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On the existence of some ARCH (∞) processes

Stochastic Processes and their Applications (2008) 118(5) 755-761
DOI: 10.1016/j.spa.2007.06.002
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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. © 2007 Elsevier Ltd. All rights reserved.

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Douc, R., Roueff, F., & Soulier, P. (2008). On the existence of some ARCH (∞) processes. Stochastic Processes and Their Applications, 118(5), 755–761. https://doi.org/10.1016/j.spa.2007.06.002

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