This paper demonstrates that the class of conditionally linear and Gaussian state-space models offers a general and convenient framework for simultaneously handling nonlinearity, structural change and outliers in time series. Many popular nonlinear time series models, including threshold, smooth transition and Markov-switching models, can be written in state-space form. It is then straightforward to add components that capture parameter instability and intervention effects. We advocate a Bayesian approach to estimation and inference, using an efficient implementation of Markov Chain Monte Carlo sampling schemes for such linear dynamic mixture models. The general modelling framework and the Bayesian methodology are illustrated by means of several examples. An application to quarterly industrial production growth rates for the G7 countries demonstrates the empirical usefulness of the approach.

Bayesian inference, Business cycle asymmetry, Markov-switching models, State-space models, Threshold models
Bayesian Analysis (jel C11), Time-Series Models; Dynamic Quantile Regressions (jel C22), Business Fluctuations; Cycles (jel E32),
Econometric Institute Reprint Series
Journal of Econometrics
Erasmus Research Institute of Management

Giordani, P, Kohn, R, & van Dijk, D.J.C. (2007). A unified approach to nonlinearity, structural change, and outliers. Journal of Econometrics, 137(1), 112–133. doi:10.1016/j.jeconom.2006.03.013