Conditional Sig-Wasserstein GANs for Time Series Generation

32 Pages Posted: 2 Jul 2020

See all articles by Hao Ni

Hao Ni

University College London - Department of Mathematics; The Alan Turing Institute

Lukasz Szpruch

University of Edinburgh - School of Mathematics

Magnus Wiese

University of Kaiserslautern - Department of Mathematics

Shujian Liao

University College London - Department of Mathematics

Baoren Xiao

University College London - Department of Mathematics; The Alan Turing Institute

Date Written: June 9, 2020

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, we integrate GANs 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 a new metric, (conditional) Sig-$W_1$, 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. Furthermore, we develop a novel generator, called the conditional AR-FNN, which is designed to capture the temporal dependence of time series and can be efficiently trained. 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.

Keywords: Conditional Generative Adversarial Network, Neural Networks, Time Series, Rough Path Theory, Generative Modelling, Wasserstein Distance, Mathematical Finance, Signatures

JEL Classification: C15, C45, C5, C53, C6, C63, G00

Suggested Citation

Ni, Hao and Szpruch, Lukasz and Wiese, Magnus and Liao, Shujian and Xiao, Baoren, Conditional Sig-Wasserstein GANs for Time Series Generation (June 9, 2020). Available at SSRN: https://ssrn.com/abstract=3623086 or http://dx.doi.org/10.2139/ssrn.3623086

Hao Ni (Contact Author)

University College London - Department of Mathematics ( email )

Gower Street
London, WC1E 6BT
United Kingdom

The Alan Turing Institute ( email )

British Library, 96 Euston Road
London, NW12DB
United Kingdom

Lukasz Szpruch

University of Edinburgh - School of Mathematics ( email )

James Clerk Maxwell Building
Peter Guthrie Tait Rd
Edinburgh, EH9 3FD
United Kingdom

Magnus Wiese

University of Kaiserslautern - Department of Mathematics ( email )

D-67653 Kaiserslautern
Germany

Shujian Liao

University College London - Department of Mathematics ( email )

Gower Street
London, WC1E 6BT
United Kingdom

Baoren Xiao

University College London - Department of Mathematics ( email )

Gower Street
London, WC1E 6BT
United Kingdom

The Alan Turing Institute ( email )

British Library, 96 Euston Road
London, NW12DB
United Kingdom

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