S-estimation of hidden Markov models

A method for robust estimation of dynamic mixtures of multivariate distributions is proposed. The EM algorithm is modified by replacing the classical M-step with high breakdown S-estimation of location and scatter, performed by using the bisquare multivariate S-estimator. Estimates are obtained by solving a system of estimating equations that are characterized by component specific sets of weights, based on robust Mahalanobis-type distances. Convergence of the resulting algorithm is proved and its finite sample behavior is investigated by means of a brief simulation study and n application to a multivariate time series of daily returns for seven stock markets.