Deistler, M.; Pötscher, B. M.; Schrader, J. The uniqueness of the transfer function of linear systems from input- output observations. (English) Zbl 0555.60028 Metrika 31, 157-181 (1984). Some problems preceding the estimation of the rational transfer function of a linear dynamical system are considered: Fairly general conditions under which these transfer functions are uniquely determined from the second moments of the observed processes and under which the relation between the second moments and the transfer functions is continuous are given. Most of these conditions include the non (asymptotically) stationary as well as the unstable case. Cited in 1 Document MSC: 60G35 Signal detection and filtering (aspects of stochastic processes) 93E10 Estimation and detection in stochastic control theory 93E03 Stochastic systems in control theory (general) 62M15 Inference from stochastic processes and spectral analysis Keywords:estimation of the rational transfer function PDFBibTeX XMLCite \textit{M. Deistler} et al., Metrika 31, 157--181 (1984; Zbl 0555.60028) Full Text: DOI EuDML References: [1] Åström, K.J., andT. Bohlin: Numerical Identification of Linear Dynamic Systems form Normal Operating Records. In: Theory of Self-Adaptive Control Systems. Ed. by E. Hammond, New York 1966, 96–111. [2] Deistler, M.: The Identifiability of Linear Econometric Models with Autocorrelated Errors. Int. Economic Review17, (1), 1976, 26–46. · Zbl 0348.90049 [3] –: The Properties of the Parameterization of ARMAX Systems and their Relevance for Structural Estimation and Dynamic Specification. Econometrica51, 1983, 1187–1207. · Zbl 0517.62090 [4] Dunsmuir, W., andE.J. Hannan: Vector Linear Time Series Models. Adv. Appl. Prob.8,1976, 339–364. · Zbl 0327.62055 [5] Hannan, E.J.: The Identification Problem for Multipie Equation Systems with Moving Average. Errors. Econometrica39, 1971, 751–765. · Zbl 0241.62049 [6] Hannan, E.J., W. Dunsmuir, andM. Deistler: Estimation of Vector ARMAX Models. J. of Multiv. Analysis10, 1980, 275–295. · Zbl 0445.62098 [7] Hatanaka, M.: On the Global Identification of the Dynamic Simultaneous Equations Model with Stationary Disturbances. Int. Economic Review16 (1), 1975, 545–554. · Zbl 0324.62073 [8] Rozanov, Yu.A.: Stationary Random Processes. San Francisco 1967. · Zbl 0152.16302 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.