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Nonstationary nonlinear quantile regression

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  • Yoshimasa Uematsu

Abstract

This study examines estimation and inference based on quantile regression for parametric nonlinear models with an integrated time series covariate. We first derive the limiting distribution of the nonlinear quantile regression estimator and then consider testing for parameter restrictions, when the regression function is specified as an asymptotically homogeneous function. We also study linear-in-parameter regression models when the regression function is given by integrable regression functions as well as asymptotically homogeneous regression functions. We, furthermore, propose a fully modified estimator to reduce the bias in the original estimator under a certain set of conditions. Finally, simulation studies show that the estimators behave well, especially when the regression error term has a fat-tailed distribution.

Suggested Citation

  • Yoshimasa Uematsu, 2019. "Nonstationary nonlinear quantile regression," Econometric Reviews, Taylor & Francis Journals, vol. 38(4), pages 386-416, April.
    • Handle: RePEc:taf:emetrv:v:38:y:2019:i:4:p:386-416
    DOI: 10.1080/07474938.2017.1308056
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    Cited by:

    1. Christis Katsouris, 2023. "Structural Break Detection in Quantile Predictive Regression Models with Persistent Covariates," Papers 2302.05193, arXiv.org.
    2. Haiqi Li Author-Name-First: Haiqi & Jing Zhang & Chaowen Zheng, 2023. "Estimating and Testing for Functional Coefficient Quantile Cointegrating Regression," Economics Discussion Papers em-dp2023-07, Department of Economics, University of Reading.
    3. Lin, Yingqian & Tu, Yundong, 2021. "On transformed linear cointegration models," Economics Letters, Elsevier, vol. 198(C).
    4. Lin, Yingqian & Tu, Yundong & Yao, Qiwei, 2020. "Estimation for double-nonlinear cointegration," LSE Research Online Documents on Economics 103830, London School of Economics and Political Science, LSE Library.
    5. Christis Katsouris, 2023. "Quantile Time Series Regression Models Revisited," Papers 2308.06617, arXiv.org, revised Aug 2023.
    6. Lin, Yingqian & Tu, Yundong & Yao, Qiwei, 2020. "Estimation for double-nonlinear cointegration," Journal of Econometrics, Elsevier, vol. 216(1), pages 175-191.
    7. 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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