This paper surveys recent developments related to the smooth transition autoregressive (STAR) time series model and several of its variants. We put emphasis on new methods for testing for STAR nonlinearity, model evaluation, and forecasting. Several useful extensions of the basic STAR model, which concern multiple regimes, time-varying non-linear properties, and models for vector time series, are also reviewed.

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Keywords Analysis of variance, Aregression (Statistics), Econometric models, Empirical research, Forecasting, Impulse response analysis, Model evaluation, Nonlinear theories, Regime-switching models, Time series model specification, Time-series analysis, Vector analysis
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Journal Econometric Reviews
van Dijk, D.J.C, Terasvirta, T, & Franses, Ph.H.B.F. (2002). Smooth transition autoregressive models - a survey of recent developments. Econometric Reviews, 1–47. doi:10.1081/ETC-120008723