Comptes Rendus
Processus dual et inverse d'un ARMA et application à la réversibilité temporelle
[Dual and inverse ARMA processes and application to time reversibility]
Comptes Rendus. Mathématique, Volume 348 (2010) no. 1-2, pp. 85-88.

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.

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.

Published online:
DOI: 10.1016/j.crma.2009.11.002

Ahmed El Ghini 1

1 Équippe / LIFL, CNRS-UMR 8022, université Lille 1, 59655 Villeneuve d'Ascq cedex, France
     author = {Ahmed El Ghini},
     title = {Processus dual et inverse d'un {ARMA} et application \`a la r\'eversibilit\'e temporelle},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {85--88},
     publisher = {Elsevier},
     volume = {348},
     number = {1-2},
     year = {2010},
     doi = {10.1016/j.crma.2009.11.002},
     language = {fr},
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JO  - Comptes Rendus. Mathématique
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VL  - 348
IS  - 1-2
PB  - Elsevier
DO  - 10.1016/j.crma.2009.11.002
LA  - fr
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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.

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