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Universal randomised signatures for generative time series modelling

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  • Francesca Biagini
  • Lukas Gonon
  • Niklas Walter

Abstract

Randomised signature has been proposed as a flexible and easily implementable alternative to the well-established path signature. In this article, we employ randomised signature to introduce a generative model for financial time series data in the spirit of reservoir computing. Specifically, we propose a novel Wasserstein-type distance based on discrete-time randomised signatures. This metric on the space of probability measures captures the distance between (conditional) distributions. Its use is justified by our novel universal approximation results for randomised signatures on the space of continuous functions taking the underlying path as an input. We then use our metric as the loss function in a non-adversarial generator model for synthetic time series data based on a reservoir neural stochastic differential equation. We compare the results of our model to benchmarks from the existing literature.

Suggested Citation

  • Francesca Biagini & Lukas Gonon & Niklas Walter, 2024. "Universal randomised signatures for generative time series modelling," Papers 2406.10214, arXiv.org, revised Sep 2024.
    • Handle: RePEc:arx:papers:2406.10214
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    References listed on IDEAS

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    1. Erdinc Akyildirim & Matteo Gambara & Josef Teichmann & Syang Zhou, 2022. "Applications of Signature Methods to Market Anomaly Detection," Papers 2201.02441, arXiv.org, revised Feb 2022.
    2. Adriano Koshiyama & Nick Firoozye & Philip Treleaven, 2021. "Generative adversarial networks for financial trading strategies fine-tuning and combination," Quantitative Finance, Taylor & Francis Journals, vol. 21(5), pages 797-813, May.
    3. Christa Cuchiero & Janka Moller, 2023. "Signature Methods in Stochastic Portfolio Theory," Papers 2310.02322, arXiv.org, revised Mar 2024.
    4. Magnus Wiese & Robert Knobloch & Ralf Korn & Peter Kretschmer, 2020. "Quant GANs: deep generation of financial time series," Quantitative Finance, Taylor & Francis Journals, vol. 20(9), pages 1419-1440, September.
    5. Takahashi, Shuntaro & Chen, Yu & Tanaka-Ishii, Kumiko, 2019. "Modeling financial time-series with generative adversarial networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 527(C).
    6. Magnus Wiese & Ben Wood & Alexandre Pachoud & Ralf Korn & Hans Buehler & Phillip Murray & Lianjun Bai, 2021. "Multi-Asset Spot and Option Market Simulation," Papers 2112.06823, arXiv.org.
    7. Magnus Wiese & Lianjun Bai & Ben Wood & Hans Buehler, 2019. "Deep Hedging: Learning to Simulate Equity Option Markets," Papers 1911.01700, arXiv.org.
    8. Samuel N. Cohen & Christoph Reisinger & Sheng Wang, 2023. "Arbitrage-Free Neural-SDE Market Models," Applied Mathematical Finance, Taylor & Francis Journals, vol. 30(1), pages 1-46, January.
    9. Solveig Flaig & Gero Junike, 2022. "Scenario Generation for Market Risk Models Using Generative Neural Networks," Risks, MDPI, vol. 10(11), pages 1-28, October.
    10. Mohamed Hamdouche & Pierre Henry-Labordere & Huyên Pham, 2023. "Generative modeling for time series via Schrödinger bridge," Working Papers hal-04063041, HAL.
    11. Mohamed Hamdouche & Pierre Henry-Labordere & Huy^en Pham, 2023. "Generative modeling for time series via Schr{\"o}dinger bridge," Papers 2304.05093, arXiv.org.
    12. Hans Buhler & Blanka Horvath & Terry Lyons & Imanol Perez Arribas & Ben Wood, 2020. "A Data-driven Market Simulator for Small Data Environments," Papers 2006.14498, arXiv.org.
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