Self-exciting point processes, such as the Hawkes process, are essential tools for modeling event sequences in finance, epidemiology, and telecommunications. The fractional extension of this process (FHP) introduces an excitation kernel based on the Mittag-Leffler function, capable of capturing long-range dependencies and persistent memory. However, classical parameter estimation (μ, γ, α, β) via maximum likelihood estimation (MLE) is computationally expensive, sensitive to outliers, and requires multiple nonlinear optimization iterations. In this context, the NeuroMem-FHP framework proposes a deep learning approach that estimates the parameters directly from sequences of inter-arrival times, bypassing the costly likelihood computation.
NeuroMem-FHP employs two neural architectures: a Long Short-Term Memory (LSTM) network and a Transformer. Both models are trained on synthetic data generated from the FHP, learning to map temporal patterns in inter-event intervals to parameter values. Experimental results on synthetic data show a drastic improvement over MLE: the Transformer achieves a mean squared error (MSE) of 0.1634, the LSTM of 0.1752, while MLE yields an MSE of 2.8032. An additional ablation study reveals how hyperparameters such as input sequence length, number of attention heads, or learning rate influence performance, providing guidelines for optimal model configuration.
The framework has also been validated on two real-world high-frequency datasets: AAPL NBBO transactions and Montgomery County 911 emergency call records. Using a predictive validation approach, event sequences simulated from the parameters estimated by the neural models faithfully reproduce the empirical distribution, tail behavior, and temporal dependence structure observed in the real data. This demonstrates that Transformer-based estimation is not only more accurate than MLE but also generalizes well to real high-variability environments.
From a technical and business perspective, the ability to quickly estimate FHP parameters opens new possibilities for real-time systems. For example, in algorithmic trading platforms, knowing the intensity of future events allows adjusting buy and sell strategies. A company like Q2BSTUDIO, specialized in custom software development, can embed such models into market monitoring solutions that process event streams and continuously update estimates.
Deploying NeuroMem-FHP in production requires scalable and resilient cloud infrastructure. Q2BSTUDIO offers services on cloud AWS/Azure that host AI models, manage real-time data pipelines, and automate resource provisioning. This combination of advanced algorithms and cloud platform ensures optimal performance even under extreme event loads.
Cybersecurity is another field where fractional Hawkes processes prove valuable. They can model network event flows or authentication logs to detect anomalies indicative of intrusions. Q2BSTUDIO, with its cybersecurity service, helps organizations audit their systems, implement early detection models, and protect sensitive data handled by these processes.
In the business intelligence (BI) domain, estimated parameters can feed Power BI dashboards that visualize the evolution of event intensity, facilitating strategic decision-making. Q2BSTUDIO has experts in BI / Power BI who design interactive dashboards, integrating predictions from models like NeuroMem-FHP directly into standard business tools.
Finally, autonomous AI agents can benefit from these models to adjust their behavior based on learned temporal patterns. Q2BSTUDIO develops custom intelligent agents that, combined with real-time estimation of fractional Hawkes processes, enable automated responses in dynamic environments such as customer service, emergency management, or network traffic control. In summary, NeuroMem-FHP represents a significant advance in parameter estimation for long-memory processes, and its integration into business solutions can be effectively driven by Q2BSTUDIO through its broad portfolio of technology services.
