Markov Switching

Markov switching models are a family of models that introduces time variation in the parameters in the form of their state, or regime-specific values. This time variation is governed by a latent discrete-valued stochastic process with limited memory. More specifically, the current value of the state indicator is determined by the value of the state indicator from the previous period only implying the Markov property. A transition matrix characterizes the properties of the Markov process by determining with what probability each of the states can be visited next period conditionally on the state in the current period. This setup decides on the two main advantages of the Markov switching models: the estimation of the probability of state occurrences in each of the sample periods by using filtering and smoothing methods and the estimation of the state-specific parameters. These two features open the possibility for interpretations of the parameters associated with specific regimes combined with the corresponding regime probabilities. The most commonly applied models from this family are those that presume a finite number of regimes and the exogeneity of the Markov process, which is defined as its independence from the model’s unpredictable innovations. In many such applications, the desired properties of the Markov switching model have been obtained either by imposing appropriate restrictions on transition probabilities or by introducing the time dependence of these probabilities determined by explanatory variables or functions of the state indicator. One of the extensions of this basic specification includes infinite hidden Markov models that provide great flexibility and excellent forecasting performance by allowing the number of states to go to infinity. Another extension, the endogenous Markov switching model, explicitly relates the state indicator to the model’s innovations, making it more interpretable and offering promising avenues for development.