Positivity conditions for stochastic state space modelling of time series

References

• Adamjan , V. M. , Arov , D. Z. and Krein , M. G. 1971 . Analytic properties of Schmidt-pairs for a Hankel operator and the generalized Schur-Takagi problem . Mathematics USSR Sbornik , 15 : 31 – 73 .
   Google Scholar
• Akaike , H. 1976 . “ Canonical correlation analysis of time series and the use of an information criterion. System identification and case studies ” . Edited by: Mehra , R. K. and Lainiotis , D. C. New York : Academic Press .
   Google Scholar
• Aoki , M. 1987 . “ State space modelling of time series ” . Berlin : Springer .
   Google Scholar
• Aoki , M. and Havenner , A. 1991 . State space modeling of multiple time series . Econometric Reviews , 10 : 93 – 99 .
   Google Scholar
• Deistler , M. , Dorfman , J. H. , Mittnik , S. and Zeliner , A. 1991 . Comment on state space modeling of multiple time series . Econometric Reviews , 10 : 91 – 92 .
   Google Scholar
• Desai , U. B. and Pal , D. . A realization approach to stochastic model reduction and balanced stochastic realization . Proceedings 16th Annual Conference on Information Science and Systems . Princeton, New Jersey
   Google Scholar
• Faurre , P. , Cierget , M. and Cermain , F. 1979 . “ Opérateurs rationnels positifs ” . Paris : Dunod .
   Google Scholar
• Glover , K. 1984 . All optimal Hankel norm approximations of linear multivariable systems and their L" error bounds . International Journal of Control , 39 : 1115 – 1193 .
   Web of Science ®Google Scholar
• Golub , G. H. and Van Loan , C. F. 1983 . “ Matrix computations. Baltimore ” . Johns Hopkins University Press .
   Google Scholar
• Hannan , E. J. and Poskitt , D. S. 1988 . Unit canonical correlations between future and past . The Annals of Statistics , 16 : 784 – 790 .
   Web of Science ®Google Scholar
• Heij , C. and Roorda , B. 1991 . “ A modified canonical correlation approach to approximate state space modelling ” . Netherlands : Erasmus University Rotterdam . Report 91524, Econometric Institute
   Google Scholar
• Hendry D. F. Mizon G. E. Evaluating dynamic econometric models by encompassing the VAR. Models, methods, and applications of econometrics Phillips P. C. B. Hall V. B. Forthcoming
   Google Scholar
• Moore , B. C. 1981 . Principal component analysis in linear systems: controllability, observability, and model reduction . IEEE Automatic Control , 26 : 17 – 32 .
   Web of Science ®Google Scholar
• Perneso , L. and Silverman , L. M. 1952 . Model reduction via balanced state space representations . lEEE Automatic Control , 27 : 382 – 387 .
   Google Scholar
• Vaughan , D. R. 1970 . A nonrecursive algebraic solution for the discrete Riccati equation . IEEE Automatic Control , 15 : 597 – 599 .
   Google Scholar