Conditional Loss and Deep Euler Scheme for Time Series Generation

TL;DR

This paper introduces three novel time series generative models based on Euler discretization of SDEs and Wasserstein metrics, with a focus on the new CEGEN method that outperforms existing models.

Contribution

The paper proposes a new generative model, CEGEN, that minimizes a specific distance between transition probabilities, with theoretical guarantees and superior empirical performance.

Findings

CEGEN outperforms state-of-the-art GANs in metrics.

CEGEN accurately captures correlation structures in high dimensions.

CEGEN is effective with limited data and transfer learning.

Abstract

We introduce three new generative models for time series that are based on Euler discretization of Stochastic Differential Equations (SDEs) and Wasserstein metrics. Two of these methods rely on the adaptation of generative adversarial networks (GANs) to time series. The third algorithm, called Conditional Euler Generator (CEGEN), minimizes a dedicated distance between the transition probability distributions over all time steps. In the context of Ito processes, we provide theoretical guarantees that minimizing this criterion implies accurate estimations of the drift and volatility parameters. We demonstrate empirically that CEGEN outperforms state-of-the-art and GAN generators on both marginal and temporal dynamics metrics. Besides, it identifies accurate correlation structures in high dimension. When few data points are available, we verify the effectiveness of CEGEN, when combined with transfer learning methods on Monte Carlo simulations. Finally, we illustrate the robustness of our method on various real-world datasets.