Result: Changepoint identification in heavy-tailed distributions

Title:
Changepoint identification in heavy-tailed distributions
Authors:
Girard, Stéphane, Opitz, Thomas, Usseglio-Carleve, Antoine, Yan, Chen
Contributors:
Modèles statistiques bayésiens et des valeurs extrêmes pour données structurées et de grande dimension (STATIFY), Centre Inria de l'Université Grenoble Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP), Université Grenoble Alpes (UGA)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP), Université Grenoble Alpes (UGA), Biostatistique et Processus Spatiaux (BioSP), Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), EA2151 Laboratoire de Mathématiques d'Avignon (LMA), Avignon Université (AU), Université du Michigan = University of Michigan [Ann Arbor] (UMich), Chaire Stress Test - BNP Paribas/Ecole polytechnique/Fondation de l'X, ANR-23-CE40-0009,EXSTA,EXtremes, apprentissage STatistique et Applications(2023)
Publisher Information:
CCSD, 2025.
Publication Year:
2025
Collection:
collection:UNIV-AVIGNON
collection:UGA
collection:CNRS
collection:INRIA
collection:INPG
collection:INRIA-RHA
collection:INSMI
collection:INRIA_TEST
collection:LJK
collection:LJK_PS
collection:TESTALAIN1
collection:INRIA2
collection:LMA-UAPV
collection:INRIA-RENGRE
collection:INRAE
collection:LJK-PS-STATIFY
collection:UGA-EPE
collection:ANR
collection:BIOSP
collection:MATHNUM
collection:INRIA-ETATSUNIS
collection:INRAEPACA
collection:TEST-MATHNUM
collection:TEST-UGA
Subject Terms:
ANOVA, changepoint detection, extreme value, statistical test, Weissman estimator, [MATH.MATH-ST]Mathematics [math], Statistics [math.ST]
Original Identifier:
HAL: hal-05044135
Document Type:
Electronic Resource preprint<br />Preprints<br />Working Papers
Language:
English
Access URL:
https://hal.science/hal-05044135
https://hal.science/hal-05044135v1/document
https://hal.science/hal-05044135v1/file/Changepoint_identification_in_heavy_tailed_distributions-1.pdf
Rights:
info:eu-repo/semantics/OpenAccess
Accession Number:
edshal.hal.05044135v1
Database:
HAL

Further Information

The problem of detecting the existence of a changepoint in a data sequence and of identifying its position is challenging when the focus is on extreme events and the distribution of data is heavy-tailed. In this setting, we propose a robust semi-parametric approach to changepoint identification that does not require the likelihood function. The changepoint is estimated as the position of the maximum of a statistic inspired by classical ANOVA to contrast the tail behavior of data to the left and right of all changepoint candidates. It is shown that the estimator is asymptotically consistent under mild assumptions. In numerical experiments, the novel method shows reliable finite-sample behavior for various simulation settings and is very competitive in comparison to alternative changepoint identification approaches from the literature, especially for small sample sizes. Finally, the utility of the method is highlighted by identifying interpretable changepoints in three real-data applications: very large motor insurance claim amounts for a French administrative region with age as covariate; daily Bitcoin cryptocurrency price data (January 2018 -- February 2025) and daily log-returns of stocks of the Boeing company (March 2015 -- March 2025) both with time as covariate.