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

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	755-761
Number of pages	7
Journal	Stochastic Processes and their Applications
Volume	118
Issue number	5
DOIs	https://doi.org/10.1016/j.spa.2007.06.002
Publication status	Published - 1 May 2008

Keywords

ARCH processes
Fractionally integrated processes
Long memory

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10.1016/j.spa.2007.06.002

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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.",

keywords = "ARCH processes, Fractionally integrated processes, Long memory",

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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

EP - 761

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

IS - 5

ER -

On the existence of some ARCH (∞) processes

Abstract

Keywords

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