Multivariate time series models, control groups and intervention analysis.

A multivariate structural time series model made up of unobserved components such as trends and seasonals is formulated. A homogeneous system, in which any linear combination of the observations follows the same time series process, is shown to correspond to a multivariate structural model in which the covariance matrices of the disturbances are proportional an intervention variable is introduced into a univariate structural model and then into a multivariate model.