## 6 Generalisation to Different Datasets
### Energy and Air Quality Datasets  
To further evaluate the capabilities of the proposed model, it was decided to extend the experimental analysis by including two new datasets from the UCI Machine Learning Repository:  
* Energy: a dataset predicting the energy consumption of household appliances, consisting of 19,735 samples with 28 continuous variables [23].
* Air: a dataset containing air quality measurements, with 9357 samples and 15 data characteristics averaged hourly [24].  
This extension of the analysis allows the model to be tested on more diverse data than previous financial datasets (Google, Tesla, Nestle). The objective is to assess its generalisation capacity considering key metrics such as the KS test and the quantitative scores. The results obtained on these new datasets are presented in Tables 16 and 17.  
Specifically, in Figure 13, which corresponds to the energy consumption dataset, there is a noticeable degree of overlap between the real and synthetic data distributions. This indicates that the model successfully captures key patterns in the dataset, generating synthetic sequences that align well with the real data. However, compared to the t-SNE plots of the stock price datasets, the separation between clusters appears slightly more pronounced, suggesting that while the model maintains the overall structure of the data, it may introduce minor deviations in certain localised regions. This could be attributed to the complex, multi-variable nature of energy consumption data, where external factors such as weather, household behaviour, and regional characteristics contribute to variations that may be harder to replicate perfectly.  
Similarly, Figure 14, which represents the Air Quality dataset, shows a reasonable alignment between real and synthetic data, though with slightly greater dispersion compared to the Energy dataset. This suggests that while the synthetic data follow the general structure of the original dataset, some finer details in the local patterns are not perfectly captured. The Air Quality dataset, which consists of various environmental indicators such as pollutant levels and meteorological conditions, exhibits a high degree of variability influenced by external and often stochastic factors. The wider spread in the t-SNE representation indicates that the model encounters more difficulty in fully capturing these complex interactions compared to financial or energy-related data.  
Figure 13: The t-sne plot of the VAE GRU with MCMC, Energy dataset.  
Finally, Figure 15 indicates a general decline in ACF differences as the lag increases, suggesting that short-term dependencies are more challenging to replicate accurately than long-term correlations. The Google dataset exhibits the smallest ACF differences, indicating that the synthetic data closely follow the real data's temporal structure. In contrast, the Air Quality and Energy datasets display higher ACF differences, particularly at lower lags, suggesting that the synthetic model struggles to replicate short-term dependencies in these datasets. Despite these differences, the ACF trends stabilize at higher lags, indicating that the model effectively captures long-term dependencies across datasets. These findings reinforce the robustness of our method while also highlighting potential areas for improvement, particularly in refining short-term dependency modelling for certain dataset types.  
Figure 14: The t-sne plot of the VAE GRU with MCMC, Air Quality.