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Local composite quantile regression smoothing for Harris recurrent Markov processes

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  • Li, Degui
  • Li, Runze

Abstract

In this paper, we study the local polynomial composite quantile regression (CQR) smoothing method for the nonlinear and nonparametric models under the Harris recurrent Markov chain framework. The local polynomial CQR regression method is a robust alternative to the widely-used local polynomial method, and has been well studied in stationary time series. In this paper, we relax the stationarity restriction on the model, and allow that the regressors are generated by a general Harris recurrent Markov process which includes both the stationary (positive recurrent) and nonstationary (null recurrent) cases. Under some mild conditions, we establish the asymptotic theory for the proposed local polynomial CQR estimator of the mean regression function, and show that the convergence rate for the estimator in nonstationary case is slower than that in stationary case. Furthermore, a weighted type local polynomial CQR estimator is provided to improve the estimation efficiency, and a data-driven bandwidth selection is introduced to choose the optimal bandwidth involved in the nonparametric estimators. Finally, we give some numerical studies to examine the finite sample performance of the developed methodology and theory.

Suggested Citation

  • Li, Degui & Li, Runze, 2016. "Local composite quantile regression smoothing for Harris recurrent Markov processes," Journal of Econometrics, Elsevier, vol. 194(1), pages 44-56.
    • Handle: RePEc:eee:econom:v:194:y:2016:i:1:p:44-56
    DOI: 10.1016/j.jeconom.2016.04.002
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    Cited by:

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    2. Qifa Xu & Zezhou Wang & Cuixia Jiang & Yezheng Liu, 2023. "Deep learning on mixed frequency data," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 42(8), pages 2099-2120, December.
    3. Xie, Qichang & Sun, Qiankun, 2019. "Computation and application of robust data-driven bandwidth selection for gradient function estimation," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 274-293.
    4. Matthew Pietrosanu & Jueyu Gao & Linglong Kong & Bei Jiang & Di Niu, 2021. "Advanced algorithms for penalized quantile and composite quantile regression," Computational Statistics, Springer, vol. 36(1), pages 333-346, March.
    5. Xiao Huang & Zhaoguo Zhan, 2022. "Local Composite Quantile Regression for Regression Discontinuity," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(4), pages 1863-1875, October.
    6. Tu, Yundong & Liang, Han-Ying & Wang, Qiying, 2022. "Nonparametric inference for quantile cointegrations with stationary covariates," Journal of Econometrics, Elsevier, vol. 230(2), pages 453-482.

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    More about this item

    Keywords

    Asymptotic theory; Bandwidth selection; β-null recurrence; Composite quantile regression; Harris recurrent Markov process; Local polynomial smoothing;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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