Generating synthetic data for financial time series poses challenges, especially considering their non-stationary nature. Traditional statistical time series models normally assume weak stationarity. However, this assumption can constrain their effectiveness. Deep learning models, particularly Generative Adversarial Networks (GANs), have exhibited considerable potential in emulating complex probability distributions. GANs employ a generator-discriminator framework, where the generator creates data samples, while the discriminator distinguishes real from generated data. In this research, we introduce the Sig-Graph GAN model, which integrates the time-series signature, offering a structured summary of its temporal evolution; the Long Short-Term Memory network, capturing its inherent autoregressive structure; and Graph Neural Networks (GNNs), leveraging geometric patterns within the time-series data. To employ GNNs optimally, we use the visibility graph algorithm to derive a graph-based representation of the underlying time series. Numerical evaluations demonstrate that the Sig-Graph GAN model outperforms baseline methods in replicating the distribution of logarithmic returns across different stock exchanges. The integration of the graph structure with the autoregressive component effectively captures both geometric and temporal patterns embedded in time-series data. This research advances the field of GAN models for time series by introducing a model capable of leveraging both autoregressive properties and geometric structures for synthetic data generation.

翻译：暂无翻译