This paper has been prepared for Handbook of Applied Economic Statistics, edited by David Giles and Aman Ullah. It considers a particular class of single-equation nonlinear multivariate models called smooth transition regression (STR) models. Inference in these models, including testing linearity against STR and testing Granger noncausality, is discussed. A modelling cycle, consisting of the specification, estimation, and evaluation of these models is presented and its different stages considered in detail. Model encompassing also receives attention. Furthermore, the chapter contains a previously unpublished empirical application of the STR model to modelling UK housing price expectations. This example illustrates the workings of the modelling cycle and possible usefulness of the STR model in dynamic macroeconomic modelling.
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