On the stability and causality of general time-dependent bilinear models

Abdelouahab Bibi

doi:10.1016/j.crma.2003.11.017

Statistics/Probability Theory

On the stability and causality of general time-dependent bilinear models

Presented by: Paul Deheuvels

Abdelouahab Bibi ¹

¹ Département de mathématiques, laboratoire de mathématiques appliquées et modélisation, Université Mentouri, Constantine, Algeria

Comptes Rendus. Mathématique, Volume 338 (2004) no. 3, pp. 245-248.

Abstract
Résumé

In this Note, sufficient conditions are given for the existence of a causal stable solution for general bilinear time series with time-dependent coefficients.

Dans cette Note, nous donnons des conditions suffisantes d'existence et d'unicité de solution causale et stable pour la classe générale de modèles bilinéaires à coefficients dépendant du temps.

Received: 2003-06-25
Accepted: 2003-11-17
Published online: 2003-12-30

DOI: 10.1016/j.crma.2003.11.017

Author's affiliations:

Abdelouahab Bibi ¹

¹ Département de mathématiques, laboratoire de mathématiques appliquées et modélisation, Université Mentouri, Constantine, Algeria

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     title = {On the stability and causality of general time-dependent bilinear~models},
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     doi = {10.1016/j.crma.2003.11.017},
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Abdelouahab Bibi. On the stability and causality of general time-dependent bilinear models. Comptes Rendus. Mathématique, Volume 338 (2004) no. 3, pp. 245-248. doi : 10.1016/j.crma.2003.11.017. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2003.11.017/

References
Cited by

[1] A. Bibi; A. Oyet A note on the properties of some time-varying bilinear models, Statist. Probab. Lett., Volume 58 (2002), pp. 399-411

[2] A. Bibi On the covariance structure of the time-varying bilinear models, Stochastic Anal. Appl., Volume 21 (2003) no. 1, pp. 25-60

[3] R. Dahlhaus On the Kullback–Leibler information divergence of locally stationary processes, Stochastic Proc. Appl., Volume 62 (1996), pp. 139-168

[4] D. Guégan Different representations for bilinear models, J. Time Series Anal., Volume 8 (1987) no. 4, pp. 389-408

[5] K.S. Miller Linear Difference Equations, Benjamin, New York, 1968

[6] T. Subba Rao The bispectral analysis of non linear stationary time series with reference to bilinear time series models (D.R. Brillinger; P.R. Krishnaiah, eds.), Handbook of Statistics, vol. 3, 1983, pp. 293-319

[7] T. Subba Rao Statistical analysis of nonlinear and nongaussian time series models (I. Csiszar; G. Michaeltzky, eds.), Stochastic Differential and Difference Equations, Birkhäuser Boston, 1997, pp. 285-298

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