Estimation for mixtures of Markov processes

Finite mixtures of Markov processes with densities belonging to exponential families are introduced. Quasi-likelihood and maximum likelihood methods are used to estimate the parameters of the mixing distributions and of the component distributions. The E-M algorithm is used to compute the ML estimates. Mixture of Autoregressive processes and of two-state Markov chains are discussed as specific examples. Simulation results on the comparison of quasi-likelihood and ML estimates are reported.