Tackling the exponential scaling of signature-based GANs for high-dimensional financial time series generation

Abstract

Generative Adversarial Networks (GANs) have been shown to be able to generate samples of complex financial time series, particularly by employing the concept of path signatures, a universal description of the geometric properties of a data stream whose expected value uniquely characterizes the time series. In particular, the SigCWGAN model is able to generate time series of arbitrary length; however, the parameters of the neural network employed grow exponentially with the dimension of the underlying time series, which makes the model intractable when seeking to generate large financial market scenarios. To overcome this curse of dimensionality, we propose an iterative generation procedure relying on the concept of hierarchies in financial markets. We construct an ensemble of GANs, that we call the Hierarchical-SigCWGAN, based on hierarchical clustering that approximate signatures in the spirit of the original model. The Hierarchical-SigCWGAN is able to scale to higher dimensions and generate large-dimensional scenarios in which the joint behavior of all the assets in the market is replicated. We validate our model by comparing its performance on a series of similarity metrics with respect to the original SigCWGAN on a dataset where it is still tractable and showcase its scalability.