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 $β\in(0,1)$ from sequences of inter-arrival times, effectively modeling their temporal dependencies. Our 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) and performs reliably across different training conditions. We tested the method on two real-world high-frequency datasets: emergency call records from Montgomery County, PA, and AAPL stock trading data. The results show that the LSTM can effectively track daily patterns and parameter changes, indicating its effectiveness on real-world data with complex time dependencies.

翻译：本文提出了一种基于递归神经网络（RNN）的框架，用于估计分数泊松过程（FPP）的参数，该过程用于建模具有记忆性和长程依赖性的事件到达。长短期记忆（LSTM）网络从到达间隔时间序列中估计关键参数 $μ>0$ 和 $β∈(0,1)$，有效建模其时间依赖性。在合成数据上的实验表明，与传统矩估计法（MOM）相比，所提方法将均方误差（MSE）降低了约55.3%，并在不同训练条件下均表现可靠。我们在两个真实世界的高频数据集上测试了该方法：宾夕法尼亚州蒙哥马利县的紧急呼叫记录和AAPL股票交易数据。结果表明，LSTM能够有效跟踪每日模式和参数变化，证明了其在具有复杂时间依赖性的真实数据上的有效性。