NeuroMem-FHP: A Likelihood-Free Deep Learning Framework for Parameter Estimation of Fractional Hawkes Process

2026-07-13

AI Summary

This study addresses the computational complexity of conventional likelihood-based methods and their inability to adequately capture long-memory dependence in parameter estimation for fractional Hawkes processes (FHP). To overcome these limitations, the authors propose NeuroMem-FHP, a novel framework that pioneers the integration of deep learning into FHP modeling. By leveraging LSTM and Transformer architectures, the method enables end-to-end parameter estimation directly from inter-event time sequences without explicitly evaluating the likelihood function. Experiments on synthetic data demonstrate substantial improvements over maximum likelihood estimation (MLE), with Transformer and LSTM achieving MSEs of 0.1634 and 0.1752, respectively, compared to MLE’s 2.8032. Furthermore, the approach accurately reproduces empirical distributions, tail behaviors, and long-range temporal dependencies in real-world datasets, including AAPL high-frequency trades and 911 emergency calls, confirming its efficacy and practical utility.

Abstract

In this paper, we propose deep learning based NeuroMem-FHP framework for estimating the parameters of the fractional Hawkes process (FHP), a self-exciting point process that captures long-range dependence through a fractional Mittag-Leffler excitation kernel. Two neural architectures, namely a Long Short-Term Memory (LSTM) network and a Transformer, are developed to estimate the model parameters $(μ,γ,α,β)$ directly from sequences of inter-arrival times without requiring computationally intensive likelihood optimization. Experiments on synthetic data that both neural models significantly outperform the classical Maximum Likelihood Estimation (MLE) method, with the Transformer achieving the highest estimation accuracy (MSE = $0.1634$), followed by the LSTM (MSE = $0.1752$), compared to MLE (MSE = $2.8032$). An ablation study further examines the effects of key hyperparameters on model performance. The proposed framework is also on two real-world high-frequency datasets, namely AAPL NBBO transaction data and Montgomery County 911 emergency call records. Using a predictive validation approach, event sequences simulated from the estimated parameters closely reproduce the empirical distribution, tail behavior, and temporal dependence structure of the observed data. These results demonstrate that Transformer-based parameter estimation provides an accurate and efficient alternative to conventional estimation techniques for FHP and offers a promising framework for modeling event-driven systems with long-memory dynamics.

Problem

• Fractional Hawkes Process
• parameter estimation
• long-range dependence
• self-exciting point process
• likelihood-free

Innovation

• likelihood-free
• fractional Hawkes process
• Transformer
• parameter estimation
• long-range dependence