In this paper, noting that the prediction of time series follows the temporal order of data, we propose a frequentist model averaging method based on forward-validation. Our method also considers the uncertainty of the window size in estimation, i.e., we allow the sample size to vary among candidate models. We establish the asymptotic optimality of our method in the sense of achieving the lowest possible squared prediction risk. We also prove that if there exists one or more correctly specified models, our method will automatically assign all the weights to them. The promising performance of our method for finite samples is demonstrated by simulations and an empirical example of predicting the equity premium. 

　　Publication: 

　　Journal of Econometrics. Available online 21 May 2022 

　　Author: 

　　Xiaomeng Zhang 

　　Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China 

　　University of Chinese Academy of Sciences, Beijing 100049, China 

　　Xinyu Zhang 

　　Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China 

　　Beijing Academy of Artificial Intelligence, Beijing 100084, China 

　　Email: xinyu@amss.ac.cn