Change point detection for nonparametric regression under strongly mixing process

Qing Yang (), Yu-Ning Li () and Yi Zhang ()
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Qing Yang: Zhejiang University
Yu-Ning Li: Zhejiang University
Yi Zhang: Zhejiang University

Statistical Papers, 2020, vol. 61, issue 4, No 6, 1465-1506

Abstract: Abstract In this article, we consider the estimation of the structural change point in the nonparametric model with dependent observations. We introduce a maximum-CUSUM-estimation procedure, where the CUSUM statistic is constructed based on the sum-of-squares aggregation of the difference of the two Nadaraya-Watson estimates using the observations before and after a specific time point. Under some mild conditions, we prove that the statistic tends to zero almost surely if there is no change, and is larger than a threshold asymptotically almost surely otherwise, which helps us to obtain a threshold-detection strategy. Furthermore, we demonstrate the strong consistency of the change point estimator. In the simulation, we discuss the selection of the bandwidth and the threshold used in the estimation, and show the robustness of our method in the long-memory scenario. We implement our method to the data of Nasdaq 100 index and find that the relation between the realized volatility and the return exhibits several structural changes in 2007–2009.

Keywords: Change point detection; CUSUM statistic; Nonparametric regression; Strongly mixing process; Structural change; Primary 62G05; Secondary 62G08; 62G20; 62M10 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (5)

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DOI: 10.1007/s00362-020-01196-y

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