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Robust nonlinear regression estimation in null recurrent time series

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  • Bravo, Francesco
  • Li, Degui
  • Tjøstheim, Dag

Abstract

In this article, we study parametric robust estimation in nonlinear regression models with regressors generated by a class of non-stationary and null recurrent Markov processes. The nonlinear regression functions can be either integrable or asymptotically homogeneous, covering many commonly-used functional forms in parametric nonlinear regression. Under regularity conditions, we derive both the consistency and limit distribution results for the developed general robust estimators (including the nonlinear least squares, least absolute deviation and Huber’s M-estimators). The convergence rates of the estimation depend on not only the functional form of the nonlinear regression, but also on the recurrence rate of the Markov process. Some Monte-Carlo simulation studies are conducted to examine the numerical performance of the proposed estimators and verify the established asymptotic properties in finite samples. Finally two empirical applications illustrate the usefulness of the proposed robust estimation method.

Suggested Citation

  • Bravo, Francesco & Li, Degui & Tjøstheim, Dag, 2021. "Robust nonlinear regression estimation in null recurrent time series," Journal of Econometrics, Elsevier, vol. 224(2), pages 416-438.
    • Handle: RePEc:eee:econom:v:224:y:2021:i:2:p:416-438
    DOI: 10.1016/j.jeconom.2020.03.028
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    2. Chaohua Dong & Jiti Gao & Bin Peng & Yundong Tu, 2023. "Smoothing the Nonsmoothness," Papers 2309.16348, arXiv.org.
    3. Tao Wang, 2024. "Nonlinear kernel mode‐based regression for dependent data," Journal of Time Series Analysis, Wiley Blackwell, vol. 45(2), pages 189-213, March.

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