  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.
