ANALYSIS OF TIME SERIES WITH MULTIPLE SHIFTS OF LEVELS AND VOLATILITIES

A practical time series model is proposed with multiple shifts of levels and volatilities to overcome the intrinsic limitations of hidden Markov models used to capture change-point type behaviors of data. This model allows the set of level change points to be different from the set of volatility change points. Least square methods are then applied to the model to estimate level and volatility change points, those levels and volatilities. Asymptotic properties of the estimators, including their consistency, convergence rates and asymptotic distributions, are established under relatively weak conditions. Some simulations are carried out, showing that this model, its inference methods, and the asymptotic theory work quite well.