Change Point Detection for Nonparametric Regression under Strongly Mixing Process

TL;DR

This paper proposes a nonparametric change point detection method for dependent data using a maximum-CUSUM approach, demonstrating strong consistency and robustness, with applications to financial data showing structural changes during 2007-2009.

Contribution

It introduces a novel CUSUM-based estimator for change points in nonparametric regression with dependent observations, proving its consistency and robustness.

Findings

The method accurately detects change points under dependent data.

The estimator is strongly consistent in various scenarios.

Application to Nasdaq 100 data reveals structural changes during 2007-2009.

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.