Model Average Estimation of Parameters in Linear Model With Multiple Change Points

ABSTRACTThis paper develops a model averaging framework for segmented linear regression with multiple structural breaks. We establish the asymptotic distribution for estimates of a linear model with gradual parameter changes, presenting the limitations of traditional methods under model misspecification of change points. Based on this, we propose the Mallows Model Average (MMA) method to assign weights to estimators from models with different numbers of change points. The MMA weights are determined by minimizing the Mallows criterion, which is an asymptotically unbiased estimate of the expected squared error plus a constant. When the real model is a change‐point model, the resulting MMA estimator is proved to be root‐n consistent. We also prove its asymptotic optimality in terms of achieving the lowest squared error, allowing for deviations from the change‐point model. Both simulation studies and empirical analyses demonstrate that our method outperforms competitive methods and has promising applications.