Extremal clustering in non-stationary random sequences
It is well known that the distribution of extreme values of strictly stationary sequences differ from those of independent and identically distributed sequences in that extremal clustering may occur. Here we consider non-stationary but identically distributed sequences of random variables subject to...
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| Published in | Extremes (Boston) Vol. 24; no. 4; pp. 725 - 752 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
New York
Springer US
01.12.2021
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1386-1999 1572-915X |
| DOI | 10.1007/s10687-021-00418-2 |
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| Abstract | It is well known that the distribution of extreme values of strictly stationary sequences differ from those of independent and identically distributed sequences in that extremal clustering may occur. Here we consider non-stationary but identically distributed sequences of random variables subject to suitable long range dependence restrictions. We find that the limiting distribution of appropriately normalized sample maxima depends on a parameter that measures the average extremal clustering of the sequence. Based on this new representation we derive the asymptotic distribution for the time between consecutive extreme observations and construct moment and likelihood based estimators for measures of extremal clustering. We specialize our results to random sequences with periodic dependence structure. |
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| AbstractList | It is well known that the distribution of extreme values of strictly stationary sequences differ from those of independent and identically distributed sequences in that extremal clustering may occur. Here we consider non-stationary but identically distributed sequences of random variables subject to suitable long range dependence restrictions. We find that the limiting distribution of appropriately normalized sample maxima depends on a parameter that measures the average extremal clustering of the sequence. Based on this new representation we derive the asymptotic distribution for the time between consecutive extreme observations and construct moment and likelihood based estimators for measures of extremal clustering. We specialize our results to random sequences with periodic dependence structure. |
| Author | Auld, Graeme Papastathopoulos, Ioannis |
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| CitedBy_id | crossref_primary_10_1007_s00704_023_04753_1 crossref_primary_10_1016_j_spl_2023_110012 crossref_primary_10_5194_hess_29_719_2025 crossref_primary_10_1214_22_EJP788 |
| Cites_doi | 10.1023/A:1009993419559 10.1007/BF00532947 10.1214/aos/1176349409 10.1137/1118033 10.1111/1467-9868.00401 10.2307/1427679 10.1214/aoms/1177703551 10.1007/978-1-4612-5449-2 10.1111/rssb.12099 10.1093/biomet/asr078 10.1016/0304-4149(91)90064-J 10.1111/1467-9868.00400 10.1214/aoms/1177700071 10.1007/s10687-007-0034-2 10.2307/3214467 10.2307/3214789 10.1093/biomet/84.2.249 10.1016/0304-4149(87)90183-9 10.1002/env.3170050304 10.2307/3214462 10.1214/09-AOAS292 10.1214/154957805100000104 10.1214/aoms/1177728670 10.1007/BF00532484 10.1007/BF00538965 10.1111/j.2517-6161.1994.tb01997.x 10.1002/0470012382 |
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| Copyright | The Author(s) 2021 The Author(s) 2021. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. |
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| Keywords | Clustering of extremes Non-stationary sequences Extremal index Interexceedance times 60G70 Periodic processes Intervals estimator |
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| SubjectTerms | Civil Engineering Clustering Economics Environmental Management Extreme values Finance Hydrogeology Insurance Management Mathematics and Statistics Quality Control Random variables Reliability Safety and Risk Statistics Statistics for Business |
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| Title | Extremal clustering in non-stationary random sequences |
| URI | https://link.springer.com/article/10.1007/s10687-021-00418-2 https://www.proquest.com/docview/2585634496 |
| Volume | 24 |
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