NeuroMemFPP: A recurrent neural approach for memory-aware parameter estimation in fractional Poisson process

In this paper, we propose a recurrent neural network (RNN)-based framework for estimating the parameters of the fractional Poisson process (FPP), which models event arrivals with memory and long-range dependence. The Long Short-Term Memory (LSTM) network estimates the key parameters μ > 0 and β ∈ (0, 1) from sequences of inter-arrival times, effectively capturing their temporal dependencies. Experiments on synthetic data show that the proposed approach reduces the mean squared error (MSE) by about 55.3% compared to the traditional method of moments (MOM) baseline. We also compare the proposed model with a Bidirectional LSTM (Bi-LSTM), which shows only a slight improvement in accuracy. Furthermore, the method is evaluated on two real-world high-frequency datasets: emergency call records from Montgomery County, PA, and AAPL stock trading data. Using a predictive validation approach, the simulated sequences from the LSTM-estimated parameters closely match the real data in terms of empirical distribution, tail behavior, and autocorrelation structure. These results demonstrate that the proposed model can effectively capture the key statistical and temporal characteristics of real-world event processes.