Multiple Chains Hidden Markov Models for Bivariate Dynamical Systems

We present a new modelling framework for the bi-variate hidden Markov model. The proposed specification is composed by five latent Markovian chains which drive the evolution of the parameters of a bi-variate Gaussian distribution. The maximum likelihood estimator is computed via an expectation conditional maximization algorithm with closed form conditional maximization steps, specifically developed for our model. Identification of model parameters, as well as consistency and asymptotic Normality of the maximum likelihood estimator are discussed. Finite sample properties of the estimator are investigated in an extensive simulation study. An empirical application with the bi-variate series of US stocks and bond returns illustrates the benefits of the new specification with respect to the standard hidden Markov model.