RegimeSwitchingModellen

Regime switching, also known as Markov-switching, is a class of time-series models that allow the underlying data-generating process to switch between a finite number of regimes. The regime is governed by a latent state variable s_t taking values in {1, ..., K}, evolving according to a Markov chain with transition probabilities p_{ij} = P(s_t = j | s_{t-1} = i). Conditional on the current regime, the observation y_t follows regime-specific dynamics, such as a regime-dependent mean, autoregressive coefficients, or volatility. A simple example is a two-regime autoregression: y_t = μ_{s_t} + φ_{s_t} y_{t-1} + ε_t, with ε_t ~ N(0, σ^2_{s_t}) and regime-dependent parameters (μ_i, φ_i, σ_i).

Estimation commonly uses maximum likelihood via the Hamilton filter, an efficient recursion for the filtered and smoothed probabilities of regimes; the EM algorithm or Bayesian methods are also used. The framework was popularized by James D. Hamilton in 1989 to model business-cycle shocks, and has since been applied in macroeconomics, finance, and other fields to capture regime shifts in growth, inflation, volatility, and risk premia.

Key features include abrupt, probabilistic regime changes, the possibility of regime durations implied by the Markov chain, and a natural way to model nonlinearities that arise from switching dynamics. Variants include regime-switching autoregressions (MS-AR), regime-switching GARCH for volatility, and more flexible models with exogenous covariates or multiple regimes. Critics note potential identifiability issues, sensitivity to priors or initialization, and data requirements for reliable estimation.

Applications range from business-cycle analysis and monetary policy to stock-market regimes and commodity-price dynamics.