This article provides a comprehensive survey of the time series models employed for the econometric analysis of business cycles. In the first half, we explain the Markov switching (MS) model and its Bayesian estimation using Markov chain Monte Carlo. We also survey the extensions of the MS model and the other econometric models for business cycles. In the latter half, we extend the MS model such that the error term follows the Student’s t-distribution, the error variance follows a stochastic volatility model, and structural changes are allowed. We apply these extended models as well as the simple MS model to the composite index in Japan.
