Universal randomised signatures for generative time series modelling

TL;DR

This paper introduces a novel generative model for financial time series using randomised signatures and a Wasserstein-type distance, providing universal approximation results and outperforming benchmarks.

Contribution

It presents a new generative framework employing randomised signatures and a Wasserstein metric, with theoretical guarantees and practical applications in financial data modeling.

Findings

Effective synthetic time series generation demonstrated.

Universal approximation properties established.

Outperforms existing benchmark models.

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.