Asymptotics for irregularly observed long memory processes
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916464104046592 |
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| author | Ould-Haye, Mohamedou Philippe, Anne |
| author_facet | Ould-Haye, Mohamedou Philippe, Anne |
| contents | 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 Lévy stable motion. Otherwise, the normalized sample mean will be asymptotically normal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_09498 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Asymptotics for irregularly observed long memory processes Ould-Haye, Mohamedou Philippe, Anne Statistics Theory Probability 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 Lévy stable motion. Otherwise, the normalized sample mean will be asymptotically normal. |
| title | Asymptotics for irregularly observed long memory processes |
| topic | Statistics Theory Probability |
| url | https://arxiv.org/abs/2409.09498 |