This paper is an overview on the extremal index for stationary time series. It provides a new interpretation in terms of α-clusters, where α is the tail-index of the series.

Recommended citation: G. Buriticá, N. Meyer, T. Mikosch, O. Wintenberger. (2021). Some variations of the extremal index. Zap. Nauchn. Semin. POMI. Volume 501, Probability and Statistics.* **30**, 52—77. To be translated in J.Math.Sci. (Springer). https://arxiv.org/abs/2106.05117

Stable sums to infer high return levels of multivariate rainfall time series

Published in Environmetrics, 2022

This paper presents the stable sums method to infer high return levels of multivariate heavy-tailed time series. This new method is justified by the large deviations of powers of α-sums, where α is the tail-index of the series. Its main advantage is that is implementation coincides for dependent and independent time series.

Recommended citation: G. Buriticá, P. Naveau. (2022). Stable sums to infer high return levels of multivariate rainfall time series, Environmetrics, e2782. https://doi.org/10.1002/env.2782

On the asymptotics of extremal lp-blocks cluster inference

Published in Submitted, 2022

Recently, we proposed a new estimator for cluster inference for heavy-tailed time series. This paper states the asymptotic normality of our α-cluster-based estimator. We infer the extremal index, the cluster lengths and other important indices in extremes. Also, we compute the asymptotic variances for ARMA models and stochastic recurrence equations, which shows our estimator compares favourably with classical approaches in terms of variance.

Recommended citation: G. Buriticá, O. Wintenberger. (2022). On the asymptotics of extremal lp-blocks cluster inference. https://arxiv.org/abs/2212.13521

Large deviations of lp-blocks of regularly varying time series and applications to cluster inference

Published in Stochastic processes and their applications, 2023

This paper studies large deviations of p-norms of stationary regularly varying time series. It introduces α-clusters, where α is the tail-index of the series, and proposes consistent disjoint blocks estimators of α-cluster features. This new methodology proves to be robust to handle time dependencies.

Recommended citation: G. Buriticá, T. Mikosch, O. Wintenberger. (2023). Large deviations of lp-blocks of regularly varying time series and applications to cluster inference. *Stochastic Processes and their Applications*. **161**, 68--101. https://doi.org/10.1016/j.spa.2023.03.013

Modeling Extreme Events: Univariate and Multivariate Data-Driven Approaches

Published in Submitted, 2024

This note presents data-driven methodologies for risk analysis based on univariate and multivariate methods from extreme value theory. It contains the contribution of team genEVA for the data challenge EVA 2023 competition organized in Milano.

Recommended citation: G. Buritica, M. Hentschel, O. C. Pasche, F. Roettger, Z. Zhang (2024). Modeling Extreme Events: Univariate and Multivariate Data-Driven Approaches. https://arxiv.org/abs/2401.14910

resources

Writing resources

Writing Resources, On how to write a scientific document, 2023

I intend to share some advice I have received during my scientific writing journal, which I have found helpful. The content comes from many sources: books, podcasts, professors, colleagues, students, and friends.