Changepoint identification in heavy-tailed distributions
Résumé
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.
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