Structural breaks estimation for non-stationary time series signals

In this work we consider the problem of modeling a class of nonstationarv time series signals using piecewise autoregressive (AR) processes. The number and locations of the piecewise autoregressive segments. as well as the orders of the respective AR processes, are assumed to be unknown. The minimum description length principle is applied to find the "best" combination of the number of the segments, the lengths of the se2ruents, and the orders of the piecewise AR processes. A genetic algorithm is implemented to solve this difficult optimization problem. We term the resulting procedure Auto-PARM. Numerical results from both simulation experiments and real data analysis show that Auto-PARM enjoys excellent empirical properties. Consistency of Auto-PARM for break point estimation can also be shown.