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Robust estimation in a nonlinear cointegration model

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  • Chen, Jia
  • Li, Degui
  • Zhang, Lixin

Abstract

This paper considers the nonparametric M-estimator in a nonlinear cointegration type model. The local time density argument, which was developed by Phillips and Park (1998)Â [6] and Wang and Phillips (2009)Â [9], is applied to establish the asymptotic theory for the nonparametric M-estimator. The weak consistency and the asymptotic distribution of the proposed estimator are established under mild conditions. Meanwhile, the asymptotic distribution of the local least squares estimator and the local least absolute distance estimator can be obtained as applications of our main results. Furthermore, an iterated procedure for obtaining the nonparametric M-estimator and a cross-validation bandwidth selection method are discussed, and some numerical examples are provided to show that the proposed methods perform well in the finite sample case.

Suggested Citation

  • Chen, Jia & Li, Degui & Zhang, Lixin, 2010. "Robust estimation in a nonlinear cointegration model," Journal of Multivariate Analysis, Elsevier, vol. 101(3), pages 706-717, March.
  • Handle: RePEc:eee:jmvana:v:101:y:2010:i:3:p:706-717
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    References listed on IDEAS

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    1. Gao, Jiti, 2007. "Nonlinear time series: semiparametric and nonparametric methods," MPRA Paper 39563, University Library of Munich, Germany, revised 01 Sep 2007.
    2. Wang, Qiying & Phillips, Peter C.B., 2009. "Asymptotic Theory For Local Time Density Estimation And Nonparametric Cointegrating Regression," Econometric Theory, Cambridge University Press, vol. 25(03), pages 710-738, June.
    3. Park, Joon Y. & Phillips, Peter C.B., 1999. "Asymptotics For Nonlinear Transformations Of Integrated Time Series," Econometric Theory, Cambridge University Press, vol. 15(03), pages 269-298, June.
    4. Elliott, Graham & Muller, Ulrich K., 2006. "Minimizing the impact of the initial condition on testing for unit roots," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 285-310.
    5. Cai, Zongwu & Ould-Saïd, Elias, 2003. "Local M-estimator for nonparametric time series," Statistics & Probability Letters, Elsevier, vol. 65(4), pages 433-449, December.
    6. Ulrich K. M¸ller & Graham Elliott, 2003. "Tests for Unit Roots and the Initial Condition," Econometrica, Econometric Society, vol. 71(4), pages 1269-1286, July.
    7. Wu, Wei Biao, 2006. "Unit Root Testing For Functionals Of Linear Processes," Econometric Theory, Cambridge University Press, vol. 22(01), pages 1-14, February.
    8. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, number 8355.
    9. Granger, C. W. J., 1981. "Some properties of time series data and their use in econometric model specification," Journal of Econometrics, Elsevier, vol. 16(1), pages 121-130, May.
    10. Zhengyan Lin & Degui Li & Jiti Gao, 2009. "Local Linear M-estimation in non-parametric spatial regression," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(3), pages 286-314, May.
    11. Cunningham, J. K. & Eubank, R. L. & Hsing, T., 1991. "M-type smoothing splines with auxiliary scale estimation," Computational Statistics & Data Analysis, Elsevier, vol. 11(1), pages 43-51, January.
    12. Härdle, Wolfgang, 1984. "Robust regression function estimation," Journal of Multivariate Analysis, Elsevier, vol. 14(2), pages 169-180, April.
    13. J. Fan & J. Chen, 1999. "One-step local quasi-likelihood estimation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(4), pages 927-943.
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    Cited by:

    1. Gao, Jiti & Kanaya, Shin & Li, Degui & Tjøstheim, Dag, 2015. "Uniform Consistency For Nonparametric Estimators In Null Recurrent Time Series," Econometric Theory, Cambridge University Press, vol. 31(05), pages 911-952, October.
    2. Jia Chen & Jiti Gao & Degui Li & Zhengyan Lin, 2015. "Specification testing in nonstationary time series models," Econometrics Journal, Royal Economic Society, vol. 18(1), pages 117-136, February.
    3. Li, Degui & Phillips, Peter C. B. & Gao, Jiti, 2016. "Uniform Consistency Of Nonstationary Kernel-Weighted Sample Covariances For Nonparametric Regression," Econometric Theory, Cambridge University Press, vol. 32(03), pages 655-685, June.
    4. Kunpeng Li & Degui Li & Zhongwen Lian & Cheng Hsiao, 2013. "Semiparametric Profile Likelihood Estimation of Varying Coefficient Models with Nonstationary Regressors," Monash Econometrics and Business Statistics Working Papers 2/13, Monash University, Department of Econometrics and Business Statistics.
    5. Honda, Toshio, 2013. "Nonparametric LAD cointegrating regression," Journal of Multivariate Analysis, Elsevier, vol. 117(C), pages 150-162.

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