mlsanityData to 7 Oct 2026

Universal randomised signatures for generative time series modelling

arXiv 2406.10214 ↗First posted 14 Jun 2024cs.LG q-fin.MF stat.MLcited by 4

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Abstract (arXiv)

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.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 41 of its 70 references that are in the map. First posted on arXiv 14 Jun 2024.

Builds on

41 of 70 references.

References · 41

  1. 2017Real-valued (Medical) Time Series Generation with Recurrent Conditional GANscited by 329
  2. 2018Adversarial Audio Synthesiscited by 222
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  12. 2022Wavelet Score-Based Generative Modelingcited by 61
29 more
  1. 2021Sig-Wasserstein GANs for Time Series Generationcited by 60
  2. 2020Approximation Bounds for Random Neural Networks and Reservoir Systemscited by 52
  3. 2018Reservoir Computing Universality With Stochastic Inputscited by 48
  4. 2017Universal discrete-time reservoir computers with stochastic inputs and linear readouts using non-homogeneous state-affine systemscited by 39
  5. 2023Non-adversarial training of Neural SDEs with signature kernel scorescited by 36
  6. 2020A Data-driven Market Simulator for Small Data Environmentscited by 34
  7. 2021Random feature neural networks learn Black-Scholes type PDEs without curse of dimensionalitycited by 34
  8. 2018Learning with SGD and Random Featurescited by 33
  9. 2021Towards Realistic Market Simulations: a Generative Adversarial Networks Approachcited by 29
  10. 2019Deep Hedging: Learning to Simulate Equity Option Marketscited by 25
  11. 2023Neural signature kernels as infinite-width-depth-limits of controlled ResNetscited by 25
  12. 2020Conditional Sig-Wasserstein GANs for Time Series Generationcited by 23
  13. 2020Discrete-time signatures and randomness in reservoir computingcited by 23
  14. 2019Generative Adversarial Networks for Financial Trading Strategies Fine-Tuning and Combinationcited by 22
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  17. 2021Multi-Asset Spot and Option Market Simulationcited by 17
  18. 2019CorrGAN: Sampling Realistic Financial Correlation Matrices Using Generative Adversarial Networkscited by 15
  19. 2024Lecture notes on rough paths and applications to machine learningcited by 13
  20. 2023Universal approximation property of Banach space-valued random feature models including random neural networkscited by 12
  21. 2023Signature Methods in Stochastic Portfolio Theorycited by 11
  22. 2022Applications of Signature Methods to Market Anomaly Detectioncited by 9
  23. 2019A neural network-based framework for financial model calibrationcited by 8
  24. 2022Path Development Network with Finite-dimensional Lie Group Representationcited by 8
  25. 2021Scenario generation for market risk models using generative neural networkscited by 7
  26. 2022Simulating financial time series using attentioncited by 4
  27. 2023G-Signatures: Global Graph Propagation With Randomized Signaturescited by 4
  28. 2023Generative Machine Learning for Multivariate Equity Returnscited by 4
  29. 2023Randomized Signature Methods in Optimal Portfolio Selectioncited by 4

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 2; 2025: 1; 2026: 1.

4 papers.

  1. 2024Time-Causal VAE: Robust Financial Time Series Generatorcited by 8
  2. 2024Infinite-dimensional Mahalanobis Distance with Applications to Kernelized Novelty Detectioncited by 1
  3. 2026Generating Financial Time Series by Matching Random Convolutional Featurescited by 1
  4. 2025Random Controlled Differential Equationscited by 0