Chapter 8: Estimation and inference in threshold type regime switching models
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The recognition that linear time series models may be too restrictive to capture economically interesting asymmetries and empirically observed non-linear dynamics has over the past twenty years generated a vast research agenda on designing models which could capture such features while remaining parsimonious and analytically tractable. Models that are capable of capturing non-linear dynamics have also been the subject of a much earlier and extensive research led by statisticians as well as practitioners in fields as broad as biology, physics and engineering with a very wide range of proposed specifications designed to capture, model and forecast field specific phenomena (for example bilinear models, random coefficient models, state dependent models and so on). The amount of research that has been devoted to describing the non-linear dynamics of sunspot numbers and Canadian lynx data is an obvious manifestation of this quest (see Tong, 1990; Granger and Terasvirta, 1993; Hansen, 1999; Terasvirta et al., 2010, and references therein). A particular behaviour of interest to economists has been that of regime change or regime switching whereby the parameters of a model are made to change depending on the occurrence of a particular event, episode or policy (for example recessions or expansions, periods of low/high stock market valuations, low/high interest rates) but are otherwise constant within regimes.

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