Neural MJD: Neural Non-Stationary Merton Jump Diffusion for Time Series Prediction
This addresses the limitation of black-box deep learning models in generalizing to non-stationary time series data with jumps, which is incremental as it combines existing stochastic processes with neural networks.
The authors tackled the problem of time series prediction with non-stationary data and abrupt changes by introducing Neural MJD, a neural network-based model that formulates forecasting as a stochastic differential equation simulation, and it consistently outperformed state-of-the-art methods in experiments.
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.