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Change point estimators by local polynomial fits under a dependence assumption

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  • Lin, Zhengyan
  • Li, Degui
  • Chen, Jia

Abstract

We study a random design regression model generated by dependent observations, when the regression function itself (or its [nu]-th derivative) may have a change or discontinuity point. A method based on the local polynomial fits with one-sided kernels to estimate the location and the jump size of the change point is applied in this paper. When the jump location is known, a central limit theorem for the estimator of the jump size is established; when the jump location is unknown, we first obtain a functional limit theorem for a local dilated-rescaled version estimator of the jump size and then give the asymptotic distributions for the estimators of the location and the jump size of the change point. The asymptotic results obtained in this paper can be viewed as extensions of corresponding results for independent observations. Furthermore, a simulated example is given to show that our theory and method perform well in practice.

Suggested Citation

  • Lin, Zhengyan & Li, Degui & Chen, Jia, 2008. "Change point estimators by local polynomial fits under a dependence assumption," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2339-2355, November.
    • Handle: RePEc:eee:jmvana:v:99:y:2008:i:10:p:2339-2355
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    References listed on IDEAS

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    1. Grégoire, Gérard & Hamrouni, Zouhir, 2002. "Change Point Estimation by Local Linear Smoothing," Journal of Multivariate Analysis, Elsevier, vol. 83(1), pages 56-83, October.
    2. Chen, Gongmeng & Choi, Yoon K. & Zhou, Yong, 2005. "Nonparametric estimation of structural change points in volatility models for time series," Journal of Econometrics, Elsevier, vol. 126(1), pages 79-114, May.
    3. Cai, Zongwu, 2002. "Regression Quantiles For Time Series," Econometric Theory, Cambridge University Press, vol. 18(1), pages 169-192, February.
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    Cited by:

    1. Yujiao Yang & Qiongxia Song, 2014. "Jump detection in time series nonparametric regression models: a polynomial spline approach," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(2), pages 325-344, April.
    2. Yuping Song & Min Zhu & Jiawei Qiu, 2024. "Asymptotic Normality of Bias Reduction Estimation for Jump Intensity Function in Financial Markets," Journal of Time Series Analysis, Wiley Blackwell, vol. 45(4), pages 558-583, July.

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