MCMC Based Estimation of Markov

Regime switching models, especially Markov switching models, are regarded as a promising way to capture nonlinearities in time series. Combining the elements of Markov switching models with full ARMA-GARCH models poses severe difficulties for the computation of parameter estimators. Existing meth-ods can become completely unfeasible due to the full path dependence of such models. In this article we demonstrate how to overcome this problem. We formulate a full Markov switching ARMA-GARCH model and its Bayes es-timator. This facilitates 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 simu-lated data and with returns from the New York Stock Exchange. Our model is then compared to other variants and proves clearly to be advantageous