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Semiparametric Regression Estimation in Null Recurrent Nonlinear Time Series

Author

Listed:
  • Jia Chen

    (School of Economics, University of Adelaide)

  • Jiti Gao

    (School of Economics, The University of Adelaide)

  • Degui Li

    (School of Economics, University of Adelaide)

Abstract

Estimation theory in a nonstationary environment has been very popular in recent years. Existing studies focus on nonstationarity in parametric linear, parametric nonlinear and nonparametric nonlinear models. In this paper, we consider a partially linear model and propose to estimate both alpha and g semiparametrically. We then show that the proposed estimator of alpha is still asymptotically normal with the same rate as for the case of stationary time series. We also establish the asymptotic normality for the nonparametric estimator of the function g and the uniform consistency of the nonparametric estimator. The simulated example is given to show that our theory and method work well in practice.

Suggested Citation

  • Jia Chen & Jiti Gao & Degui Li, 2009. "Semiparametric Regression Estimation in Null Recurrent Nonlinear Time Series," School of Economics and Public Policy Working Papers 2009-02, University of Adelaide, School of Economics and Public Policy.
    • Handle: RePEc:adl:wpaper:2009-02
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    File URL: https://media.adelaide.edu.au/economics/papers/doc/wp2009-02.pdf
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    Citations

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    Cited by:

    1. Jiti Gao & Peter C.B. Phillips, 2011. "Semiparametric Estimation in Multivariate Nonstationary Time Series Models," Monash Econometrics and Business Statistics Working Papers 17/11, Monash University, Department of Econometrics and Business Statistics.
    2. Gao, Jiti & Tjøstheim, Dag & Yin, Jiying, 2013. "Estimation in threshold autoregressive models with a stationary and a unit root regime," Journal of Econometrics, Elsevier, vol. 172(1), pages 1-13.
    3. Honda, Toshio, 2013. "Nonparametric LAD cointegrating regression," Journal of Multivariate Analysis, Elsevier, vol. 117(C), pages 150-162.
    4. 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(5), pages 911-952, October.
    5. Jiti Gao & Maxwell King, 2011. "A New Test in Parametric Linear Models against Nonparametric Autoregressive Errors," Monash Econometrics and Business Statistics Working Papers 20/11, Monash University, Department of Econometrics and Business Statistics.

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