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We introduce three new generative models for time series that are based onEuler discretization of Stochastic Differential Equations (SDEs) andWasserstein metrics. Two of these methods rely on the adaptation of generativeadversarial networks (GANs) to time series. The third algorithm, calledConditional Euler Generator (CEGEN), minimizes a dedicated distance between thetransition probability distributions over all time steps. In the context of Itoprocesses, we provide theoretical guarantees that minimizing this criterionimplies accurate estimations of the drift and volatility parameters. Wedemonstrate empirically that CEGEN outperforms state-of-the-art and GANgenerators on both marginal and temporal dynamics metrics. Besides, itidentifies accurate correlation structures in high dimension. When few datapoints are available, we verify the effectiveness of CEGEN, when combined withtransfer learning methods on Monte Carlo simulations. Finally, we illustratethe robustness of our method on various real-world datasets.

Conditional Loss and Deep Euler Scheme for Time Series Generation