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

Fran\c{c}ois Roueff (LTCI); Philippe Soulier (MODAL'X); Randal Douc (CMAP)

arxiv: math/0611339 · v3 · submitted 2006-11-11 · 🧮 math.ST · math.PR· stat.TH

On the existence of some ARCH(infty) processes

Randal Douc (CMAP) , Fran\c{c}ois Roueff (LTCI) , Philippe Soulier (MODAL'X) This is my paper

classification 🧮 math.ST math.PRstat.TH

keywords existencearchconditioninftyprocessesallowsappliedcausal

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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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On the existence of some ARCH(infty) processes

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