ABSTRACT
The use of discrete and continuous mixtures of distributions of tractable forms, such as mixtures of normals, is pervasive in time series analysis and forecasting, as in many other areas. Mixtures arise broadly as components of practical models, and mixture structure is often usefully exploited in model analysis and fitting. This chapter discusses a selection of mixture models that we have found useful in specific applied settings, pointing the reader to several key references. Extensive development of several mixture modeling approaches in time series and forecasting — of relevance more broadly in statistical analysis — are introduced and covered in several chapters of West and Harrison (1997), with references. The more recent book on finite mixtures and Markov switching models, Fru¨hwirth-Schnatter (2006), is a key reference that deals with theory, inference, and application of finite mixture models for temporal and nontemporal data. In particular, Bayesian inference for Markov switching models and switching state-space models as well as related theory and examples are discussed in Chapters 10 to 13 of Fru¨hwirth-Schnatter (2006) and further references therein.
