Regime Switching GARCH Models

We develop univariate regime-switching GARCH (RS-GARCH) models wherein the con- ditional variance switches in time from one GARCH process to another. The switching is governed by a time-varying probability, specifled as a function of past information. We provide su-cient conditions for geometric ergodicity and existence of moments. Because of path dependence, maximum likelihood estimation is not feasible. By enlarging the pa- rameter space to include the state variables, Bayesian estimation using a Gibbs sampling algorithm is feasible. We apply this model using the NASDAQ daily return series.