Abstract: Considering the problems of change-points estimation and model selection for nonstationary time series such as piecewise stationary autoregressive (PSAR) processes, a method which can simultaneously conduct change-point estimation and model selection with a two-stage LASSO (TS-LASSO) algorithm based on the existing method to transform the problem of change-points estimation into the problem of variable selection was proposed. Specifically, in the first stage, the preliminary estimation of change-points and the selection of the models can be derived by LASSO algorithm. Then, in the second stage, a modified adaptive LASSO algorithm was used to screen the overestimated results, so the consistent estimation could be obtained and the accurate model could be selected. The large sample properties of the results for the variable-point estimation. In addition, the TS-LASSO algorithm can also achieve the estimation and recognition for the mean change-points sequences and no change-points sequences in special cases effectively. Finally, combined with the test of different type of simulative sequences and the case study of a seismic wave data, it was shown that TS-LASSO algorithm is effective and has certain practicability.

Key words: piecewise stationary autoregressive, change-points estimation, model selection, adaptive LASSO