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according to proposition algorithms anticausal appendix approximate modelling approximate system assumption autoregressive canonical forms chapter consider corollary corresponding corroboration covariance matrix ctol data consists defined in section definition 3-3 denote descriptive misfit deterministic time series dynamical systems equation structure etol exact modelling example exists follows given hence holds true HT(w identified model implies impulse response input Interpretation isometry lemma lexicographic ordering linear linear subspace linearly dependent matrix measure minimal realization model approximation model class modelling problem modelling procedures Moreover Notation observation optimal model order laws orthogonal orthonormal basis output parametrization phenomenon polynomial predictive misfit Proof of lemma Proof of proposition proof of theorem proposition 3-3 prove remarkable laws respect satisfied scattering representation series analysis shift invariant simulation singular value decomposition solution space specification step stochastic stochastic process subspace suppose surjective t-th order teZ+ tightest equation representation unique utility variables weB0 zero order