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Switching regression models are models that allow §parameters of the conditional distribution, such as §the mean and variance, to vary according to a finite-§valued stochastic process with states or regimes. §The regime changes aim at capturing changes in the §underlying financial and economic mechanism through §the observed time series. These models have proven §very useful in modeling economic and financial time §series. §In this book, we generalized this modeling approach. §We consider models that allow occasional, recurrent §and independent switches in disjoint subsets of the §parameters of the conditional distribution. These §are determined by the realization of several latent §state variables. The state variable probabilities §can be constant or change over time. We call these §extended switching regression models. We develop an §EM algorithm for estimation, give conditions for §consistency and asymptotic normality and apply our §models to combine conditional volatility forecasts §of several exchange rates. We also consider the §penalized likelihood method for selecting the §correct latent structure of these models.
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