[Paper Review] Wasserstein GAN: Deep Generation applied on Bitcoins financial time series

Samuel Rikli, Daniel Nico Bigler+2 more|arXiv (Cornell University)|Jul 13, 2021

Stock Market Forecasting Methods18 references4 citations

TL;DR

This paper proposes a WGAN-GP with LSTM architecture to generate synthetic Bitcoin financial time series, leveraging adversarial training to learn the underlying distribution of volatile price movements. The model produces visually indistinguishable synthetic data, though statistical properties like autocorrelation and tail behavior show measurable differences from real data, indicating stable training but room for hyperparameter optimization.

ABSTRACT

Modeling financial time series is challenging due to their high volatility and unexpected happenings on the market. Most financial models and algorithms trying to fill the lack of historical financial time series struggle to perform and are highly vulnerable to overfitting. As an alternative, we introduce in this paper a deep neural network called the WGAN-GP, a data-driven model that focuses on sample generation. The WGAN-GP consists of a generator and discriminator function which utilize an LSTM architecture. The WGAN-GP is supposed to learn the underlying structure of the input data, which in our case, is the Bitcoin. Bitcoin is unique in its behavior; the prices fluctuate what makes guessing the price trend hardly impossible. Through adversarial training, the WGAN-GP should learn the underlying structure of the bitcoin and generate very similar samples of the bitcoin distribution. The generated synthetic time series are visually indistinguishable from the real data. But the numerical results show that the generated data were close to the real data distribution but distinguishable. The model mainly shows a stable learning behavior. However, the model has space for optimization, which could be achieved by adjusting the hyperparameters.

Motivation & Objective

• To address the challenge of generating realistic financial time series for high-volatility assets like Bitcoin.
• To overcome limitations of traditional models in handling non-stationarity, fat tails, and volatility clustering in financial data.
• To evaluate the performance of a WGAN-GP with LSTM on capturing the statistical and temporal dynamics of real Bitcoin price movements.
• To explore the feasibility of using deep generative models for synthetic data creation in finance while preserving data integrity and privacy.

Proposed method

• The model employs a Wasserstein GAN with gradient penalty (WGAN-GP) to stabilize training and enforce the Lipschitz constraint.
• A Long Short-Term Memory (LSTM) network is used in both the generator and discriminator to model sequential dependencies in time series data.
• The generator learns to map random noise to synthetic Bitcoin log returns, while the discriminator (critic) evaluates the realism of generated sequences.
• Training uses a minimax loss with gradient penalty to ensure the critic’s gradient norm remains close to one, improving training stability.
• The model is trained on historical Bitcoin daily log returns, with hyperparameters tuned for stability and convergence.
• Evaluation includes visual comparison, QQ-plots, ACF analysis, and loss monitoring to assess distributional and temporal fidelity.

Experimental results

Research questions

• RQ1 Can a WGAN-GP with LSTM architecture effectively generate synthetic Bitcoin time series that resemble real market dynamics?
• RQ2 How well does the generated data preserve key statistical properties such as fat tails, skewness, and volatility clustering?
• RQ3 To what extent does the model capture the autocorrelation structure of real financial returns?
• RQ4 Why does the loss function exhibit oscillatory behavior instead of converging to a minimum during training?
• RQ5 How do the generated data compare to real data in terms of extreme value behavior and tail characteristics?

Key findings

• The generated synthetic time series are visually indistinguishable from real Bitcoin log returns, indicating strong perceptual similarity.
• Statistical comparison shows the synthetic data distribution is left-skewed with a heavier left tail, reflecting more significant losses than gains.
• The ACF of synthetic returns exhibits higher and more fluctuating autocorrelation compared to real data, suggesting stronger persistence in volatility.
• The generator and discriminator loss functions converge stably with oscillatory behavior around a minimum, indicating robust training dynamics.
• Despite visual similarity, the model struggles to fully replicate extreme outliers and tail events, leading to detectable statistical differences.
• The model shows stable learning behavior overall, but oscillation in loss suggests potential for improvement via hyperparameter tuning or longer training.