Markov chain Monte Carlo methods for parameter estimation in multidimensional continuous time Markov switching models

We present Markov chain Monte Carlo methods for estimating parameters
of multidimensional, continuous time Markov switching models.
The observation process can be seen as a diffusion, where drift
and volatility coefficients are modeled as continuous time, finite state Markov chains with a common state process. The states for drift and volatility and the rate matrix of the underlying Markov chain have
to be estimated. Applications to simulated data indicate that the
proposed algorithm can outperform the expectation maximization algorithm
for difficult cases, e.g. for high rates. Application to financial
market data shows that the Markov chain Monte Carlo method indeed
provides sufficiently stable estimates.