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Asymptotic Properties of the M-estimation for an AR(1) Process with a General Autoregressive Coefficient

Author

Listed:
  • Xinghui Wang

    (Anhui University
    Hefei University of Technology)

  • Wenjing Geng

    (Anhui University)

  • Ruidong Han

    (Renmin University of China)

  • Qifa Xu

    (Hefei University of Technology)

Abstract

In this paper, we consider a first-order autoregressive process with a general autoregressive coefficient. Asymptotic behaviors of an M-estimator of the autoregressive coefficient are established for the nearly stationary and mildly explosive cases, respectively. The rate of convergence of the robust estimators for the two cases are provided. The results extend ones for the least squares and least absolute deviation estimators to the robust estimator under the weaker initial conditions in the literature. Some simulations are carried out to assess the performance of our procedure.

Suggested Citation

  • Xinghui Wang & Wenjing Geng & Ruidong Han & Qifa Xu, 2023. "Asymptotic Properties of the M-estimation for an AR(1) Process with a General Autoregressive Coefficient," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-23, March.
    • Handle: RePEc:spr:metcap:v:25:y:2023:i:1:d:10.1007_s11009-023-10005-6
    DOI: 10.1007/s11009-023-10005-6
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    References listed on IDEAS

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    1. Liudas Giraitis & Peter C. B. Phillips, 2006. "Uniform Limit Theory for Stationary Autoregression," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(1), pages 51-60, January.
    2. Aue, Alexander & Horváth, Lajos, 2007. "A Limit Theorem For Mildly Explosive Autoregression With Stable Errors," Econometric Theory, Cambridge University Press, vol. 23(2), pages 201-220, April.
    3. Davis, Richard A. & Knight, Keith & Liu, Jian, 1992. "M-estimation for autoregressions with infinite variance," Stochastic Processes and their Applications, Elsevier, vol. 40(1), pages 145-180, February.
    4. Zhou, Zhiyong & Lin, Zhengyan, 2014. "Asymptotic theory for LAD estimation of moderate deviations from a unit root," Statistics & Probability Letters, Elsevier, vol. 90(C), pages 25-32.
    5. Phillips, Peter C.B. & Magdalinos, Tassos, 2007. "Limit theory for moderate deviations from a unit root," Journal of Econometrics, Elsevier, vol. 136(1), pages 115-130, January.
    6. Pollard, David, 1991. "Asymptotics for Least Absolute Deviation Regression Estimators," Econometric Theory, Cambridge University Press, vol. 7(2), pages 186-199, June.
    7. Yu Miao & Yanling Wang & Guangyu Yang, 2015. "Moderate Deviation Principles for Empirical Covariance in the Neighbourhood of the Unit Root," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(1), pages 234-255, March.
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