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Nonparametric LAD cointegrating regression

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  • Honda, Toshio

Abstract

We deal with nonparametric estimation in a nonlinear cointegration model whose regressor and error term can be contemporaneously correlated. The asymptotic properties of the Nadaraya–Watson estimator are already examined in the literature. In this paper, we consider nonparametric least absolute deviation (LAD) regression and derive the asymptotic distributions of the local constant and local linear estimators by appealing to the local time approach. We also present the results of a small simulation study.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Multivariate Analysis.

Volume (Year): 117 (2013)
Issue (Month): C ()
Pages: 150-162

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Handle: RePEc:eee:jmvana:v:117:y:2013:i:c:p:150-162

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Related research

Keywords: Nonlinear cointegration; Integrated process; Local time; Least absolute deviation; Local polynomial regression; Bias;

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References

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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. Qiying Wang & Peter C.B. Phillips, 2008. "Structural Nonparametric Cointegrating Regression," Cowles Foundation Discussion Papers 1657, Cowles Foundation for Research in Economics, Yale University.
  3. Roger Koenker & Kevin F. Hallock, 2001. "Quantile Regression," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 143-156, Fall.
  4. 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.
  5. Cai, Zongwu, 2002. "Regression Quantiles For Time Series," Econometric Theory, Cambridge University Press, vol. 18(01), pages 169-192, February.
  6. Xiao, Zhijie, 2009. "Quantile cointegrating regression," Journal of Econometrics, Elsevier, vol. 150(2), pages 248-260, June.
  7. Wang, Qiying & Phillips, Peter C.B., 2011. "Asymptotic Theory For Zero Energy Functionals With Nonparametric Regression Applications," Econometric Theory, Cambridge University Press, vol. 27(02), pages 235-259, April.
  8. 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.
  9. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
  10. Honda, Toshio, 2007. "Nonparametric Estimation of Conditional Medians for Linear and Related Processes," Discussion Papers 2005-04, Graduate School of Economics, Hitotsubashi University.
  11. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
  12. Engle, Robert F & Granger, Clive W J, 1987. "Co-integration and Error Correction: Representation, Estimation, and Testing," Econometrica, Econometric Society, vol. 55(2), pages 251-76, March.
  13. Jia Chen & Jiti Gao & Degui Li, 2009. "Semiparametric Regression Estimation in Null Recurrent Nonlinear Time Series," School of Economics Working Papers 2009-02, University of Adelaide, School of Economics.
  14. Toshio Honda, 2000. "Nonparametric Estimation of a Conditional Quantile for α-Mixing Processes," Annals of the Institute of Statistical Mathematics, Springer, vol. 52(3), pages 459-470, September.
  15. Cai, Zongwu & Li, Qi & Park, Joon Y., 2009. "Functional-coefficient models for nonstationary time series data," Journal of Econometrics, Elsevier, vol. 148(2), pages 101-113, February.
  16. 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.
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