W e analyze a class o f state space identification algorithms for time series, based on canonical correlation analysis in the ligth o f recent results on stochastic systems theory called « subspace methods ». These can be describe as covariance estimation followed by 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 into the solution o f Riccati equation but introduce at the same

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... me some nontrivial mathematical problems related to positivity. The states o f the forward-backward innovations representation have an interpretation: Instrumental Variables estimators.