Margin-closed regime-switching multivariate time series models

A regime-switching multivariate time series model which is closed under margins is built. The model imposes a restriction on all lower-dimensional sub-processes to follow a regime-switching process sharing the same latent regime sequence and having the same Markov order as the original process. The margin-closed regime-switching model is constructed by considering the multivariate margin-closed Gaussian VAR($k$) dependence as a copula within each regime, and builds dependence between observations in different regimes by requiring the first observation in the new regime to depend on the last observation in the previous regime. The property of closure under margins allows inference on the latent regimes based on lower-dimensional selected sub-processes and estimation of univariate parameters from univariate sub-processes, and enables the use of multi-stage estimation procedure for the model. The parsimonious dependence structure of the model also avoids a large number of parameters under the regime-switching setting. The proposed model is applied to a macroeconomic data set to infer the latent business cycle and compared with the relevant benchmark.