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Uniform Consistency for Nonparametric Estimators in Null Recurrent Time Series

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Author Info

  • Jiti Gao

    ()
    (Monash University)

  • Shin Kanaya

    ()
    (Aarhus University and CREATES)

  • Degui Li

    ()
    (University of York)

  • Dag Tjøstheim

    ()
    (University of Bergen)

Abstract

This paper establishes uniform consistency results for nonparametric kernel density and regression estimators when time series regressors concerned are nonstationary null recurrent Markov chains. Under suitable regularity conditions, we derive uniform convergence rates of the estimators. Our results can be viewed as a nonstationary extension of some well-known uniform consistency results for stationary time series.

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Bibliographic Info

Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2013-29.

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Length: 40
Date of creation: 09 Nov 2013
Date of revision:
Handle: RePEc:aah:create:2013-29

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Web page: http://www.econ.au.dk/afn/

Related research

Keywords: ß-null recurrence; Harris recurrent Markov chain; nonparametric estimation; rate of convergence; uniform consistency;

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References

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  1. Peter C.B. Phillips & Joon Y. Park, 1998. "Nonstationary Density Estimation and Kernel Autoregression," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 1181, Cowles Foundation for Research in Economics, Yale University.
  2. Gao, Jiti, 2007. "Nonlinear time series: semiparametric and nonparametric methods," MPRA Paper 39563, University Library of Munich, Germany, revised 01 Sep 2007.
  3. Dennis Kristensen, 2008. "Uniform Convergence Rates of Kernel Estimators with Heterogenous, Dependent Data," CREATES Research Papers, School of Economics and Management, University of Aarhus 2008-37, School of Economics and Management, University of Aarhus.
  4. Gao, Jiti & King, Maxwell & Lu, Zudi & Tjøstheim, Dag, 2009. "Nonparametric Specification Testing For Nonlinear Time Series With Nonstationarity," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 25(06), pages 1869-1892, December.
  5. Wang, Qiying & Phillips, Peter C.B., 2009. "Asymptotic Theory For Local Time Density Estimation And Nonparametric Cointegrating Regression," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 25(03), pages 710-738, June.
  6. Hansen, Bruce E., 2008. "Uniform Convergence Rates For Kernel Estimation With Dependent Data," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 24(03), pages 726-748, June.
  7. repec:wop:humbsf:1998-50 is not listed on IDEAS
  8. Qiying Wang & Peter C.B. Phillips, 2008. "Structural Nonparametric Cointegrating Regression," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 1657, Cowles Foundation for Research in Economics, Yale University.
  9. Roussas, George G., 1990. "Nonparametric regression estimation under mixing conditions," Stochastic Processes and their Applications, Elsevier, Elsevier, vol. 36(1), pages 107-116, October.
  10. Cai, Zongwu & Li, Qi & Park, Joon Y., 2009. "Functional-coefficient models for nonstationary time series data," Journal of Econometrics, Elsevier, Elsevier, vol. 148(2), pages 101-113, February.
  11. Gao, Jiti & Tjøstheim, Dag & Yin, Jiying, 2013. "Estimation in threshold autoregressive models with a stationary and a unit root regime," Journal of Econometrics, Elsevier, Elsevier, vol. 172(1), pages 1-13.
  12. Jia Chen & Jiti Gao & Degui Li, 2009. "Semiparametric Regression Estimation in Null Recurrent Nonlinear Time Series," School of Economics Working Papers, University of Adelaide, School of Economics 2009-02, University of Adelaide, School of Economics.
  13. Bandi, Federico & Moloche, Guillermo, 2008. "On the functional estimation of multivariate diffusion processes," MPRA Paper 43681, University Library of Munich, Germany.
  14. Chen, Jia & Li, Degui & Zhang, Lixin, 2010. "Robust estimation in a nonlinear cointegration model," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 101(3), pages 706-717, March.
  15. Andrews, Donald W.K., 1995. "Nonparametric Kernel Estimation for Semiparametric Models," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 11(03), pages 560-586, June.
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Citations

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Cited by:
  1. Degui Li & Peter C. B. Phillips & Jiti Gao, 2013. "Uniform Consistency of Nonstationary Kernel-Weighted Sample Covariances for Nonparametric Regression," Monash Econometrics and Business Statistics Working Papers, Monash University, Department of Econometrics and Business Statistics 27/13, Monash University, Department of Econometrics and Business Statistics.
  2. Degui Li & Dag Tjøstheim & Jiti Gao, 2012. "Nonlinear Regression with Harris Recurrent Markov Chains," Monash Econometrics and Business Statistics Working Papers, Monash University, Department of Econometrics and Business Statistics 14/12, Monash University, Department of Econometrics and Business Statistics.

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