Wavelet Identification of Structural Change Points in Volatility Models for Time Series

We propose two estimators, an integral estimator and a discretized estimator, for the wavelet coefficient of volatility in time series models. These estimators can be used to detect the changes of volatility in time series models. The location estimators of the jump points, we proposed, have been shown to have the minimax convergence rate, which is the optimal rate for the estimation of change points. The jump sizes and locations of change points can be consistently estimated by wavelet coefficients. The convergency rates of these estimators are derived and the asymptotic distributions of the statistics are established.