## 7 Discussion  
The results presented in the experiments demonstrate that the proposed VAE-GRU-MCMC model is highly effective in generating synthetic financial time series that closely resemble real stock price movements. The quantitative evaluations, including the discriminative and predictive scores, confirm that the model successfully preserves statistical and temporal properties, making it a competitive alternative to existing generative approaches such as TimeGAN. However, beyond these numerical results, a deeper analysis is necessary to interpret the implications of these findings, compare them with existing models, and understand the limitations and areas for future improvements. One of the most significant contributions of this study is the hybridisation of VAE with MCMC sampling, which introduces a more structured latent space exploration. The comparison with baseline models, such as the convolutional VAE and GRU-based VAE, highlights the importance of capturing long-term dependencies in financial time series. While convolutional layers are effective in learning local patterns, they struggle with sequential dependencies, leading to less accurate synthetic data. The transition to GRU layers allowed the model to learn temporal structures more effectively, as reflected in improved discriminative and predictive scores. Furthermore, the integration of MCMC sampling refined the latent space representation, reducing divergence between real and synthetic distributions. This approach provided more stable and robust synthetic data, as confirmed by the lower KS test values. Compared to TimeGAN, which has been considered a state-of-the-art generative model for sequential data, the VAE-GRU-MCMC model demonstrates competitive performance while maintaining a simpler and more interpretable architecture. TimeGAN integrates an adversarial training mechanism, which, while effective, can suffer from issues such as mode collapse and training instability. In contrast, the proposed model avoids these problems by leveraging variational inference and structured sampling techniques. The results indicate that although TimeGAN marginally outperforms the VAE-GRU-MCMC  
Figure 15: Energy, Air Quality, and Google datasets’ ACFs. model in some metrics, the latter offers advantages in computational efficiency and ease of implementation, making it a viable alternative for synthetic financial data generation. The ability to generate high-quality synthetic stock price data has several practical applications. In finance, synthetic data can be used to augment training datasets for predictive modelling, reducing dependency on historical data that may be subject to confidentiality constraints. This is particularly useful for stress testing trading algorithms, where diverse market conditions must be simulated. The model's demonstrated robustness to missing data also makes it suitable for financial environments where datasets are often incomplete due to reporting delays or data corruption. Additionally, the ability to generalise to non-financial datasets, such as energy consumption and air quality data, suggests that the methodology can be extended to other domains where sequential data are prevalent. Despite its strong performance, the proposed model has certain limitations. The analysis of synthetic stock price data for Google, Tesla, and Nestle revealed that while the model performs well for stable and moderately volatile stocks, it struggles slightly with highly volatile assets such as Tesla. This suggests that the model may not fully capture extreme fluctuations in stock prices, which could be addressed by incorporating additional mechanisms, such as attention layers, to better model volatility. Another limitation concerns computational efficiency. While the VAE-GRU-MCMC model is more stable than GAN-based methods, the integration of MCMC sampling increases training time compared to traditional VAE approaches. Future work could explore more efficient sampling techniques or hybrid methods that balance stability and computational cost.