Perfect synchronization, that is a common single cycle governing all variables, is almost uniformly accepted assumption when multivariate regime-switching models are considered. Although this assumption is relaxed in some studies, this relaxation comes with various limitations regarding the number of regimes as well as the dynamics of covariance matrix. In this paper, we develop a general flexible framework where we can simultaneously estimate the degree of synchronization together with the regimes, without imposing any restriction on the number of regimes as well on the variance dynamics. In two empirical illustrations using macroeconomic and financial data we document the potential of our framework. We show that a three regimes model of business cycle where the additional “severe recession” regime of the composite leading indicator leads that of industrial production by 6.5 months explains the data better than the two regimes models with only “recession” and “expansion” regimes.
In financial application we show that large-cap portfolio excess returns lead that of small-cap portfolio by one month during “normal” times, whereas in “turbulent” times both portfolios evolve simultaneously.