Abstract
In this paper, first we give a brief introduction to the canonical correlation analysis (CCA) for two sets of random variables, and present a method of computing the canonical correlations by using the singular value decomposition (SVD). After introducing an innovation model, we state the stochastic realization problem, together with some definitions. We show that predictor spaces play the role of memory for exchange information between the past and future in stochastic dynamical systems. Then we review the classical balanced stochastic realization results based on the CCA between the past and future of a stationary time series. Moreover, defining the conditional canonical correlations between the past and future of a stochastic system in the presence of exogenous inputs, we derive a stochastic realization algorithm with exogenous inputs. A numerical result is also included.
