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If the parameters of a time-series process are subject to change over time, then a full description of the data-generating process must include a specification of the probability law governing these changes, for example, postulating that the parameters evolve according to the realization of an unobserved Markov chain. This article describes classical and Bayesian algorithms for estimation and inference in such models and discusses some of the issues that arise in particular cases such as GARCH and state-space models.
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