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Une approche géométrique des processus ARMA

Christian Gourieroux
Annales d'Économie et de Statistique
No. 8 (Oct. - Dec., 1987), pp. 135-159
Published by: GENES on behalf of ADRES
DOI: 10.2307/20075674
Stable URL: http://www.jstor.org/stable/20075674
Page Count: 25
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Une approche géométrique des processus ARMA
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Abstract

Diverses propriétés importantes des processus stationnaires, en particulier la décomposition de Wold, peuvent être montrées en utilisant des arguments géométriques. Nous introduisons dans cet article les notions de passé lointain et passé proche en terme d'espaces vectoriels. L'étude géométrique de ces espaces et de leur corrélation permet alors de retrouver diverses caractérisations classiques des ordres p et q d'un processus ARMA. /// A number of interesting properties of stationary processes, in particular Wold decomposition, can be derived using a geometrical approach. In this paper we introduce the notions of recent past and old past by means of well chosen vector spaces. A geometrical study of these spaces and of their correlation allows the derivation of several classical characterizations of the orders p and q of an ARMA process.

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