A structural time series model with explanatory variables collapses to a standard regression model when the stochastic components other than the irregular term are dropped. Thus many of the concepts and modelling procedures associated with regression are relevant to the models considered in this chapter. Some of these ideas, particularly those developed in econometrics, are reviewed in section 7.1 and an indication is given as to how they fit in with the structural approach to time series modelling.

Estimation of structural models with explanatory variables is covered in section 7.3. The preceding section lays some of the groundwork by reviewing the methods by which classical regression models may be estimated in the frequency domain. The tests set out in section 7.4 are essentially generalisations of the tests given in chapter 5 and modifications of tests used in regression. A model selection strategy is developed in section 7.5. The applications illustrate how some of the key ideas concerning model selection used in econometrics can be taken on board in the structural approach. This methodology is extended to modelling the effects of interventions in section 7.6 and a number of new diagnostics specifically designed for interventions are introduced.