State-Varying Model Averaging Prediction*

This paper proposes a novel state-varying model averaging prediction for varyingcoefficient models that accounts for 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. This complements existing model averaging methods that primarily focus on minimizing the in-sample squared error loss. Besides, when the set of candidate models includes correctly specified models, the proposed approach asymptotically assigns full weight 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.