IDEAS home Printed from https://ideas.repec.org/a/oup/biomet/v92y2005i2p477-484.html
   My bibliography  Save this article

Weighted least absolute deviations estimation for an AR(1) process with ARCH(1) errors

Author

Listed:
  • Ngai Hang Chan
  • Liang Peng

Abstract

The weighted least absolute deviations estimator is studied for an AR(1) process with ARCH(1) errors ϵ-sub-t. Unlike for the quasi maximum likelihood estimator, the estimator's, limiting distribution is shown to be normal even when E(ϵ-sub-t-super-4) = ∞. Furthermore, the estimator can be applied to examine the symmetry of the density of ϵ-sub-t and to estimate the quantity E(log |α + λ-super-½ ϵ-sub-t|), which are of crucial importance for conducting asymptotic inference for quasi maximum likelihood estimators and weighted least absolute deviations estimators. Copyright 2005, Oxford University Press.

Suggested Citation

  • Ngai Hang Chan & Liang Peng, 2005. "Weighted least absolute deviations estimation for an AR(1) process with ARCH(1) errors," Biometrika, Biometrika Trust, vol. 92(2), pages 477-484, June.
    • Handle: RePEc:oup:biomet:v:92:y:2005:i:2:p:477-484
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1093/biomet/92.2.477
    Download Restriction: Access to full text is restricted to subscribers.
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Guo, Shaojun & Li, Dong & Li, Muyi, 2019. "Strict stationarity testing and GLAD estimation of double autoregressive models," Journal of Econometrics, Elsevier, vol. 211(2), pages 319-337.
    2. Ke Zhu & Shiqing Ling, 2015. "LADE-Based Inference for ARMA Models With Unspecified and Heavy-Tailed Heteroscedastic Noises," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(510), pages 784-794, June.
    3. Min Chen & Dong Li & Shiqing Ling, 2014. "Non-Stationarity And Quasi-Maximum Likelihood Estimation On A Double Autoregressive Model," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(3), pages 189-202, May.
    4. Dong Li & Shiqing Ling & Rongmao Zhang, 2016. "On a Threshold Double Autoregressive Model," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(1), pages 68-80, January.
    5. Ruidong Han & Xinghui Wang & Shuhe Hu, 2018. "Asymptotics of the weighted least squares estimation for AR(1) processes with applications to confidence intervals," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(3), pages 479-490, August.
    6. Ling, Shiqing, 2007. "Self-weighted and local quasi-maximum likelihood estimators for ARMA-GARCH/IGARCH models," Journal of Econometrics, Elsevier, vol. 140(2), pages 849-873, October.
    7. So, Mike K.P. & Chung, Ray S.W., 2015. "Statistical inference for conditional quantiles in nonlinear time series models," Journal of Econometrics, Elsevier, vol. 189(2), pages 457-472.
    8. Huan Gong & Dong Li, 2020. "On the three‐step non‐Gaussian quasi‐maximum likelihood estimation of heavy‐tailed double autoregressive models," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(6), pages 883-891, November.
    9. Yaxing Yang & Shiqing Ling, 2017. "Inference for Heavy-Tailed and Multiple-Threshold Double Autoregressive Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(2), pages 318-333, April.
    10. Zongwu Cai & Seong Yeon Chang, 2018. "A New Test In A Predictive Regression with Structural Breaks," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201811, University of Kansas, Department of Economics, revised Dec 2018.
    11. Zhu, Ke & Ling, Shiqing, 2013. "Global self-weighted and local quasi-maximum exponential likelihood estimators for ARMA-GARCH/IGARCH models," MPRA Paper 51509, University Library of Munich, Germany.
    12. Li, Dong & Tao, Yuxin & Yang, Yaxing & Zhang, Rongmao, 2023. "Maximum likelihood estimation for α-stable double autoregressive models," Journal of Econometrics, Elsevier, vol. 236(1).
    13. Yoon, Gawon, 2016. "Stochastic unit root processes: Maximum likelihood estimation, and new Lagrange multiplier and likelihood ratio tests," Economic Modelling, Elsevier, vol. 52(PB), pages 725-732.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:oup:biomet:v:92:y:2005:i:2:p:477-484. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Oxford University Press (email available below). General contact details of provider: https://academic.oup.com/biomet .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.