Generalized exponential autoregressive models for nonlinear time series: Stationarity, estimation and applications

The generalized exponential autoregressive (GExpAR) models are extensions of the classic exponential autoregressive (ExpAR) model with much more flexibility. In this paper, we first review some development of the ExpAR models, and then discuss the stationary conditions of the GExpAR model. A new estimation algorithm based on the variable projection method is proposed for the GExpAR models. Finally, the models are applied to two real-world time series modeling and prediction. Comparison results show that (i) the proposed estimation approach is much more efficient than the classic method, (ii) the GExpAR models are more powerful in modeling the nonlinear time series.