Sig-Splines: Universal Approximation and Convex Calibration of Time Series Generative Models

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.

Keywords: generative modelling, market simulation, signatures, time series

JEL Classification: C15, C45, C5, C53, C6, C63