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Jump-detection-based estimation in time-varying coefficient models and empirical applications

Author

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  • Yan-Yong Zhao

    (Nanjing Audit University)

  • Jin-Guan Lin

    (Nanjing Audit University)

  • Hong-Xia Wang

    (Nanjing Audit University)

  • Xing-Fang Huang

    (Nanjing Audit University)

Abstract

Time-varying coefficient models are very important tools to explore the hidden structure between the response variable and its predictors. In some applications, the coefficient curves have singularities, including jump points at some unknown positions, representing structural changes of the related processes. Detection of such singularities is important for understanding the structural changes. In this paper, an alternative jump-detection procedure is proposed based on the first-order and second-order derivatives of the coefficient curves. Based on the detected jump points, a coefficient curve estimation procedure is also proposed, which can preserve the jump structure well when the noise level is small. Further, the implementation of turning parameters is discussed. Under some mild conditions, the asymptotic properties of the proposed estimators are established not only in the continuous regions of coefficient functions, but also in the neighborhoods of the jump points. Finally, we demonstrate, using both simulation and empirical examples, that the proposed methodologies perform well.

Suggested Citation

  • Yan-Yong Zhao & Jin-Guan Lin & Hong-Xia Wang & Xing-Fang Huang, 2017. "Jump-detection-based estimation in time-varying coefficient models and empirical applications," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(3), pages 574-599, September.
    • Handle: RePEc:spr:testjl:v:26:y:2017:i:3:d:10.1007_s11749-017-0525-7
    DOI: 10.1007/s11749-017-0525-7
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    Cited by:

    1. Čížek, Pavel & Koo, Chao Hui, 2021. "Jump-preserving varying-coefficient models for nonlinear time series," Econometrics and Statistics, Elsevier, vol. 19(C), pages 58-96.
    2. Koo, Chao, 2018. "Essays on functional coefficient models," Other publications TiSEM ba87b8a5-3c55-40ec-967d-9, Tilburg University, School of Economics and Management.
    3. Zhao, Yan-Yong & Lin, Jin-Guan, 2019. "Estimation and test of jump discontinuities in varying coefficient models with empirical applications," Computational Statistics & Data Analysis, Elsevier, vol. 139(C), pages 145-163.
    4. Čížek, Pavel & Koo, Chao Hui, 2021. "Jump-preserving varying-coefficient models for nonlinear time series," Econometrics and Statistics, Elsevier, vol. 19(C), pages 58-96.
    5. Han, Zhong-Cheng & Lin, Jin-Guan & Zhao, Yan-Yong, 2020. "Adaptive semiparametric estimation for single index models with jumps," Computational Statistics & Data Analysis, Elsevier, vol. 151(C).

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