Identification, Estimation and Specification in a Class of Semi-Linear Time Series Models

In this paper, we consider some identification, estimation and specification problems in a class of semi-linear time series models. Existing studies for the stationary time series case have been reviewed and discussed. We also establish some new results for the integrated time series case. In the meantime, we propose a new estimation method and establish a new theory for a class of semi-linear nonstationary autoregressive models. In addition, we discuss certain directions for further research.