On the existence of some ARCH() processes

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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.

MSC

60G10
62M10

Keywords

ARCH processes
Fractionally integrated processes
Long memory

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