Posts by Collection

portfolio

publications

Some variations of the extremal index

Published in Zap. Nauchn. Semin. POMI. Volume 501, Probability and Statistics, 2021

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

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

Published in Submitted, 2022

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. (2022). Large deviations of lp-blocks of regularly varying time series and applications to cluster inference. https://arxiv.org/abs/2106.12822

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

talks

teaching

Basic statistics

Graduate course M1, Sorbonne Université, Mathématiques et applications, 2019

Code assignments for the course taught by [Maud Thomas] in the Fall of 2019 and 2020.

Time series

Graduate course M1, ISUP, actuarial sciences, 2019

Exercises assignments for the course on Time series taught by [Olivier Wintenberger] in the Fall 2019, 2020 and 2021.