# Sig-Wasserstein GANs for Time Series Generation

arXiv: https://arxiv.org/abs/2111.01207 · HTML: https://mlsanity.com/paper/2111.01207/

## Key facts

- Cited by 60 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 26 references that are in the map.
- First posted on arXiv 1 Nov 2021.

## Builds on (most cited first, 16 of 16)

- [Neural Controlled Differential Equations for Irregular Time Series](https://mlsanity.com/paper/2005.08926/) (2020)
- [On Gradient Descent Ascent for Nonconvex-Concave Minimax Problems](https://mlsanity.com/paper/1906.00331/) (2019)
- [Are GANs Created Equal? A Large-Scale Study](https://mlsanity.com/paper/1711.10337/) (2017)
- [Training GANs with Optimism](https://mlsanity.com/paper/1711.00141/) (2017)
- [Cycles in adversarial regularized learning](https://mlsanity.com/paper/1709.02738/) (2017)
- [Quant GANs: Deep Generation of Financial Time Series](https://mlsanity.com/paper/1907.06673/) (2019)
- [The Limit Points of (Optimistic) Gradient Descent in Min-Max Optimization](https://mlsanity.com/paper/1807.03907/) (2018)
- [Signature moments to characterize laws of stochastic processes](https://mlsanity.com/paper/1810.10971/) (2018)
- [A Data-driven Market Simulator for Small Data Environments](https://mlsanity.com/paper/2006.14498/) (2020)
- [A generative adversarial network approach to calibration of local stochastic volatility models](https://mlsanity.com/paper/2005.02505/) (2020)
- [Deep Hedging: Learning to Simulate Equity Option Markets](https://mlsanity.com/paper/1911.01700/) (2019)
- [Generative Adversarial Networks for Financial Trading Strategies Fine-Tuning and Combination](https://mlsanity.com/paper/1901.01751/) (2019)
- [Robust pricing and hedging via neural SDEs](https://mlsanity.com/paper/2007.04154/) (2020)
- [GANs May Have No Nash Equilibria](https://mlsanity.com/paper/2002.09124/) (2020)
- [Learning stochastic differential equations using RNN with log signature features](https://mlsanity.com/paper/1908.08286/) (2019)
- [Logsig-RNN: a novel network for robust and efficient skeleton-based action recognition](https://mlsanity.com/paper/2110.13008/) (2021)

## Built on by (most cited first, 30 of 60)

- [FinDiff: Diffusion Models for Financial Tabular Data Generation](https://mlsanity.com/paper/2309.01472/) (2023)
- [Non-adversarial training of Neural SDEs with signature kernel scores](https://mlsanity.com/paper/2305.16274/) (2023)
- [TSGBench: Time Series Generation Benchmark](https://mlsanity.com/paper/2309.03755/) (2023)
- [Designing Universal Causal Deep Learning Models: The Geometric (Hyper)Transformer](https://mlsanity.com/paper/2201.13094/) (2022)
- [Global universal approximation of functional input maps on weighted spaces](https://mlsanity.com/paper/2306.03303/) (2023)
- [TSGM: A Flexible Framework for Generative Modeling of Synthetic Time Series](https://mlsanity.com/paper/2305.11567/) (2023)
- [Multi-Asset Spot and Option Market Simulation](https://mlsanity.com/paper/2112.06823/) (2021)
- [PCF-GAN: generating sequential data via the characteristic function of measures on the path space](https://mlsanity.com/paper/2305.12511/) (2023)
- [TransFusion: Generating Long, High Fidelity Time Series using Diffusion Models with Transformers](https://mlsanity.com/paper/2307.12667/) (2023)
- [Fractional SDE-Net: Generation of Time Series Data with Long-term Memory](https://mlsanity.com/paper/2201.05974/) (2022)
- [Random Fourier Signature Features](https://mlsanity.com/paper/2311.12214/) (2023)
- [Structured Agentic Workflows for Financial Time-Series Modeling with LLMs and Reflective Feedback](https://mlsanity.com/paper/2508.13915/) (2025)
- [Time-Causal VAE: Robust Financial Time Series Generator](https://mlsanity.com/paper/2411.02947/) (2024)
- [Improving Astronomical Time-series Classification via Data Augmentation with Generative Adversarial Networks](https://mlsanity.com/paper/2205.06758/) (2022)
- [AIGC for Industrial Time Series: From Deep Generative Models to Large Generative Models](https://mlsanity.com/paper/2407.11480/) (2024)
- [Continuous-time stochastic gradient descent for optimizing over the stationary distribution of stochastic differential equations](https://mlsanity.com/paper/2202.06637/) (2022)
- [Towards Controllable Time Series Generation](https://mlsanity.com/paper/2403.03698/) (2024)
- [Universal randomised signatures for generative time series modelling](https://mlsanity.com/paper/2406.10214/) (2024)
- [Efficient Training of Neural Stochastic Differential Equations by Matching Finite Dimensional Distributions](https://mlsanity.com/paper/2410.03973/) (2024)
- [WaveStitch: Flexible and Fast Conditional Time Series Generation with Diffusion Models](https://mlsanity.com/paper/2503.06231/) (2025)
- [Deep Learning for Systemic Risk Measures](https://mlsanity.com/paper/2207.00739/) (2022)
- [Generative Modelling of L'evy Area for High Order SDE Simulation](https://mlsanity.com/paper/2308.02452/) (2023)
- [GCN-DevLSTM: Path Development for Skeleton-Based Action Recognition](https://mlsanity.com/paper/2403.15212/) (2024)
- [Synthetic Aircraft Trajectory Generation Using Time-Based VQ-VAE](https://mlsanity.com/paper/2504.09101/) (2025)
- [Signature Maximum Mean Discrepancy Two-Sample Statistical Tests](https://mlsanity.com/paper/2506.01718/) (2025)
- [CTBench: Cryptocurrency Time Series Generation Benchmark](https://mlsanity.com/paper/2508.02758/) (2025)
- [Risk-Neutral Market Simulation](https://mlsanity.com/paper/2202.13996/) (2022)
- [Non-parametric online market regime detection and regime clustering for multidimensional and path-dependent data structures](https://mlsanity.com/paper/2306.15835/) (2023)
- [Risk factor aggregation and stress testing](https://mlsanity.com/paper/2310.04511/) (2023)
- [RHiOTS: A Framework for Evaluating Hierarchical Time Series Forecasting Algorithms](https://mlsanity.com/paper/2408.03399/) (2024)

## Abstract (arXiv)

Synthetic data is an emerging technology that can significantly accelerate the development and deployment of AI machine learning pipelines. In this work, we develop high-fidelity time-series generators, the SigWGAN, by combining continuous-time stochastic models with the newly proposed signature W1 metric. The former are the Logsig-RNN models based on the stochastic differential equations, whereas the latter originates from the universal and principled mathematical features to characterize the measure induced by time series. SigWGAN allows turning computationally challenging GAN min-max problem into supervised learning while generating high fidelity samples. We validate the proposed model on both synthetic data generated by popular quantitative risk models and empirical financial data. Codes are available at https://github.com/SigCGANs/Sig-Wasserstein-GANs.git.