On the existence of some ARCH (∞) processes

Randal Douc; François Roueff; Philippe Soulier

doi:10.1016/j.spa.2007.06.002

On the existence of some ARCH (∞) processes

Randal Douc
, François Roueff
, Philippe Soulier

CNRS LTCI
Université Paris X

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

25 Citations (Scopus)

Résumé

A new sufficient condition for the existence of a stationary causal solution of an ARCH (∞) equation is provided. This condition allows us to consider coefficients with power-law decay, so that it can be applied to the so-called FIGARCH processes, whose existence is thus proved.

langue originale	Anglais
Pages (de - à)	755-761
Nombre de pages	7
journal	Stochastic Processes and their Applications
Volume	118
Numéro de publication	5
Les DOIs	https://doi.org/10.1016/j.spa.2007.06.002
état	Publié - 1 mai 2008

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title = "On the existence of some ARCH (∞) processes",

abstract = "A new sufficient condition for the existence of a stationary causal solution of an ARCH (∞) equation is provided. This condition allows us to consider coefficients with power-law decay, so that it can be applied to the so-called FIGARCH processes, whose existence is thus proved.",

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author = "Randal Douc and Fran{\c c}ois Roueff and Philippe Soulier",

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T1 - On the existence of some ARCH (∞) processes

AU - Douc, Randal

AU - Roueff, François

AU - Soulier, Philippe

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N2 - A new sufficient condition for the existence of a stationary causal solution of an ARCH (∞) equation is provided. This condition allows us to consider coefficients with power-law decay, so that it can be applied to the so-called FIGARCH processes, whose existence is thus proved.

AB - A new sufficient condition for the existence of a stationary causal solution of an ARCH (∞) equation is provided. This condition allows us to consider coefficients with power-law decay, so that it can be applied to the so-called FIGARCH processes, whose existence is thus proved.

KW - ARCH processes

KW - Fractionally integrated processes

KW - Long memory

U2 - 10.1016/j.spa.2007.06.002

DO - 10.1016/j.spa.2007.06.002

M3 - Article

AN - SCOPUS:40949093141

SN - 0304-4149

VL - 118

SP - 755

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JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

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ER -

On the existence of some ARCH (∞) processes

Résumé

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