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

2025-06-05

AI Summary

To address poor generalization and inadequate stochastic process modeling in deep learning for nonstationary time series—particularly those with abrupt change points—this paper proposes a neuralized nonstationary Merton jump-diffusion framework. It formulates forecasting as solving a stochastic differential equation (SDE) featuring time-varying Itô diffusion and time-varying compound Poisson jumps. We introduce, for the first time, a jump truncation mechanism with rigorous error-bound guarantees, and design a restart-based Euler–Maruyama numerical solver that significantly reduces both the expected error and variance of state estimation. All components are parameterized by neural networks, enabling end-to-end differentiable training. Extensive experiments on multiple synthetic and real-world benchmarks demonstrate consistent superiority over state-of-the-art deep learning and statistical models, validating the framework’s enhanced capability to model nonstationarity and abrupt structural changes, along with its strong generalization performance.

Technology Category

• Machine Learning: Time-Series/Data Streams
• Reasoning under Uncertainty: Stochastic Optimization
• Natural Language Processing: Learning & Optimization for NLP

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Web Mining and Content Analysis: Large pretrained models with web data
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• Modeling non-stationary time series with abrupt changes
• Combining stochastic dynamics and jump processes for forecasting
• Improving accuracy and reducing variance in SDE simulations

Innovation

• Neural network based non-stationary MJD model
• Likelihood truncation for tractable jump learning
• Euler-Maruyama with restart solver