Sig-Splines: universal approximation and convex calibration of time series generative models
This work addresses the need for improved generative models in time series analysis, offering a method with theoretical guarantees like universality and convexity, though it appears incremental by building on neural spline flows.
The authors tackled the problem of generating multivariate discrete-time time series data by proposing a novel generative model that replaces traditional neural networks with linear transformations and the signature transform, achieving universality and convexity in parameters.
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.