Schr\"odinger bridges with jumps for time series generation

TL;DR

This paper introduces a jump-diffusion Schr"odinger bridge model for time series generation, capturing discontinuities and regime changes in financial and energy data more effectively than diffusion-only models.

Contribution

It extends existing diffusion-based models by incorporating jumps, formulating a stochastic control problem, and developing algorithms for data-driven training and sampling.

Findings

Incorporating jumps improves realism of generated data.

The model captures abrupt movements and heavy tails.

Numerical experiments demonstrate superior performance on real datasets.

Abstract

We study generative modeling for time series using entropic optimal transport and the Schr\"odinger bridge (SB) framework, with a focus on applications in finance and energy modeling. Extending the diffusion-based approach of Hamdouche, Henry-Labord\`ere, Pham, 2023, we introduce a jump-diffusion Schr\"odinger bridge model that allows for discontinuities in the generative dynamics. Starting from a Schr\"odinger bridge entropy minimization problem, we reformulate the task as a stochastic control problem whose solution characterizes the optimal controlled jump-diffusion process. When sampled on a fixed time grid, this process generates synthetic time series matching the joint distributions of the observed data. The model is fully data-driven, as both the drift and the jump intensity are learned directly from the data. We propose practical algorithms for training, sampling, and hyperparameter calibration. Numerical experiments on simulated and real datasets, including financial and energy time series, show that incorporating jumps substantially improves the realism of the generated data, in particular by capturing abrupt movements, heavy tails, and regime changes that diffusion-only models fail to reproduce. Comparisons with state-of-the-art generative models highlight the benefits and limitations of the proposed approach.