[Paper Review] Conditional Sig-Wasserstein GANs for Time Series Generation

Shujian Liao, Hao Ni+4 more|arXiv (Cornell University)|Jun 9, 2020

Generative Adversarial Networks and Image Synthesis29 references18 citations

TL;DR

This paper proposes Conditional Sig-Wasserstein GANs (SigCWGANs), a novel framework that leverages the path signature from rough path theory to model the conditional distribution of future time series given past observations. By using the signature feature space to explicitly represent the $W_1$-Wasserstein metric, the method enables efficient training without costly discriminator approximation, achieving state-of-the-art performance in generating realistic multivariate time series across synthetic and real-world datasets including stock prices and Bitcoin-USD data.

ABSTRACT

Generative adversarial networks (GANs) have been extremely successful in generating samples, from seemingly high dimensional probability measures. However, these methods struggle to capture the temporal dependence of joint probability distributions induced by time-series data. Furthermore, long time-series data streams hugely increase the dimension of the target space, which may render generative modelling infeasible. To overcome these challenges, motivated by the autoregressive models in econometric, we are interested in the conditional distribution of future time series given the past information. We propose the generic conditional Sig-WGAN framework by integrating Wasserstein-GANs (WGANs) with mathematically principled and efficient path feature extraction called the signature of a path. The signature of a path is a graded sequence of statistics that provides a universal description for a stream of data, and its expected value characterises the law of the time-series model. In particular, we develop the conditional Sig-$W_1$ metric, that captures the conditional joint law of time series models, and use it as a discriminator. The signature feature space enables the explicit representation of the proposed discriminators which alleviates the need for expensive training. We validate our method on both synthetic and empirical dataset and observe that our method consistently and significantly outperforms state-of-the-art benchmarks with respect to measures of similarity and predictive ability.

Motivation & Objective

• To address the challenge of modeling complex temporal dependencies in high-dimensional multivariate time series using data-driven, non-parametric methods.
• To overcome the limitations of standard GANs in capturing joint laws of time series due to high dimensionality and complex temporal-spatial interactions.
• To develop a conditional generative model that learns the distribution of future time series given past observations, enabling forecasting and counterfactual generation.
• To reduce training complexity by replacing implicit discriminator learning with explicit, signature-based $W_1$ metric approximation.
• To validate the method on both synthetic and empirical datasets, demonstrating superior performance in distributional similarity and predictive accuracy.

Proposed method

• The method integrates Wasserstein GANs (WGANs) with the signature of a path—a universal, graded feature representation of time series data that captures temporal dynamics up to a specified depth.
• It introduces the conditional Sig-$W_1$ metric, which quantifies the distance between conditional laws of time series by comparing the expected signatures of future paths given past paths.
• The discriminator is explicitly constructed using signature features, eliminating the need for end-to-end training of a neural network critic.
• The generator is trained to minimize the conditional Sig-$W_1$ distance between real and generated future time series, conditioned on past segments.
• The framework uses sliding windows to extract multiple training samples from a single long time series, improving data efficiency.
• The model is trained using a minimax objective based on the signature-based $W_1$ metric, enabling stable and efficient optimization.

Experimental results

Research questions

• RQ1 Can the signature of a path be used to construct an efficient and interpretable discriminator for conditional time series generation?
• RQ2 Does the conditional Sig-$W_1$ metric effectively capture the joint law of time series while preserving temporal dependencies?
• RQ3 Can a signature-based $W_1$ metric replace the need for training a deep neural network discriminator, thereby simplifying training and improving stability?
• RQ4 How does the SigCWGAN framework compare to state-of-the-art GANs in modeling marginal distributions, autocorrelations, and predictive $R^2$ in real-world time series?
• RQ5 To what extent does the method generalize across different time series modalities, such as financial returns and cryptocurrency prices?

Key findings

• On the SPX and DJI dataset, SigCWGAN achieved the lowest marginal distribution error (0.47107) and auto-correlation error (0.04075), outperforming all baselines including GANs and GARCH models.
• For the Bitcoin-USD dataset, SigCWGAN achieved an $R^2$ score of 0.3320, slightly below RCGAN (0.3165), but significantly outperformed it in marginal distribution (2.0532 vs. 2.8603) and auto-correlation (0.091 vs. 0.0532).
• The method demonstrated superior performance in capturing cross-correlation structures, as shown in Figure 9, where synthetic matrices closely matched real ones in structure and magnitude.
• ACF plots (Figure 10) confirmed that SigCWGAN-generated time series preserved long-range temporal dependencies, with the smallest sum of absolute differences from real ACFs.
• The model achieved state-of-the-art results on both synthetic and empirical datasets, with consistent improvements in distributional similarity and predictive ability metrics.
• The explicit use of signature features eliminated the need for training a deep neural network discriminator, significantly simplifying training and improving convergence stability.