Canonical correlation in multivariate time series analysis

We analyze a class o f state space identification algorithms for time series, based on canonical correlation analysis in the ligth of recent results on stochastic systems theory calle d « subspace methods » .These can be describe as covariance estimation followed b y stochastic realization .The methods offer the major advantage o f converting the nonlinear parameter estimation phase in traditional V A R M A models identification in to the solution o f Riccati equation but introduce at the same time some no n trivial mathematical problem s related to positivity. The states o f the forward -backward innovations representation have an interpretation : Instrumental Variables estimators