| Abstract [eng] |
Financial time series, such as daily stock index returns, exhibit complex statistical properties: heavy tails, volatility clustering, asymmetry, and non-linear dependencies. Traditional econometric models (ARMA, GARCH) can capture linear dependencies and conditional volatility, but often inadequately describe more complex relationships and quick market changes. Generative Adversarial Networks (GAN) offer a flexible approach to modeling complex data distributions. However, traditional GANs based on the Jensen-Shannon divergence suffer from training instability, vanishing gradients, and mode collapse. Wasserstein GAN (WGAN) introduces the Wasserstein distance as the objective function, ensuring smoother gradients and more stable training even when distributions differ significantly. The gradient penalty method enforces the Lipschitz constraint and improves practical stability. In this work, WGAN is applied to daily return data from the OMX Baltic Benchmark Gross Index (OMXBBGI). The model is evaluated using a rolling window approach over the 2020–2024 period: each training window covers 2000 trading days of historical data (around 8 years), then 60-day forecasts are generated, the window is shifted forward by 20 days, and the process repeats. Results show that WGAN achieves stable training without mode collapse and can approximate the central part of the distribution. However, the model exhibits significant limitations: distribution tests (KS p < 10⁻¹³, Wasserstein W₁ = 0.995, Maximum Mean Discrepancy = 0.881) show statistically significant differences from real data; autocorrelation function distances exceed 1.0, indicating insufficient capture of volatility clustering; VaR exceedance rates (7.95% and 16.38%) substantially exceed expected levels (1% and 5%), and backtesting tests reject the calibration null hypothesis. The primary issue is overly thin tails and inadequate modeling of extreme events, which is critical for risk management. The conclusions confirm that while WGAN architecture provides stability advantages over traditional GANs, it remains insufficient to fully capture the dynamics of financial returns. Reliable synthetic data generation requires further model improvements, including better capture of time series structure, stricter constraints on generating extreme values, and direct calibration mechanisms for risk metrics. |
