no. 1-2
Probabilitiés
Processus dual et inverse d'un ARMA et application à la réversibilité temporelle

Présenté par : Paul Deheuvels

El Ghini, Ahmed1
1 Équippe / LIFL, CNRS-UMR 8022, université Lille 1, 59655 Villeneuve d'Ascq cedex, France
Comptes Rendus. Mathématique, Tome 348 (2010) no. 1-2, pp. 85-88.

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2009.11.002
El Ghini, Ahmed 1

1 Équippe / LIFL, CNRS-UMR 8022, université Lille 1, 59655 Villeneuve d'Ascq cedex, France 
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El Ghini, Ahmed. Processus dual et inverse d'un ARMA et application à la réversibilité temporelle. Comptes Rendus. Mathématique, Tome 348 (2010) no. 1-2, pp. 85-88. doi : 10.1016/j.crma.2009.11.002. http://www.numdam.org/articles/10.1016/j.crma.2009.11.002/

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