Neural MJD: Neural Non-Stationary Merton Jump Diffusion for Time Series Prediction

• URL: http://arxiv.org/abs/2506.04542v1
• Date: Thu, 05 Jun 2025 01:23:28 GMT
• Title: Neural MJD: Neural Non-Stationary Merton Jump Diffusion for Time Series Prediction
• Authors: Yuanpei Gao, Qi Yan, Yan Leng, Renjie Liao,
• Abstract summary: We introduce Neural MJD, a neural network based non-stationary Merton diffusion (MJD) model.<n>Our model explicitly formulates forecasting as a Poisson equation (SDE) simulation problem.<n>To enable tractable learning, we introduce a likelihood truncation mechanism that caps the number of jumps within small time intervals.
• Score: 13.819057582932214
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: While deep learning methods have achieved strong performance in time series prediction, their black-box nature and inability to explicitly model underlying stochastic processes often limit their generalization to non-stationary data, especially in the presence of abrupt changes. In this work, we introduce Neural MJD, a neural network based non-stationary Merton jump diffusion (MJD) model. Our model explicitly formulates forecasting as a stochastic differential equation (SDE) simulation problem, combining a time-inhomogeneous It\^o diffusion to capture non-stationary stochastic dynamics with a time-inhomogeneous compound Poisson process to model abrupt jumps. To enable tractable learning, we introduce a likelihood truncation mechanism that caps the number of jumps within small time intervals and provide a theoretical error bound for this approximation. Additionally, we propose an Euler-Maruyama with restart solver, which achieves a provably lower error bound in estimating expected states and reduced variance compared to the standard solver. Experiments on both synthetic and real-world datasets demonstrate that Neural MJD consistently outperforms state-of-the-art deep learning and statistical learning methods.

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