A1224
Title: Sparse clustering for extremes
Authors: Nicolas Meyer - Université de Montpellier (France) [presenting]
Abstract: Identifying patterns of similar extremal behavior remains a central challenge in extreme value analysis. In a multivariate setting, the objective is to detect directions in which extreme events tend to concentrate, while in time series analysis, the goal shifts to identifying consecutive time intervals exhibiting extremal characteristics. Standard clustering techniques often prove inadequate due to the high dimensionality of the data relative to the scarcity of extreme observations. To address this limitation, sparse clustering methods offer a principled way to reduce dimensionality while preserving relevant extremal structure. The aim is to present a methodology based on the Euclidean projection onto the simplex to induce sparsity, leading to the concept of sparse regular variation. This framework provides a natural extension of multivariate regular variation, allowing for the identification of clusters of variables that exhibit similar tail dependence features. These clusters are often low-dimensional, which allows for a better interpretation. The proposed approach is illustrated through an application to average daily returns of 49 industry portfolios, highlighting its interpretability and practical relevance.
