Regime-Switching Models

Econometrics Toolbox™ supports nonlinear models that describe the dynamic behavior of economic time series variables in the presence of structural breaks or regime changes. The models have two main components: a discrete state-space variable S_t representing the regime series, and a collection of dynamic regression (ARX or VARX) submodels that describe the dynamic behavior of the univariate or multivariate time series Y_t within each regime. S_t is a fixed set of values or a random variable.

The threshold-switching dynamic regression model treats S_t as a fixed variable. The level of an observed threshold variable determines the regime at time t (the value of S_t), but threshold values that determine when regimes shift are unknown parameters. The threshold variable can be exogenous or endogenous, and transitions between states can be abrupt or smooth.

The Markov-switching dynamic regression model treats S_t as a latent, random discrete-time Markov chain, which is a state-space Markov process represented by a directed graph and described by a right-stochastic transition matrix P. The distribution of states at time t + 1 is the distribution of states at time t multiplied by P. The structure of P determines the evolutionary trajectory of the chain, including asymptotics.