Illustrations and Extensions of Standard DLMS

Abstract

In the preceding Chapters the focus has been on the theoretical structure and analysis of DLMs with little reference to practical aspects of modelling. Here we switch the focus to the latter to consolidate what has been developed in theory, illustrating many basic concepts via analyses of typical datasets. We consider both retrospective analysis of a time series as well as forecasting with an existing model, and describe a variety of modelling activities using the class of models built up from the trend, seasonal and regression components of Chapters 7, 8 and 9. Together these three components provide for the majority of forms of behaviour encountered in commercial and economic areas, and thus this class, of what may be referred to as standard models, forms a central core of structures for the time series analyst. In approaching the problem of modelling a new series, the basic trend and seasonal components are a useful first attack. If retrospective analysis is the primary goal, then these simple and purely descriptive models may be adequate in themselves, providing estimates of the trend (or deseasonalised series), seasonal pattern (detrended series) and irregular or random component over time. In addition to retrospective time series decomposition, these models can prove adequate for forecasting in the short term. The inclusion of regression terms is the next step, representing an attempt to move away from simple descriptions via explanatory relationships with other variables. Linking in such variables is also the route to firmer, more credible and reliable short/medium-term forecasting, the key idea being that future changes in a series not catered for within a simpler trend/seasonal description may be adequately predicted (at least qualitatively) by one or a small number of regression variables. Identifying the important variables is, of course and as usual in statistics generally, the major problem.