Rate-Based Causal Discovery for Heavy-Tailed Models

Abstract

In many complex systems, such as river networks and financial markets, extreme events propagate from causes to their effects, and the largest observations carry the most information about the underlying causal structure. Existing methods for causal discovery in extremes, however, are tailored to specific mechanisms, such as linear or max-linear models. This work develops causal discovery for heavy-tailed homogeneous structural causal models, a flexible class that contains linear, max-linear and norm-type mechanisms, which may differ from node to node. In these models, the causal structure is encoded by ancestral impulse responses, which measure how a shock at one node is transmitted to its descendants. We propose the extremal minimum ratio estimator of these responses, which uses only observations in which the potential cause is extreme. The estimator is consistent under regular variation alone, and we derive its exact rates of convergence and limiting distributions, which depend on both the causal relation and the type of mechanism. Building on these rates, we construct consistent estimators of the causal order and of the full set of ancestral relations, using a threshold that adapts to the data and requires no knowledge of the tail index. The method is illustrated on simulated data and on river discharges in the upper Danube basin.