Optimal model averaging based on leave‐h‐out forward‐validation for threshold autoregressive models

Abstract

The threshold autoregressive (TAR) model has received considerable attention in nonlinear time series literature. To weaken the impacts coming from model uncertainty and to improve the prediction accuracy, this paper develops a leave‐ ‐out forward‐validation model averaging (LhoFVMA) method to average predictions from the TAR model. We establish our method's asymptotic optimality in the sense of achieving the lowest possible squared prediction risk. Simulation experiments show that our method is generally more efficient than other methods. For illustration, we future apply the proposed method to the basis of CSI 300 stock index futures.