Nonlinear regime-switching behavior and structural change are often perceived as competing alternatives to linearity. In this article we study the so-called time-varying smooth transition autoregressive (TV-STAR) model, which can be used both for describing simultaneous nonlinearity and structural change and for distinguishing between these features. Two modeling strategies for empirical specification of TV-STAR models are developed. Monte Carlo simulations show that neither of the two strategies dominates the other. A specific-to-general-to-specific procedure is best suited for obtaining a first impression of the importance of nonlinearity and/or structural change for a particular time series. A specific-to-general procedure is most useful in careful specification of a model with nonlinear and/or time-varying properties. An empirical application to a large dataset of U.S. macroeconomic time series illustrates the relative merits of both modeling strategies.

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Journal of Business and Economic Statistics
Erasmus Research Institute of Management

Lundbergh, S., Terasvirta, T., & van Dijk, D. (2003). Time-Varying Smooth Transition Autoregressive Models. Journal of Business and Economic Statistics, 21(1), 104–121. doi:10.1198/073500102288618810