MCMC-based estimation of Markov Switching ARMA-GARCH models

Regime switching models, especially Markov Switching (MS) models, are regarded as a promising way to capture nonlinearities in time series. Combining the elements of MS models with full Autoregressive Moving Average-Generalized Autoregressive Conditional Heteroskedasticity (ARMA-GARCH) models poses severe difficulties for the computation of parameter estimators. Existing methods 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 MS-ARMA-GARCH model and its Bayes estimator. 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 simulated data and with returns from the New York Stock Exchange (NYSE). Our model is then compared to other approaches and clearly proves to be advantageous.