MCMC methods for the estimation of MS-ARMA-GARCH Models

Regime Switching models, especially Markov switching models, are regarded as a promising way to capture nonlinearities in time series. They can account for sudden changes in the structure of the mean or the variance of a process and give a straightforward interpretation of these shifts. Such shifts would cause regu-lar ARMA-GARCH models to imply non-stationary processes. Combining the ele-ments of Markov switching models with full ARMA-GARCH models poses severe difficulties when it comes to understanding their dynamic properties and for the computation of parameter estimators. Maximum Likelihood estimation can become completely unfeasible due to the full path dependence of such models. Estimation methods such as the EM algorithm can be used for the ML estimation of sim-ple Markov switching AR-ARCH models but become unfeasible if MA or GARCH components are introduced. In this article we formulate a full Markov switching ARMA-GARCH model and estimate based on the Bayesian framework. This facil-itates the use of Markov Chain Monte Carlo methods and allows us to develop an algorithm to compute the Bayes estimator of the regimes and parameters of our model. The approach is illustrated on simulated data and with returns from the New York Stock exchange. Our model is then compared to MS-AR-ARCH variants and proves clearly to be advantageous