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Random sampling of long-memory stationary processes |
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| Authors: | Anne Philippe Marie-Claude Viano |
| Institution: | 1. Université de Nantes, Laboratoire de Mathématiques Jean Leray, UMR CNRS 6629, 2 rue de la Houssinière - BP 92208, 44322 Nantes Cedex 3, France;2. Laboratoire Paul Painlevé UMR CNRS 8524, UFR de Mathématiques - Bat M2, Université Lille 1, Villeneuve d’Ascq, 59655 Cedex, France |
| Abstract: | 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. |
| Keywords: | Aliasing FARIMA processes Generalised fractional processes Regularly varying covariance Seasonal long-memory Spectral density |
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