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Asymptotics for the conditional self-weighted M-estimator of GRCA(1) models with possibly heavy-tailed errors

Author

Listed:
  • Ke-Ang Fu

    (Zhejiang Gongshang University)

  • Ting Li

    (Zhejiang Gongshang University)

  • Chang Ni

    (Zhejiang Gongshang University)

  • Wenkai He

    (Zhejiang Gongshang University)

  • Renshui Wu

    (Sun Yat-sen University
    Zhuhai Financial Investment Holdings Group Co., Ltd.)

Abstract

Consider a generalized random coefficient AR(1) model, $$y_t=\Phi _t y_{t-1}+u_t$$ y t = Φ t y t - 1 + u t , where $$\{(\Phi _t, u_t)^\prime , t\ge 1\}$$ { ( Φ t , u t ) ′ , t ≥ 1 } is a sequences of i.i.d. random vectors, and a conditional self-weighted M-estimator of $$\textsf {E}\Phi _t$$ E Φ t is proposed. The asymptotically normality of this new estimator is established with $$\textsf {E}u_t^2$$ E u t 2 being possibly infinite. Simulation experiments are carried out to assess the performance of the theory and method in finite samples and a real data example is given.

Suggested Citation

  • Ke-Ang Fu & Ting Li & Chang Ni & Wenkai He & Renshui Wu, 2021. "Asymptotics for the conditional self-weighted M-estimator of GRCA(1) models with possibly heavy-tailed errors," Statistical Papers, Springer, vol. 62(3), pages 1407-1419, June.
    • Handle: RePEc:spr:stpapr:v:62:y:2021:i:3:d:10.1007_s00362-019-01141-8
    DOI: 10.1007/s00362-019-01141-8
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    References listed on IDEAS

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    1. Pan, Jiazhu & Wang, Hui & Yao, Qiwei, 2007. "Weighted least absolute deviations estimation for ARMA models with infinite variance," LSE Research Online Documents on Economics 5405, London School of Economics and Political Science, LSE Library.
    2. Shiqing Ling, 2005. "Self‐weighted least absolute deviation estimation for infinite variance autoregressive models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(3), pages 381-393, June.
    3. Xinghui Wang & Shuhe Hu, 2017. "Asymptotics of self-weighted M-estimators for autoregressive models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(1), pages 83-92, January.
    4. Pan, Jiazhu & Wang, Hui & Yao, Qiwei, 2007. "Weighted Least Absolute Deviations Estimation For Arma Models With Infinite Variance," Econometric Theory, Cambridge University Press, vol. 23(5), pages 852-879, October.
    5. Hwang, S. Y. & Basawa, I. V., 1997. "The local asymptotic normality of a class of generalized random coefficient autoregressive processes," Statistics & Probability Letters, Elsevier, vol. 34(2), pages 165-170, June.
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    Cited by:

    1. Chi Yao & Wei Yu & Xuejun Wang, 2023. "Strong Consistency for the Conditional Self-weighted M Estimator of GRCA(p) Models," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-21, March.

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