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Polynomial network autoregressive models with divergent orders

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Abstract

This study proposes a novel polynomial network autoregressive model by incorporating higher-order connected relationships to simultaneously model the effects of both direct and indirect connections. A quasi-maximum likelihood estimation method is proposed to estimate the unknown influence parameters, and demonstrates its consistency and asymptotic normality without imposing any distribution assumption. Moreover, an extended Bayesian information criterion is set for order selection with a divergent upper order. The application of the proposed polynomial network autoregressive model is demonstrated through both the simulation and the real data analysis.

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Acknowledgements

The first author was supported by the Fundamental Research Funds for the Central Universities (Grant No. JBK2207075). The second author was supported by National Natural Science Foundation of China (Grant Nos. 71991472, 12171395, 11931014 and 71532001), the Joint Lab of Data Science and Business Intelligence at Southwestern University of Finance and Economics and the Fundamental Research Funds for the Central Universities (Grant No. JBK1806002). The fourth author was supported by the Humanity and Social Science Youth Foundation of Ministry of Education of China (Grant No. 19YJC790204). The authors are grateful to the referees for their insightful comments and constructive suggestions.

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Authors and Affiliations

  1. School of Statistics and Center of Statistical Research, Southwestern University of Finance and Economics, Chengdu, 611130, China

    Bo Lei & Wei Lan

  2. School of Finance, Southwestern University of Finance and Economics, Chengdu, 611130, China

    Nengsheng Fang

  3. School of International Business, Southwestern University of Finance and Economics, Chengdu, 611130, China

    Jing Zhou

Authors
  1. Bo Lei
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  2. Wei Lan
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  3. Nengsheng Fang
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  4. Jing Zhou
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Correspondence to Wei Lan.

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Lei, B., Lan, W., Fang, N. et al. Polynomial network autoregressive models with divergent orders. Sci. China Math. 66, 1073–1086 (2023). https://doi.org/10.1007/s11425-021-1978-7

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  • DOI: https://doi.org/10.1007/s11425-021-1978-7

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