Disaggregation of Long Memory Processes on $mathcal{C}^{infty}$ Class
Didier Dacunha-Castelle, Universite Paris-Sud
Lisandro J Fermín, Universite Paris-Sud and Universidad Central de Venezuela
Abstract
We prove that a large set of long memory (LM) processes
(including classical LM processes and all processes whose spectral
densities have a countable number of singularities controlled by
exponential functions) are obtained by an aggregation procedure
involving short memory (SM) processes whose spectral densities are
infinitely differentiable (C∞). We show that the
C∞ class of spectral densities infinitely
differentiable is the best class to get a general result for
disaggregation of LM processes in SM processes, in the sense that the
result given in C∞ class cannot be improved by taking
for instance analytic functions instead of indefinitely derivable
functions.
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