Asymptotics for irregularly observed long memory processes

Autor:	Ould-Haye, Mohamedou, Philippe, Anne
Rok vydání:	2024
Předmět:	Mathematics - Statistics Theory Mathematics - Probability
Druh dokumentu:	Working Paper
Popis:	We study the effect of observing a stationary process at irregular time points via a renewal process. We establish a sharp difference in the asymptotic behaviour of the self-normalized sample mean of the observed process depending on the renewal process. In particular, we show that if the renewal process has a moderate heavy tail distribution then the limit is a so-called Normal Variance Mixture (NVM) and we characterize the randomized variance part of the limiting NVM as an integral function of a L\'evy stable motion. Otherwise, the normalized sample mean will be asymptotically normal.
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2409.09498 Zobrazit plný text záznamu View this record from Arxiv