Change Point Detection for Nonparametric Regression under Strongly Mixing Process
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In this article, we consider 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 sum-of-squares aggregation of the difference of 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 if there is no change, and is larger than a threshold otherwise. Furthermore, we demonstrate the almost surely convergency of the change point estimator. In the simulation, we discuss the selection of bandwidth and threshold used in the estimation, and show the robustness of our method in the long memory scenario. We implement our method to Nasdaq 100 index data and find that the relation between the realized volatility and the return exhibits several structural changes in 20072009.
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