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

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

2006-11-11

arxiv.org/abs/math/0611339v3

Stochastic Processes and their Applications 118, 5 (2008) 755-761

Mathematics

Statistics Theory

Scientific paper

10.1016/j.spa.2007.06.002

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.

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