Processus dual et inverse d'un ARMA et application à la réversibilité temporelle

Ahmed El Ghini

doi:10.1016/j.crma.2009.11.002

Probabilitiés

Processus dual et inverse d'un ARMA et application à la réversibilité temporelle
[Dual and inverse ARMA processes and application to time reversibility]

Presented by: Paul Deheuvels

Ahmed El Ghini ¹

¹ Équippe / LIFL, CNRS-UMR 8022, université Lille 1, 59655 Villeneuve d'Ascq cedex, France

Comptes Rendus. Mathématique, Volume 348 (2010) no. 1-2, pp. 85-88.

Résumé (Original language)
Abstract

Pour la classe des processus autorégressifs-moyenne mobile, nous étudions le lien entre les processus dual et inverse. Nous établissons explicitement la représentation causale et inversible $ARMA (q, p)$ du processus inverse d'un $ARMA (p, q)$ canonique. De plus, nous montrons que cette représentation est forte si et seulement si le processus générateur est gaussien. Une application pour la réversibilité temporelle est traitée avec quelques exemples d'illustration.

For the class of autoregressive-moving average (ARMA) processes, the relationship between the dual and the inverse processes is examined. It is shown that the inverse process generated by a causal and invertible $ARMA (p, q)$ process is a causal and invertible $ARMA (q, p)$ . Moreover, it is established that this representation is strong if and only if the generating process is Gaussian. Some examples and applications to time reversibility are given to illustrate these theoretical results.

Received: 2009-05-29
Accepted: 2009-11-04
Published online: 2009-12-22

DOI: 10.1016/j.crma.2009.11.002

Author's affiliations:

Ahmed El Ghini ¹

¹ Équippe / LIFL, CNRS-UMR 8022, université Lille 1, 59655 Villeneuve d'Ascq cedex, France

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     author = {Ahmed El Ghini},
     title = {Processus dual et inverse d'un {ARMA} et application \`a la r\'eversibilit\'e temporelle},
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     publisher = {Elsevier},
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     doi = {10.1016/j.crma.2009.11.002},
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Ahmed El Ghini. Processus dual et inverse d'un ARMA et application à la réversibilité temporelle. Comptes Rendus. Mathématique, Volume 348 (2010) no. 1-2, pp. 85-88. doi : 10.1016/j.crma.2009.11.002. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.11.002/

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