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Une méthode d’identification pour un modèle de fonctions de transfert. (An identification method for a transfer functions model). (French) Zbl 0672.93071
Summary: The transfer function models generalize the multiple regression models. Namely, each independent variable (or input) can influence the dependent variable (or output) with a lag structure and the noise is an ARMA process. A transfer function model is characterized by a rational function of the lag operator for each input variable and the autoregressive and moving average polynomials of the noise model. The identification of such a model consists in determining the degrees of each polynomial. We propose here an identification procedure in the case of single input or multiple uncorrelated inputs. It is based on the corner theorem of Hassens and Liu which is a generalization of the identification theorem of Beguin, Gouriéroux and Monfort for an ARMA process. A complete proof is given. This theorem is using of the cross- correlation structure between the output variable and one input variable. In practice, we have only an observed cross-correlation structure obtained from time series.

93E12 Identification in stochastic control theory
93C55 Discrete-time control/observation systems
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
93B17 Transformations
93B30 System identification