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Geometric ergodicity and conditional self‐weighted M‐estimator of a GRCAR(p) model with heavy‐tailed errors

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  • Xiaoyan Li
  • Jiazhu Pan
  • Anchao Song

Abstract

We establish the geometric ergodicity for general stochastic functional autoregressive (linear and nonlinear) models with heavy‐tailed errors. The stationarity conditions for a generalized random coefficient autoregressive model (GRCAR(p)) are presented as a corollary. And then, a conditional self‐weighted M‐estimator for parameters in the GRCAR(p) is proposed. The asymptotic normality of this estimator is discussed by allowing infinite variance innovations. Simulation experiments are carried out to assess the finite‐sample performance of the proposed methodology and theory, and a real heavy‐tailed data example is given as illustration.

Suggested Citation

  • Xiaoyan Li & Jiazhu Pan & Anchao Song, 2023. "Geometric ergodicity and conditional self‐weighted M‐estimator of a GRCAR(p) model with heavy‐tailed errors," Journal of Time Series Analysis, Wiley Blackwell, vol. 44(4), pages 418-436, July.
    • Handle: RePEc:bla:jtsera:v:44:y:2023:i:4:p:418-436
    DOI: 10.1111/jtsa.12680
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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," Econometric Theory, Cambridge University Press, vol. 23(5), pages 852-879, October.
    2. 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.
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    Cited by:

    1. Song, Yuping & Cai, Chunchun & Mao, Huijue & Zhu, Min, 2024. "Self-weighted quantile regression estimation for diffusion parameter in jump–diffusion models," Statistics & Probability Letters, Elsevier, vol. 206(C).

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