Dokument: Statistics for Time Series Extremes
| Titel: | Statistics for Time Series Extremes | |||||||
| URL für Lesezeichen: | https://docserv.uni-duesseldorf.de/servlets/DocumentServlet?id=60229 | |||||||
| URN (NBN): | urn:nbn:de:hbz:061-20220721-111605-4 | |||||||
| Kollektion: | Dissertationen | |||||||
| Sprache: | Englisch | |||||||
| Dokumententyp: | Wissenschaftliche Abschlussarbeiten » Dissertation | |||||||
| Medientyp: | Text | |||||||
| Autor: | M.Sc. Jennessen, Tobias [Autor] | |||||||
| Dateien: |
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| Beitragende: | Prof. Dr. Bücher, Axel [Gutachter] Prof. Dr. Stanislav Volgushev [Gutachter] | |||||||
| Dewey Dezimal-Klassifikation: | 500 Naturwissenschaften und Mathematik » 510 Mathematik | |||||||
| Beschreibung: | An understanding of the extremal behavior of time series is of importance in many applications. For stationary time series, the extremes typically occur in clusters. The extremal index, representing the reciprocal of the expected cluster size, and the limiting cluster size distribution are important measures for analyzing the serial dependence of the extremes of stationary time series. In this thesis, new estimators for the extremal index and the limiting cluster size distribution based on the blocks method are proposed. In contrast to many competing estimators
from the literature, these estimators only depend on one tuning parameter, i.e., the block length. The introduced estimators are analyzed theoretically, establishing their asymptotic normality, and by means of a large-scale simulation study. Thereby, both disjoint and sliding blocks versions are considered. The sliding blocks estimators are shown to exhibit a smaller asymptotic variance than the corresponding disjoint blocks versions. Further, the sliding blocks estimators perform better with regard to their finite-sample behavior in the context of the simulation study. In specific scenarios, they are also found to be superior to recent competitors from the literature. In various situations, time series data also exhibit non-stationary behavior, which needs to be accounted for in the statistical analysis. As an approach for modeling nonstationary time series extremes, the proportional tails model introduced by Einmahl, de Haan and Zhou (2016, Journal of the Royal Statistical Society: Series B (Statistical Methodology), 78(1), 31-51) is extended to allow for serially dependent observations. Here, the proportionality is described by the so-called scedasis function c, which can be interpreted as the frequency of extremes; the case where this frequency c is not constant is referred to as heteroscedastic extremes. Central limit theorems for estimators for the scedasis function and for the integrated scedasis function are provided. Moreover, different test procedures for assessing whether the extremes are heteroscedastic are developed that are based on a multiplier bootstrap-scheme and on the idea of self-normalization. These tests are examined theoretically, proving their consistency, and shown to perform well within a simulation study. Finally, an estimator for the extremal index of the underlying stationary time series, which governs the dynamics of the extremes, is proposed; its consistency is derived and it is investigated empirically. | |||||||
| Lizenz: |  Urheberrechtsschutz | |||||||
| Fachbereich / Einrichtung: | Mathematisch- Naturwissenschaftliche Fakultät » WE Mathematik » Mathematische Statistik und Wahrscheinlichkeitstheorie | |||||||
| Dokument erstellt am: | 21.07.2022 | |||||||
| Dateien geändert am: | 21.07.2022 | |||||||
| Promotionsantrag am: | 03.05.2022 | |||||||
| Datum der Promotion: | 14.07.2022 |
