Econometrics: Models of Regime Changes

Abstract

Filtered probability of a regime The probability that the unobserved Markov chain for a Markov-switching model is in a particular regime in period t, conditional on observing sample information up to period t. Gibbs sampler An algorithm to generate a sequence of samples from the joint probability distribution of a group of random variables by repeatedly sampling from the full set of conditional distributions for the random variables. Markov chain A process that consists of a finite number of states, or regimes, where the probability of moving to a future state conditional on the present state is independent of past states. Markov-switching model A regime-switching model in which the shifts between regimes evolve according to an unobserved Markov chain. Regime-Switching Model A parametric model of a time series in which parameters are allowed to take on different values in each of some fixed number of regimes. Smooth transition threshold model A threshold model in which the effect of a regime shift on model parameters is phased in gradually, rather than occurring abruptly. Smoothed probability of a regime The probability that the unobserved Markov chain for a Markov-switching model is in a particular regime in period t, conditional on observing all sample information. Threshold model A regime-switching model in which the shifts between regimes are triggered by the level of an observed economic variable in relation to an unobserved threshold. Time-varying transition probability A transition probability for a Markov chain that is allowed to vary depending on the outcome of observed information. Transition probability The probability that a Markov chain will move from state j to state i.