### Model Averaging Multistep Prediction in an Infinite Order Autoregressive Process

YUAN Huifang1,2, LIN Peng3, JIANG Tao1,4, XU Jinfeng5

1. 1. School of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou 310018, China;
2. School of Mathematics and Statistics, Zaozhuang University, Zaozhuang 277000, China;
3. School of Mathematics and Statistics, Shandong University of Technology, Zibo 255000, China;
4. Hangzhou College of Commerce, Zhejiang Gongshang University, Tonglu 311599, China;
5. Department of Statistics and Actuarial Science, The University of Hong Kong, HongKong 999077, China
• Received:2020-12-06 Revised:2021-12-23 Online:2022-10-25 Published:2022-10-12
• Supported by:
This research was supported by the National Natural Science Foundation of China under Grant No.11971433,First Class Discipline of Zhejiang-A (Zhejiang Gongshang University-Statistics),the Characteristic&Preponderant Discipline of Key Construction Universities in Zhejiang Province (Zhejiang Gongshang University-Statistics),Collaborative Innovation Center of Statistical Data Engineering Technology&Application.

YUAN Huifang, LIN Peng, JIANG Tao, XU Jinfeng. Model Averaging Multistep Prediction in an Infinite Order Autoregressive Process[J]. Journal of Systems Science and Complexity, 2022, 35(5): 1875-1901.

The key issue in the frequentist model averaging is the choice of weights.In this paper,the authors advocate an asymptotic framework of mean-squared prediction error (MSPE) and develop a model averaging criterion for multistep prediction in an infinite order autoregressive (AR (∞)) process.Under the assumption that the order of the candidate model is bounded,this criterion is proved to be asymptotically optimal,in the sense of achieving the lowest out of sample MSPE for the samerealization prediction.Simulations and real data analysis further demonstrate the effectiveness and the efficiency of the theoretical results.
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