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Asymptotic theory for LAD estimation of moderate deviations from a unit root

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  • Zhou, Zhiyong
  • Lin, Zhengyan

Abstract

An asymptotic result is given for the least absolute deviations (LAD) estimation of autoregressive time series with a root of the form ρn=1+c/kn, where kn increases to infinity at a rate slower than n. For c<0, a nkn rate of convergence and asymptotic normality for the serial correlation coefficient are provided. While in the case of c>0, the serial correlation coefficient is shown to have a Cauchy limit distribution with a knρnn convergence rate. The results are complementary to the limit theory of least squares (LS) estimator which has been established in Phillips and Magdalinos (2007a).

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:90:y:2014:i:c:p:25-32
    DOI: 10.1016/j.spl.2014.03.004
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    References listed on IDEAS

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    1. Herce, Miguel A., 1996. "Asymptotic Theory of LAD Estimation in a Unit Root Process with Finite Variance Errors," Econometric Theory, Cambridge University Press, vol. 12(1), pages 129-153, March.
    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. 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.
    5. Pollard, David, 1991. "Asymptotics for Least Absolute Deviation Regression Estimators," Econometric Theory, Cambridge University Press, vol. 7(2), pages 186-199, June.
    6. Magdalinos, Tassos, 2012. "Mildly explosive autoregression under weak and strong dependence," Journal of Econometrics, Elsevier, vol. 169(2), pages 179-187.
    7. 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.
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    Cited by:

    1. 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.
    2. Nannan Ma & Hailin Sang & Guangyu Yang, 2023. "Least absolute deviation estimation for AR(1) processes with roots close to unity," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 75(5), pages 799-832, October.

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