Neural Hawkes: Non-Parametric Estimation in High Dimension and Causality Analysis in Cryptocurrency Markets

Abstract

We propose a novel approach to marked Hawkes kernel inference which we name the moment-based neural Hawkes estimation method. Hawkes processes are fully characterized by their first and second order statistics through a Fredholm integral equation of the second kind. Using recent advances in solving partial differential equations with physics-informed neural networks, we provide a numerical procedure to solve this integral equation in high dimension. Together with an adapted training pipeline, we give a generic set of hyperparameters that produces robust results across a wide range of kernel shapes. We conduct an extensive numerical validation on simulated data. We finally propose two applications of the method to the analysis of the microstructure of cryptocurrency markets. In a first application we extract the influence of volume on the arrival rate of BTC-USD trades and in a second application we analyze the causality relationships and their directions amongst a universe of 15 cryptocurrency pairs in a centralized exchange.

Updated with numerical examples on high-dimensional and multimodal kernels as well as and extended empirical results

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