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Asymptotics of self-weighted M-estimators for autoregressive models

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  • Xinghui Wang

    (Anhui University)

  • Shuhe Hu

    (Anhui University)

Abstract

In this paper, we consider a stationary autoregressive AR(p) time series $$y_t=\phi _0+\phi _1y_{t-1}+\cdots +\phi _{p}y_{t-p}+u_t$$ y t = ϕ 0 + ϕ 1 y t - 1 + ⋯ + ϕ p y t - p + u t . A self-weighted M-estimator for the AR(p) model is proposed. The asymptotic normality of this estimator is established, which includes the asymptotic properties under the innovations with finite or infinite variance. The result generalizes and improves the known one in the literature.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metrik:v:80:y:2017:i:1:d:10.1007_s00184-016-0592-x
    DOI: 10.1007/s00184-016-0592-x
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    References listed on IDEAS

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    8. Zhao Chen & Runze Li & Yaohua Wu, 2012. "Weighted quantile regression for AR model with infinite variance errors," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(3), pages 715-731.
    9. 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.
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    Cited by:

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    2. 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.

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