Detection of the jump points of a heteroscedastic regression model by wavelets

Wavelets are applied to detect the jumps in a heteroscedastic regression model. By the empirical wavelet coefficients of the conditional mean and the conditional variance of the time series under consideration, it is shown that the wavelet coefficients exhibit high peaks near the jump points, based on which a procedure is developed to identify and then to locate the jumps. All estimators are proved to be consistent.