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 is the optimal 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 taking for instance analytic functions instead of indefinitely derivable functions.
Cite
@article{arxiv.math/0509308,
title = {Disaggregation of Long Memory Processes on C^{\infty} Class},
author = {Didier Dacunha-Castelle and Lisandro Fermín},
journal= {arXiv preprint arXiv:math/0509308},
year = {2016}
}
Comments
Submitted to Electronic Communications in Probability. 10 pages