Sig-Splines: universal approximation and convex calibration of time series generative models

TL;DR

This paper introduces Sig-Splines, a new generative model for multivariate discrete-time time series that combines linear transformations and signature transforms, achieving universality and convexity in parameters.

Contribution

The paper presents Sig-Splines, a novel model that replaces neural networks with linear transformations and signature transforms, ensuring universality and convexity.

Findings

Achieves universal approximation for time series data.

Introduces convexity in model parameters for easier optimization.

Demonstrates effectiveness on multivariate discrete-time series.

Abstract

We propose a novel generative model for multivariate discrete-time time series data. Drawing inspiration from the construction of neural spline flows, our algorithm incorporates linear transformations and the signature transform as a seamless substitution for traditional neural networks. This approach enables us to achieve not only the universality property inherent in neural networks but also introduces convexity in the model's parameters.