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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.04542 |
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| _version_ | 1866914315134566400 |
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| author | Gao, Yuanpei Yan, Qi Leng, Yan Liao, Renjie |
| author_facet | Gao, Yuanpei Yan, Qi Leng, Yan Liao, Renjie |
| contents | 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 Itô 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_04542 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Neural MJD: Neural Non-Stationary Merton Jump Diffusion for Time Series Prediction Gao, Yuanpei Yan, Qi Leng, Yan Liao, Renjie Machine Learning 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 Itô 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. |
| title | Neural MJD: Neural Non-Stationary Merton Jump Diffusion for Time Series Prediction |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2506.04542 |