Model specification

Abstract

This chapter is devoted to the description of specific classes of DLMs that, alone or in combinations, are most often used to model univariate or multivariate time series. The additive structure of DLMs makes it easy to think of the observed series as originating from the sum of different components, a long term trend and a seasonal component, for example, possibly subject to an observational error. The basic models introduced in this chapter are in this view elementary building blocks in the hands of the modeler, who has to combine them in an appropriate way to analyze any specific data set. The focus of the chapter is the description of the basic models together with their properties; estimation of unknown parameters will be treated in the following chapter. For completeness we include in Section 3.1 a brief review of some traditional methods used for time series analysis. As we will see, those methods can be cast in a natural way in the DLM framework.