In discussing univariate models, it was argued that the nature of the problem allows fairly strong restrictions to be imposed. These restrictions are not normally enforced within the traditional ARIMA framework. In a multivariate set-up, the number of parameters to be estimated increases rapidly as more series are included and in a vector ARMA model the issues concerned with identifiability become quite complicated; see Hannan (1969). Hence it is even more important to formulate models which take account of the nature of the problem. Apart from saving on the number of parameters to be estimated, such models are also likely to provide more useful information on the dynamic properties of the series.

In section 1.3 a distinction was drawn between multivariate models for cross-sections of time series and multivariate models for interactive systems. This distinction is important in considering the kind of multivariate structural time series models to be entertained. For cross-sections of time series, the class of univariate structural time series models generalises in a rather natural way, as discussed in sections 8.2 to 8.4. However, the fact that several series are now being modelled together suggests the possibility of common factors. Models of this kind are introduced in section 8.5. Section 8.6 examines the way in which control groups can be handled within the statistical framework of multivariate structural time series models, while section 8.7 looks at the handling of various data irregularities.