IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v126y2017icp157-163.html
   My bibliography  Save this article

Asymptotic distributions of some robust scale estimators in explosive AR(1) model

Author

Listed:
  • Koul, Hira L.
  • Vellaisamy, P.

Abstract

This note establishes the asymptotic normality of the median of the absolute residuals and the median of the absolute differences of pairwise residuals in the first order explosive autoregressive time series. These estimators are useful for obtaining some scale invariant estimators of the autoregressive parameter.

Suggested Citation

  • Koul, Hira L. & Vellaisamy, P., 2017. "Asymptotic distributions of some robust scale estimators in explosive AR(1) model," Statistics & Probability Letters, Elsevier, vol. 126(C), pages 157-163.
    • Handle: RePEc:eee:stapro:v:126:y:2017:i:c:p:157-163
    DOI: 10.1016/j.spl.2017.03.007
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715217300986
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2017.03.007?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

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

    References listed on IDEAS

    as
    1. Datta, Somnath, 1995. "Limit theory and bootstrap for explosive and partially explosive autoregression," Stochastic Processes and their Applications, Elsevier, vol. 57(2), pages 285-304, June.
    2. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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. Jeremy Berkowitz & Lutz Kilian, 2000. "Recent developments in bootstrapping time series," Econometric Reviews, Taylor & Francis Journals, vol. 19(1), pages 1-48.
    3. Ngai Chan & Rongmao Zhang, 2009. "M-estimation in nonparametric regression under strong dependence and infinite variance," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(2), pages 391-411, June.
    4. Mohamed El Ghourabi & Christian Francq & Fedya Telmoudi, 2016. "Consistent Estimation of the Value at Risk When the Error Distribution of the Volatility Model is Misspecified," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(1), pages 46-76, January.
    5. Rongning Wu & Richard A. Davis, 2010. "Least absolute deviation estimation for general autoregressive moving average time‐series models," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(2), pages 98-112, March.
    6. Richard A. Davis & William T. M. Dunsmuir, 1997. "Least Absolute Deviation Estimation for Regression with ARMA Errors," Journal of Theoretical Probability, Springer, vol. 10(2), pages 481-497, April.
    7. 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.
    8. Chaohua Dong & Jiti Gao & Bin Peng & Yundong Tu, 2021. "Multiple-index Nonstationary Time Series Models: Robust Estimation Theory and Practice," Papers 2111.02023, arXiv.org.
    9. Datta, Somnath, 1995. "Limit theory and bootstrap for explosive and partially explosive autoregression," Stochastic Processes and their Applications, Elsevier, vol. 57(2), pages 285-304, June.
    10. Benjamin Poignard, 2020. "Asymptotic theory of the adaptive Sparse Group Lasso," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(1), pages 297-328, February.
    11. D. M. Mahinda Samarakoon & Keith Knight, 2009. "A Note on Unit Root Tests with Infinite Variance Noise," Econometric Reviews, Taylor & Francis Journals, vol. 28(4), pages 314-334.
    12. Alain Hecq & Joao Victor Issler & Sean Telg, 2020. "Mixed causal–noncausal autoregressions with exogenous regressors," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 35(3), pages 328-343, April.
    13. 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.
    14. Zhang, Xingfa & Zhang, Rongmao & Li, Yuan & Ling, Shiqing, 2022. "LADE-based inferences for autoregressive models with heavy-tailed G-GARCH(1, 1) noise," Journal of Econometrics, Elsevier, vol. 227(1), pages 228-240.
    15. Andrews, Beth & Davis, Richard A. & Jay Breidt, F., 2006. "Maximum likelihood estimation for all-pass time series models," Journal of Multivariate Analysis, Elsevier, vol. 97(7), pages 1638-1659, August.
    16. Xiaofei Hu & Beth Andrews, 2021. "Integer‐valued asymmetric garch modeling," Journal of Time Series Analysis, Wiley Blackwell, vol. 42(5-6), pages 737-751, September.
    17. Hill, Jonathan B. & Aguilar, Mike, 2013. "Moment condition tests for heavy tailed time series," Journal of Econometrics, Elsevier, vol. 172(2), pages 255-274.
    18. Chan, Ngai Hang & Zhang, Rong-Mao, 2009. "Quantile inference for near-integrated autoregressive time series under infinite variance and strong dependence," Stochastic Processes and their Applications, Elsevier, vol. 119(12), pages 4124-4148, December.
    19. Chaohua Dong & Jiti Gao & Bin Peng & Yundong Tu, 2023. "Robust M-Estimation for Additive Single-Index Cointegrating Time Series Models," Monash Econometrics and Business Statistics Working Papers 2/23, Monash University, Department of Econometrics and Business Statistics.
    20. 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.

    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:eee:stapro:v:126:y:2017:i:c:p:157-163. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.