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Model Averaging Multistep Prediction in an Infinite Order Autoregressive Process

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Abstract

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 same-realization prediction. Simulations and real data analysis further demonstrate the effectiveness and the efficiency of the theoretical results.

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Author information

Authors and Affiliations

  1. School of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou, 310018, China

    Huifang Yuan & Tao Jiang

  2. School of Mathematics and Statistics, Zaozhuang University, Zaozhuang, 277000, China

    Huifang Yuan

  3. School of Mathematics and Statistics, Shandong University of Technology, Zibo, 255000, China

    Peng Lin

  4. Hangzhou College of Commerce, Zhejiang Gongshang University, Tonglu, Hangzhou, 311599, China

    Tao Jiang

  5. Department of Statistics and Actuarial Science, The University of Hong Kong, HongKong, 999077, China

    Jinfeng Xu

Authors
  1. Huifang Yuan
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  2. Peng Lin
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  3. Tao Jiang
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  4. Jinfeng Xu
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Corresponding author

Correspondence to Tao Jiang.

Additional information

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.

This paper was recommended for publication by Editor ZHANG Xinyu.

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Yuan, H., Lin, P., Jiang, T. et al. Model Averaging Multistep Prediction in an Infinite Order Autoregressive Process. J Syst Sci Complex 35, 1875–1901 (2022). https://doi.org/10.1007/s11424-022-0311-9

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  • DOI: https://doi.org/10.1007/s11424-022-0311-9

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