Global Total Least Squares: A Method for the Construction of Open Approximate Models from Vector Time Series |
Contents
Introduction | 1 |
GTLS Models | 9 |
Evaluation of the Misfit | 53 |
Copyright | |
6 other sections not shown
Common terms and phrases
Appendix approximation error asymptotically stable auxiliary inputs basis transformation canonical correlations components consider corresponding dashed line defined Definition denote described determine deviations difference equations dimension dynamic effect equals equivalent finite intervals follows Gauss-Newton algorithm given system GTLS approach GTLS criterion GTLS method GTLS model GTLS problem Hankel matrices i/s/o-representation impulse response îN+1 initial models input/output instant isometric state representations ISR's iterative Lemma linear space locally optimal matrix minimal model class model improvement constructions norm observation interval observed time series optimal approximation order GTLS model orthogonal complement orthogonal projection output parameters past and future periodic phenomenon Proof of Proposition recursive relative misfit restrictions sample interval Section shift-invariant singular values solution SR's stabilizable static stationary point stochastic system trajectory term interest rates Theorem time-invariant total least squares unitary unitary matrix validation interval zero