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.
Categories: q-fin.MF