  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.
