Random sampling of long-memory stationary processe

Anne Philippe (1) , Marie-Claude Viano (2)

1 LMJL - Laboratoire de Mathématiques Jean Leray
2 LPP - Laboratoire Paul Painlevé - UMR 8524

This paper investigates the second order properties of a stationary process after random sampling. While a short memory process gives always rise to a short memory one, we prove that long-memory can disappear when the sampling law has heavy enough tails. We prove that under rather general conditions the existence of the spectral density is preserved by random sampling. We also investigate the effects of deterministic sampling on seasonal long-memory.

Mots clés: Aliasing; FARIMA Processes; Generalised Fractional Processes; Regularly varying covariance; Seasonal long-memory; Spectral density

Domaines: Statistiques [math.ST]

Anne Philippe, Marie-Claude Viano. Random sampling of long-memory stationary processe. 2008. ⟨hal-00328168⟩