## 6 Generalisation to Different Datasets  
The incorporation of MCMC sampling into the VAE-GRU network has been shown to significantly improve the performance and quality of the generated synthetic data. However, this enhancement comes at the expense of increased computational cost. Specifically, the training time increased from approximately 10.22 min (613 s) to 21.61 min (1296 s), accompanied by a rise in RAM usage from 277 MB to 398 MB. This trade-off highlights that the improved accuracy and robustness achieved through MCMC sampling necessitate a more resource-intensive training process. Nonetheless, these additional computational requirements yield substantial improvements in model performance, particularly in terms of the realism and precision of the generated synthetic data. In applications where the fidelity of synthetic outputs or the robustness of the model is paramount--such as in research or industrial scenarios--this increase in computational demand is justified. To comprehensively evaluate the model's generalisation capabilities and adaptability across varying levels of volatility, demand cycles, and sector-specific dynamics, additional analyses were conducted beyond the initial focus on Google's stock. Specifically, the model was assessed using data from Tesla and Nestle stocks, representing distinct industries and geographical contexts. A common time window was selected to ensure consistency and comparability across these evaluations. The findings derived from the analysis of three distinct evaluation approaches, quantitative metrics (as per Table 12), statistical tests (as per Table 13), and t-SNE plot analysis (as per Figures 5 and 10-12), demonstrate that the final VAE-GRU model with MCMC sampling, previously assessed using Google stock data, achieves superior performance when applied to other categories of stock data. The discriminative and predictive scores highlight the model's ability to generate synthetic data that closely mirror the corresponding original data. In Figure 5, which depicts the t-SNE representation for Google stock data, there is a strong overlap between the real and synthetic points. This suggests that the model successfully learns and replicates the patterns present in Google's historical prices. The synthetic distribution follows the real one closely, indicating that key statistical and temporal characteristics are well preserved. The presence of well-defined clusters further confirms that the model is capturing the local structures of the data rather than producing overly smoothed or distorted distributions. \begin{table}
\begin{tabular}{l c} \hline \hline
**Dataset** & **KS Test Statistic Value** \\ \hline Google & 0.1318 \\ \hline Tesla & 0.1256 \\ \hline Nestle & 0.1130 \\ \hline \hline \end{tabular}
\end{table} 
Table 13: Kolmogorov–Smirnov test (KS test) statistic values for different datasets. \begin{table}
\begin{tabular}{l c c} \hline \hline
**Dataset** & **Discriminative Score** & **Predictive Score** \\ \hline Google & 0.1985 \(\pm\) 0.2159 & 0.0673 \(\pm\) 0.00026 \\ \hline Tesla & 0.1963 \(\pm\) 0.2128 & 0.0913 \(\pm\) 0.0002 \\ \hline Nestle & 0.2023 \(\pm\) 0.22819 & 0.0611 \(\pm\) 0.0002 \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Discriminative and predictive scores for different datasets. Figure 11: T-SNE plot of the VAE-GRU with MCMC model (Nestlé). Figure 10: T-SNE plot of the VAE-GRU with MCMC model (Tesla). Figure 10, which presents the t-SNE plot for Tesla stock data, shows a similar trend, though with slightly more variance in the synthetic data. Tesla's stock is known for its high volatility and rapid fluctuations, making it a more challenging dataset to model accurately. While the generated data largely align with the real distribution, some discrepancies appear, particularly in the finer details of certain clusters. This suggests that while the model can reproduce general trends and patterns in Tesla's price movements, it may struggle to fully capture the extreme fluctuations characteristic of this stock.