A modified canonical correlation approach to approximate state space modelling

The authors describe a procedure for modeling observed time series by means of a linear system. A system is characterized by its behavior, i.e., the set of all time series compatible with the system laws. The objective is to find a simple system that contains a time series that is close to the observed one. The dynamical relations between the variables are modeled in two steps. First, an approximate state trajectory is constructed, and then an approximate linear system is determined on the basis of the observed time series and its state trajectory. The structure of the resulting system, i.e., the decomposition of variables into inputs and outputs and the number of state variables, is not specified a priori, but is chosen on basis of the data. The authors consider some alternative ways to construct a state trajectory, using canonical correlation and singular value analysis. The resulting procedures are illustrated by some simulations