Open Access
2006 Disaggregation of Long Memory Processes on $\mathcal{C}^{\infty}$ Class
Didier Dacunha-Castelle, Lisandro Fermin
Author Affiliations +
Electron. Commun. Probab. 11: 35-44 (2006). DOI: 10.1214/ECP.v11-1133


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 ($C^\infty$). We show that the $C^\infty$ 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 $C^\infty$ class cannot be improved by taking for instance analytic functions instead of indefinitely derivable functions.


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Didier Dacunha-Castelle. Lisandro Fermin. "Disaggregation of Long Memory Processes on $\mathcal{C}^{\infty}$ Class." Electron. Commun. Probab. 11 35 - 44, 2006.


Accepted: 9 May 2006; Published: 2006
First available in Project Euclid: 4 June 2016

zbMATH: 1112.62089
MathSciNet: MR2219344
Digital Object Identifier: 10.1214/ECP.v11-1133

Primary: 60E07
Secondary: 60G10 , 60G50 , 62M10

Keywords: Aggregation , disaggregation , long memory process , mixture

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