From time series to linear system:Part II. Exact modelling

In the second part of this paper the problem of finding an exact model for a q-dimensional infinite time series is considered. First a mathematical vocabulary for discussing exact modelling is developed. It is then shown how the results of Part I guarantee the existence of a most powerful (AR) model for an observed time series. Two algorithms for obtaining such an (AR) model are subsequently derived. One of these algorithms gives a shortest lag input/output model. The problem of obtaining a minimal state space realization of the observed time series is also considered. In order to do that, realization theory based on the truncated behaviour is developed. As an extensive example, the classical situation with impulse response measurements is discusse