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() 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}
}