Asymptotics for irregularly observed long memory processes

Mohamedou Ould Haye and Anne Philippe

Stochastic Processes and their Applications, 2025, vol. 185, issue C

Abstract: We study the effect of observing a long-memory 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 Lévy stable motion. Otherwise, the normalized sample mean will be asymptotically normal.

Keywords: Irregular time series; Linear processes; Long memory; Normal Variance Mixture; Short memory; Stationarity (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1016/j.spa.2025.104631

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