Generative modelling of financial time series with structured noise and MMD-based signature learning

Generating synthetic financial time series data that accurately reflects real-world market dynamics holds tremendous potential for various applications, including portfolio optimization, risk management, and large scale machine learning. We present an approach that uses structured noise for training generative models for financial time series. The expressive power of the signature transform has been shown to be able to capture the complex dependencies and temporal structures inherent in financial data when used to train generative models in the form of a signature kernel. We employ a moving average model to model the variance of the noise input, enhancing the model’s ability to reproduce stylized facts such as volatility clustering. Through empirical experiments on S&P 500 index data, we demonstrate that our model effectively captures key characteristics of financial time series and outperforms comparable approaches. In addition, we explore the application of the synthetic data generated to train a reinforcement learning agent for portfolio management, achieving promising results. Finally, we propose a method to add robustness to the generative model by tweaking the noise input so that the generated sequences can be adjusted to different market environments with minimal data.