Detection of Change Points in Volatility of Non-Parametric Regression by Wavelets

This paper studies the detection and estimation of change points in volatility under nonparametric regression models. Wavelet methods are applied to construct the test statistics which can be used to detect change points in volatility. The asymptotic distributions of the test statistics are established. We also utilize the test statistics to construct the estimators for the locations and jump sizes of the change points in volatility. The asymptotic properties of these estimators are derived. Some simulation studies are conducted to assess the finite sample performance of the proposed procedures.