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 Electronic Communications in Probability > Vol. 11 (2006) > Paper 4 open journal systems 


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.


Full text: PDF

Pages: 35--44

Published on: May 9, 2006
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Electronic Communications in Probability. ISSN: 1083-589X