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

ArXiv ID: 2401.09361 “View on arXiv”

Authors: Unknown

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.

Keywords: Hawkes Processes, Market Microstructure, Kernel Inference, Cryptocurrency, Neural Networks, Cryptocurrency

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail
• Why: The paper involves advanced mathematics including Fredholm integral equations, PDEs solved with physics-informed neural networks, and high-dimensional non-parametric estimation. It demonstrates strong empirical rigor through extensive numerical validation on simulated data and two specific applications on high-frequency cryptocurrency market data, though it lacks live trading results or deployment code.

  flowchart TD
    A["Research Goal: Non-Parametric<br>Hawkes Kernel Inference<br>in High Dimensions"] --> B["Methodology: Moment-Based<br>Neural Hawkes Estimation"]
    B --> C["Key Component:<br>Physics-Informed Neural Networks<br>solve Fredholm Integral Equations"]
    B --> D["Key Component:<br>Adapted Training Pipeline<br>for Robust Kernel Shapes"]
    C & D --> E["Inputs: Simulated Data<br>for Validation & Cryptocurrency Market Data<br>BTC-USD + 15 Pairs"]
    E --> F{"Computational Process"}
    F --> G["High-Dimensional<br>Kernel Inference"]
    G --> H["Key Findings & Outcomes"]
    H --> I["Validation: Robust results<br>across diverse kernel shapes"]
    H --> J["Application 1: Extracted<br>Volume influence on BTC-USD<br>arrival rates"]
    H --> K["Application 2: Analyzed causality<br>directions amongst 15 crypto pairs"]