Abstract
By studying the geometry of relevant Hilbert spaces, we give a characterization of the identifiable standard representations of multivariate ARMA models in terms of the autocovariance function.
Similar content being viewed by others
References
Berlinet, A.: Estimating the degrees of an ARMA model, Compstat Lectures 3 (1984), 61-94.
Berlinet, A. and Francq, C.: Geometry of multivariate ARMA models and their identification, Publication ENSAM-INRA-UM II, Montpellier, Rapport de Recherche 97-01, 1997a.
Berlinet, A. and Francq, C.: On Bartlett's formula for nonlinear processes, J. Time Ser. Anal. 18 (1997b), 535-552.
Brockwell, P. J. and Davis, R. A.: Time Series: Theory and Methods, Springer-Verlag, 1991.
Choi, B.: ARMA Models Identification, Springer-Verlag, 1992.
Deistler, M.: The properties of the parameterization of ARMAX systems and their relevance for structural and dynamic specification, Econometrica 51 (1983), 1187-1207.
Deistler, M. and Schrader, J.: Linear models with autocorrelated errors: structural identifiability in the absence of minimality assumptions, Econometrica 47 (1979), 495-504.
Gouriéroux, C.: Une approche géométrique des processus ARMA, Annales d'Économie et de Statistique 8 (1987), 132-159.
Hannan, E. J. (1969) The identification of vector mixed autoregressive-moving average systems, Biometrika 56 (1969), 223-225.
Hannan, E. J.: The identification problem for multiple equation systems with moving average errors, Econometrica 39 (1971), 751-765.
Hannan, E. J. and Deistler, M.: The Statistical Theory of Linear Systems, Wiley, New York, 1988.
Lütkepohl, H.: Introduction to Multiple Time Series Analysis, Springer-Verlag, Berlin, Heildelberg, 1993.
Rozanov, Y. A.: Stationary Random Processes, Holden-Day, San Francisco, 1967.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Berlinet, A., Francq, C. On the Identifiability of Minimal VARMA Representations. Statistical Inference for Stochastic Processes 1, 1–15 (1998). https://doi.org/10.1023/A:1009955223247
Issue Date:
DOI: https://doi.org/10.1023/A:1009955223247