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

Renjie Liao, Qi Yan, Yuanpei Gao, Yan Leng

arXiv · PDF · Open in the Atlas

Code that ran

We lifted 2 functions out of this paper's own repositories and ran 2 of them in a sandbox. "Ran" means the function executed on a synthesized input and returned a value. It is not a reproduction of the paper's results.

Repositories linked to this paper

• DSL-Lab/neural-MJD

Some links come from the archived Papers with Code dataset (CC BY-SA 4.0): attribution and licence.

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 robustness handling 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 stateof-the-art deep learning and statistical learning methods. Our code is available at https://github.com/DSL-Lab/neural-MJD.

For agents

The same record, over MCP at https://syntology.ai/mcp:

get_harvested_code_for_paper("2506.04542")
get_code_for_paper("2506.04542")
have("2506.04542")

Connect an agent — have() is free.