Multiple Chains Markov Switching Vector Autoregression

Both the U.S. stock and bond returns exhibit distinct Markovian regimes. However, because these regimes display limited coherence, conventional models typically require highly parameterized systems to adequately capture their joint distribution. This paper proposes a novel framework for the bivariate MS-VAR model that more effectively characterizes the regime dynamics of U.S. stock and bond returns. The specification leverages six latent Markov chains to govern the evolution of the model's parameters. Empirical evidence shows that this approach delivers more interpretable estimates of conditional moments and yields more informative decoding of the latent states than the standard MS-VAR model. The maximum likelihood estimator is implemented via an expectation-conditional maximization algorithm with closed-form conditional maximization steps. Moreover, the large-sample properties of the estimator are formally established.