This paper develops a Markov-Switching vector autoregressive model that allows for imperfect synchronization of cyclical regimes in multiple variables, due to phase shifts of a single common cycle. The model has three key features: (i) the amount of phase shift can be different across regimes (as well as across variables), (ii) it allows the cycle to consist of any number of regimes J is larger than or equal to 2, and (iii) it allows for regime-dependent volatilities and correlations. In an empirical application to monthly returns on size-based stock portfolios, a three-regime model with asymmetric phase shifts and regime-dependent heteroscedasticity is found to characterize the joint distribution of returns most adequately. While large- and small-cap portfolios switch contemporaneously into boom and crash regimes, the large-cap portfolio leads the small-cap portfolio for switches to a moderate regime by a month.

Bayesian analysis, imperfect synchronization, phase shifts, regime-switching models
Bayesian Analysis (jel C11), Time-Series Models; Dynamic Quantile Regressions (jel C32), Model Construction and Estimation (jel C51), Model Evaluation and Testing (jel C52)
Tinbergen Institute
Tinbergen Institute Discussion Paper Series
Discussion paper / Tinbergen Institute
Tinbergen Institute

Cakmakli, C, Paap, R, & van Dijk, D.J.C. (2010). Modeling and Estimation of Synchronization in Multistate Markov-Switching Models (No. TI 2011-002/4). Discussion paper / Tinbergen Institute. Tinbergen Institute. Retrieved from