# Universal randomised signatures for generative time series modelling

arXiv: https://arxiv.org/abs/2406.10214 · HTML: https://mlsanity.com/paper/2406.10214/

## Key facts

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

## Builds on (most cited first, 30 of 41)

- [Real-valued (Medical) Time Series Generation with Recurrent Conditional GANs](https://mlsanity.com/paper/1706.02633/) (2017)
- [Adversarial Audio Synthesis](https://mlsanity.com/paper/1802.04208/) (2018)
- [Training GANs with Optimism](https://mlsanity.com/paper/1711.00141/) (2017)
- [Generalization Properties of Learning with Random Features](https://mlsanity.com/paper/1602.04474/) (2016)
- [C-RNN-GAN: Continuous recurrent neural networks with adversarial training](https://mlsanity.com/paper/1611.09904/) (2016)
- [Generalization error of random features and kernel methods: hypercontractivity and kernel matrix concentration](https://mlsanity.com/paper/2101.10588/) (2021)
- [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)
- [Neural SDE: Stabilizing Neural ODE Networks with Stochastic Noise](https://mlsanity.com/paper/1906.02355/) (2019)
- [Echo state networks are universal](https://mlsanity.com/paper/1806.00797/) (2018)
- [COT-GAN: Generating Sequential Data via Causal Optimal Transport](https://mlsanity.com/paper/2006.08571/) (2020)
- [Wavelet Score-Based Generative Modeling](https://mlsanity.com/paper/2208.05003/) (2022)
- [Sig-Wasserstein GANs for Time Series Generation](https://mlsanity.com/paper/2111.01207/) (2021)
- [Approximation Bounds for Random Neural Networks and Reservoir Systems](https://mlsanity.com/paper/2002.05933/) (2020)
- [Reservoir Computing Universality With Stochastic Inputs](https://mlsanity.com/paper/1807.02621/) (2018)
- [Universal discrete-time reservoir computers with stochastic inputs and linear readouts using non-homogeneous state-affine systems](https://mlsanity.com/paper/1712.00754/) (2017)
- [Non-adversarial training of Neural SDEs with signature kernel scores](https://mlsanity.com/paper/2305.16274/) (2023)
- [A Data-driven Market Simulator for Small Data Environments](https://mlsanity.com/paper/2006.14498/) (2020)
- [Random feature neural networks learn Black-Scholes type PDEs without curse of dimensionality](https://mlsanity.com/paper/2106.08900/) (2021)
- [Learning with SGD and Random Features](https://mlsanity.com/paper/1807.06343/) (2018)
- [Towards Realistic Market Simulations: a Generative Adversarial Networks Approach](https://mlsanity.com/paper/2110.13287/) (2021)
- [Deep Hedging: Learning to Simulate Equity Option Markets](https://mlsanity.com/paper/1911.01700/) (2019)
- [Neural signature kernels as infinite-width-depth-limits of controlled ResNets](https://mlsanity.com/paper/2303.17671/) (2023)
- [Conditional Sig-Wasserstein GANs for Time Series Generation](https://mlsanity.com/paper/2006.05421/) (2020)
- [Discrete-time signatures and randomness in reservoir computing](https://mlsanity.com/paper/2010.14615/) (2020)
- [Generative Adversarial Networks for Financial Trading Strategies Fine-Tuning and Combination](https://mlsanity.com/paper/1901.01751/) (2019)
- [Arbitrage-free neural-SDE market models](https://mlsanity.com/paper/2105.11053/) (2021)
- [Generative modeling for time series via Schr"odinger bridge](https://mlsanity.com/paper/2304.05093/) (2023)
- [Multi-Asset Spot and Option Market Simulation](https://mlsanity.com/paper/2112.06823/) (2021)
- [CorrGAN: Sampling Realistic Financial Correlation Matrices Using Generative Adversarial Networks](https://mlsanity.com/paper/1910.09504/) (2019)

## Built on by (most cited first, 4 of 4)

- [Time-Causal VAE: Robust Financial Time Series Generator](https://mlsanity.com/paper/2411.02947/) (2024)
- [Infinite-dimensional Mahalanobis Distance with Applications to Kernelized Novelty Detection](https://mlsanity.com/paper/2407.11873/) (2024)
- [Generating Financial Time Series by Matching Random Convolutional Features](https://mlsanity.com/paper/2606.05138/) (2026)
- [Random Controlled Differential Equations](https://mlsanity.com/paper/2512.23670/) (2025)

## 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.