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

TL;DR

Neural MJD introduces a neural network model based on a non-stationary jump diffusion process, explicitly modeling stochastic dynamics and jumps for improved time series prediction, especially in non-stationary and abrupt change scenarios.

Contribution

The paper presents Neural MJD, a novel neural network framework that explicitly models non-stationary stochastic processes with jumps using SDE simulation, including a likelihood truncation and a new solver.

Findings

Outperforms state-of-the-art methods on synthetic and real data

Provides theoretical error bounds for approximation methods

Effectively captures non-stationary dynamics and jumps

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.