Multiple Chains Markov Switching Vector Autoregression

Abstract

The marginal distributions of US stocks and bond returns are characterized by well-defined Markovian regimes. Though, since there is very little coherence between these regimes, an highly parameterized system is usually estimated to properly describe their joint distribution. This paper proposes a new modelling framework for the bivariate MS-VAR model which better describes the US stocks and bond returns regimes. The proposed specification is composed by six latent Markov chains that drive the evolution of the parameters of the model. Results illustrate that the proposed specification provides more interpretable estimates of the conditional moments of the series and decoded latent variables with respect to the standard MS-VAR model. The maximum likelihood estimator is computed via an expectation conditional maximization algorithm with closed form conditional maximization steps. The large sample properties of the maximum likelihood estimator are established.

Keywords: Hidden Markov Models, Multiple Markov Chains, Expectation Conditional Maximization

JEL Classification: C32, C38, C51