Semiparametric Bayesian modelling of nonstationary joint extremes: how do big tech’s extreme losses behave?

Motivated by the hype surrounding Artificial Intelligence (AI) and big tech stocks, we develop a model for tracking the dynamics of their combined extreme losses over time. Specifically, we propose a novel Bayesian model for inferring about the intensity of observations in the joint tail over time, and for assessing if two stochastic processes are asymptotically dependent. To model the intensity of observations exceeding a high threshold, we develop a Bayesian nonparametric approach that defines a prior on the space of what we define as Extremal Dependence Intensity functions. In addition, a parametric prior is set on the coefficient of tail dependence. An extensive battery of experiments on simulated data show that the proposed method are able to recover the true targets in a variety of scenarios. An application of the proposed methodology to a set of big tech stocks—known as FAANG (Meta’s Facebook, Apple, Amazon, Netflix and Alphabet’s Google)—sheds light on some interesting features on the dynamics of their combined losses over time.