Tackling the Exponential Scaling of Signature-Based Generative Adversarial Networks for High-Dimensional Financial Time-Series Generation

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. Specifically, the SigCWGAN model (Ni et al. 2020) can 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 problem of dimensionality, the authors propose an iterative generation procedure relying on the concept of hierarchies in financial markets. The authors construct an ensemble of GANs that they call the Hierarchical-SigCWGAN, which is based on hierarchical clustering that approximates signatures in the spirit of the original model. The Hierarchical-SigCWGAN can scale to higher dimensions and generate large-dimensional scenarios in which the joint behavior of all the assets in the market is replicated. The model is validated by comparing its performance on a series of similarity metrics with respect to the original SigCWGAN on a dataset in which it is still tractable and by showing its scalability on a larger dataset.