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Disaggregation of Long Memory Processes on $\mathcal{C}^{\infty}$ Class

   
@article{ECP1133,
	author = {Didier Dacunha-Castelle and Lisandro Fermin},
	title = {Disaggregation of Long Memory Processes on $\mathcal{C}^{\infty}$ Class},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {11},
	year = {2006},
	keywords = {Aggregation; disaggregation; long memory process; mixture.},
	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 ($C^\infty$).    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.},
	pages = {no. 4, 35--44},
	issn = {1083-589X},
	doi = {10.1214/ECP.v11-1133},    
        url = {http://ecp.ejpecp.org/article/view/1133}}