State-Varying Model Averaging Prediction*

This paper proposes a novel state-varying model averaging predictor for varying-coefficient models that accommodates parameter uncertainty and model misspecification. We develop a leave-h-out state-dependent forward-validation criterion to select state-varying combination weights. It is shown that the proposed averaging prediction is asymptotically optimal in the sense of achieving the lowest possible out-of-sample prediction risk in a class of model averaging estimators. Besides, when the set of candidate models includes correctly specified models, the proposed approach asymptotically assigns all the weights to these models. Furthermore, the proposed approach is flexible and encompasses special cases including ultra-high dimensional models as well as state-varying factor-augmented regression models. Simulation studies and empirical applications highlight the merits of the proposed averaging prediction relative to other existing model averaging and model selection methods.