthermore, the proposed approach encompasses special cases including time-varying VAR models with exogenous predictors, as well as time-varying FAVAR models. Simulations and an empirical application illustrate the proposed TVMA method outperforms some commonly used model averaging and selection methods in the presence of structural changes.