A unified approach to nonlinearity, structural change, and outliers

• Published in: Journal of econometrics Vol. 137; no. 1; pp. 112 - 133
• Main Authors: Giordani, Paolo, Kohn, Robert, van Dijk, Dick
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.03.2007; Elsevier; Elsevier Sequoia S.A
• Series: Journal of Econometrics
• Subjects: Applications; Applied sciences; Bayesian analysis; Bayesian inference; Bayesian method; Business cycle asymmetry; Business cycles; Exact sciences and technology; Inference from stochastic processes; time series analysis; Insurance, economics, finance; Markov analysis; Markov-switching models; Markovian processes; Mathematics; Non-linear models; Nonlinear programming; Normal distribution; Operational research and scientific management; Operational research. Management science; Probability and statistics; Sciences and techniques of general use; State-space models; Statistics; Studies; Threshold models; Time series; Business cycle asymmetry; C11; C22; E32; Threshold models; Markov-switching models; Bayesian inference; State-space models; Industrial production; Growth rate; Industrial application; Bayes inference; Linear model; Markov chain; Outlier; Estimator efficiency; Production rate; Dynamics; Dynamic model; Bayes estimation; Mixed distribution; Monte Carlo method; Time series; Statistical estimation; Markov model; State space method; Switching; Statistical method; Non linear model; Instability; Nonlinearity; Econometrics; Handling
• ISSN: 0304-4076; 1872-6895
• DOI: 10.1016/j.jeconom.2006.03.013

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.