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Uniform Consistency for Nonparametric Estimators in Null Recurrent Time Series

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  • Jiti Gao

    ()

  • Degui Li

    ()

  • Dag Tjøstheim

Abstract

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

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File URL: http://www.buseco.monash.edu.au/ebs/pubs/wpapers/2011/wp13-11.pdf
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Bibliographic Info

Paper provided by Monash University, Department of Econometrics and Business Statistics in its series Monash Econometrics and Business Statistics Working Papers with number 13/11.

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Length: 32 pages
Date of creation: Sep 2011
Date of revision:
Handle: RePEc:msh:ebswps:2011-13

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Keywords: β-null recurrent Markov chain; nonparametric estimation; rate of convergence; uniform consistency;

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References

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  1. Hansen, Bruce E., 2008. "Uniform Convergence Rates For Kernel Estimation With Dependent Data," Econometric Theory, Cambridge University Press, vol. 24(03), pages 726-748, June.
  2. Gao, Jiti & King, Maxwell & Lu, Zudi & Tjøstheim, Dag, 2009. "Nonparametric Specification Testing For Nonlinear Time Series With Nonstationarity," Econometric Theory, Cambridge University Press, vol. 25(06), pages 1869-1892, December.
  3. Roussas, George G., 1990. "Nonparametric regression estimation under mixing conditions," Stochastic Processes and their Applications, Elsevier, vol. 36(1), pages 107-116, October.
  4. Gao, Jiti, 2007. "Nonlinear time series: semiparametric and nonparametric methods," MPRA Paper 39563, University Library of Munich, Germany, revised 01 Sep 2007.
  5. Jiti Gao & Dag Tjøstheim & Jiying Yin, 2011. "Estimation in threshold autoregressive models with a stationary and a unit root regime," Monash Econometrics and Business Statistics Working Papers 21/11, Monash University, Department of Econometrics and Business Statistics.
  6. Dennis Kristensen, 2008. "Uniform Convergence Rates of Kernel Estimators with Heterogenous, Dependent Data," CREATES Research Papers 2008-37, School of Economics and Management, University of Aarhus.
  7. Qiying Wang & Peter C.B. Phillips, 2006. "Asymptotic Theory for Local Time Density Estimation and Nonparametric Cointegrating Regression," Cowles Foundation Discussion Papers 1594, Cowles Foundation for Research in Economics, Yale University.
  8. Qiying Wang & Peter C.B. Phillips, 2008. "Structural Nonparametric Cointegrating Regression," Cowles Foundation Discussion Papers 1657, Cowles Foundation for Research in Economics, Yale University.
  9. 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.
  10. 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.
  11. repec:wop:humbsf:1998-50 is not listed on IDEAS
  12. Bandi, Federico & Moloche, Guillermo, 2008. "On the functional estimation of multivariate diffusion processes," MPRA Paper 43681, University Library of Munich, Germany.
  13. Peter C.B. Phillips & Joon Y. Park, 1998. "Nonstationary Density Estimation and Kernel Autoregression," Cowles Foundation Discussion Papers 1181, Cowles Foundation for Research in Economics, Yale University.
  14. 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.
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Cited by:
  1. Degui Li & Dag Tjøstheim & Jiti Gao, 2012. "Nonlinear Regression with Harris Recurrent Markov Chains," Monash Econometrics and Business Statistics Working Papers 14/12, Monash University, Department of Econometrics and Business Statistics.

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