English

On the existence of some ARCH($\infty$) processes

Statistics Theory 2009-01-06 v3 Probability Statistics Theory

Abstract

A new sufficient condition for the existence of a stationary causal solution of an ARCH(\infty) equation is provided. This condition allows to consider polynomially decaying coefficients, so that it can be applied to the so-called FIGARCH processes, whose existence is thus proved.

Cite

@article{arxiv.math/0611339,
  title  = {On the existence of some ARCH($\infty$) processes},
  author = {Randal Douc and François Roueff and Philippe Soulier},
  journal= {arXiv preprint arXiv:math/0611339},
  year   = {2009}
}
R2 v1 2026-07-22T17:46:09.101Z