Bayesian inference in dynamic models with latent factors

In time series analysis, latent factors are often introduced to model the heterogeneous time evolution of the observed process. The presence of unobserved components makes the maximum likelihood estimation method more difficult to apply. Thus a Bayesian approach is sometimes preferable since it allows to treat general state space models and makes easier the simulation based approach to parameters estimation and latent factors filtering. The paper examines economic time series models in a Bayesian perspective focusing, through some examples, on the extraction of the Business Cycle components like cycle and trend. We briefly review some general univariate and multivariate Bayesian dynamic models and discuss the simulation based techniques, such as Gibbs sampling, adaptive importance sampling and particle filter, useful for parameter estimation and latent factor extraction.