IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v81y2002i1p167-186.html
   My bibliography  Save this article

R-estimation in Autoregression with Square-Integrable Score Function

Author

Listed:
  • Mukherjee, Kanchan
  • Bai, Z. D.

Abstract

This paper develops an asymptotic theory for R-estimation based on a square-integrable, not necessarily bounded, score function in the pth order stationary autoregressive model. Asymptotic uniform linearity of a class of linear rank statistics is established and the asymptotic normality of the corresponding R-estimators is derived. This paper thus solves a long-standing problem in the development of the asymptotics for rank estimators under the autoregressive setup. The proofs use a combination of the approximation technique, the contiguity technique and the weak convergence technique of Hajek, Jurecková and Koul, respectively.

Suggested Citation

  • Mukherjee, Kanchan & Bai, Z. D., 2002. "R-estimation in Autoregression with Square-Integrable Score Function," Journal of Multivariate Analysis, Elsevier, vol. 81(1), pages 167-186, April.
    • Handle: RePEc:eee:jmvana:v:81:y:2002:i:1:p:167-186
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(01)91998-0
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Marc Hallin & Madan Lal Puri, 1994. "Aligned rank tests for linear models with autocorrelated errors," ULB Institutional Repository 2013/2045, ULB -- Universite Libre de Bruxelles.
    2. Marc Hallin & Jean-François Ingenbleek & Madan Lal Puri, 1984. "Linear serial rank tests for randomness against ARMA alternatives," ULB Institutional Repository 2013/2167, ULB -- Universite Libre de Bruxelles.
    3. Hallin, M. & Puri, M. L., 1994. "Aligned Rank Tests for Linear Models with Autocorrelated Error Terms," Journal of Multivariate Analysis, Elsevier, vol. 50(2), pages 175-237, August.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. M. Hallin & D. La Vecchia & H. Liu, 2022. "Center-Outward R-Estimation for Semiparametric VARMA Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 117(538), pages 925-938, April.
    2. Hallin, Marc & La Vecchia, Davide, 2020. "A Simple R-estimation method for semiparametric duration models," Journal of Econometrics, Elsevier, vol. 218(2), pages 736-749.
    3. Hang Liu & Kanchan Mukherjee, 2022. "R-estimators in GARCH models: asymptotics and applications," The Econometrics Journal, Royal Economic Society, vol. 25(1), pages 98-113.
    4. Marc Hallin & Davide La Vecchia, 2014. "Semiparametrically Efficient R-Estimation for Dynamic Location-Scale Models," Working Papers ECARES ECARES 2014-45, ULB -- Universite Libre de Bruxelles.
    5. Hallin, Marc & La Vecchia, Davide, 2017. "R-estimation in semiparametric dynamic location-scale models," Journal of Econometrics, Elsevier, vol. 196(2), pages 233-247.
    6. Mukherjee, Kanchan, 2007. "Generalized R-estimators under conditional heteroscedasticity," Journal of Econometrics, Elsevier, vol. 141(2), pages 383-415, December.

    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. Hallin, Marc & La Vecchia, Davide, 2020. "A Simple R-estimation method for semiparametric duration models," Journal of Econometrics, Elsevier, vol. 218(2), pages 736-749.
    2. M. Hallin & D. La Vecchia & H. Liu, 2022. "Center-Outward R-Estimation for Semiparametric VARMA Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 117(538), pages 925-938, April.
    3. Marc Hallin & Khalid Rifi, 1997. "A Berry-Esséen Theorem for Serial Rank Statistics," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 49(4), pages 777-799, December.
    4. Garel, Bernard & Hallin, Marc, 2000. "Rank-based partial autocorrelations are not asymptotically distribution-free," Statistics & Probability Letters, Elsevier, vol. 47(3), pages 219-227, April.
    5. Hallin, M. & Vermandele, C. & Werker, B.J.M., 2003. "Serial and Nonserial Sign-and-Rank Statistics : Asymptotic Representation and Asymptotic Normality," Discussion Paper 2003-23, Tilburg University, Center for Economic Research.
    6. Nabil Azouagh & Said El Melhaoui, 2021. "Detection of EXPAR nonlinearity in the Presence of a Nuisance Unidentified Under the Null Hypothesis," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 397-429, November.
    7. Marc Hallin & Bas Werker, 2003. "Semiparametric efficiency, distribution-freeness, and invariance," ULB Institutional Repository 2013/2119, ULB -- Universite Libre de Bruxelles.
    8. Allal, Jelloul & Kaaouachi, Abdelali & Paindaveine, Davy, 2001. "R-estimation for ARMA models," MPRA Paper 21167, University Library of Munich, Germany.
    9. Hallin, Marc & La Vecchia, Davide, 2017. "R-estimation in semiparametric dynamic location-scale models," Journal of Econometrics, Elsevier, vol. 196(2), pages 233-247.
    10. Marc Hallin & Catherine Vermandele & Bas J. M. Werker, 2008. "Semiparametrically efficient inference based on signs and ranks for median‐restricted models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(2), pages 389-412, April.
    11. Marc Hallin & Abdeslam Serroukh, 1998. "Adaptive Estimation of the Lag of a Long–memory Process," Statistical Inference for Stochastic Processes, Springer, vol. 1(2), pages 111-129, May.
    12. M. Angeles Carnero & Ana Pérez & Esther Ruiz, 2016. "Identification of asymmetric conditional heteroscedasticity in the presence of outliers," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 7(1), pages 179-201, March.
    13. Paindaveine, Davy, 2006. "A Chernoff-Savage result for shape:On the non-admissibility of pseudo-Gaussian methods," Journal of Multivariate Analysis, Elsevier, vol. 97(10), pages 2206-2220, November.
    14. Hallin, Marc & Paindaveine, Davy, 2005. "Affine-invariant aligned rank tests for the multivariate general linear model with VARMA errors," Journal of Multivariate Analysis, Elsevier, vol. 93(1), pages 122-163, March.
    15. Dette, Holger & Spreckelsen, Ingrid, 2000. "A test for randomness against ARMA alternatives," Stochastic Processes and their Applications, Elsevier, vol. 89(1), pages 131-139, September.
    16. Hasan, Mohammad N., 2001. "Rank tests of unit root hypothesis with infinite variance errors," Journal of Econometrics, Elsevier, vol. 104(1), pages 49-65, August.
    17. Bramati, Maria Caterina, 2013. "Optimal rank-based tests for block exogeneity in vector autoregressions," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 141-162.
    18. Pinkse, Joris, 1998. "A consistent nonparametric test for serial independence," Journal of Econometrics, Elsevier, vol. 84(2), pages 205-231, June.
    19. Lanh Tran, 1988. "Rank order statistics for time series models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 40(2), pages 247-260, June.
    20. Cho, Jin Seo & White, Halbert, 2011. "Generalized runs tests for the IID hypothesis," Journal of Econometrics, Elsevier, vol. 162(2), pages 326-344, June.

    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:jmvana:v:81:y:2002:i:1:p:167-186. 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.