Causal discovery in heavy‐tailed linear structural equation models via scalings

Abstract Causal dependence modelling of multivariate extremes is intended to improve our understanding of the relationships among variables associated with rare events. Regular variation provides a standard framework in the study of extremes. This paper concerns the extremal causal dependence of the linear structural equation model with regularly varying noise variables. We focus on extreme observations generated from such a model and propose a causal discovery method based on the scaling parameters of its extremal angular measure. We implement the method as an algorithm, establish its consistency and evaluate it by simulation and by application to river discharge datasets. We propose a selection procedure for its hyperparameters based on a notion of stability. Comparison with the only alternative extremal method for such model reveals its competitive performance.