## 7 Discussion
An additional approach to potentially learning stock-specific features and improving the RSQGAN performance is to jointly condition regime categorical classes with continuous variables such as rolling volatility, correlation, or recent historical time series such as that demonstrated by [PERSON] et al. [13], [PERSON] [14], [PERSON] et al. [15]. 2. **A higher-capacity topology appears to further improve the RSQGAN performance relative to QGAN. ** A larger-capacity RSQGAN/QGAN network with seven hidden layers and skip layer connections of 60 nodes each led to RSQGAN outperforming in nine out of nine SF test metrics for the training stock set. However, RSQGAN outperformed in only two out of nine SF test metrics for the validation stock set. An examination of training losses indicates that this was partially due to training instability, which could be rectified by improved objective loss functions and early stopping criteria. This is left for future investigation. A poor performance on the validation stock set could also be due to the RSQGAN topology not being flexible enough to learn necessary stock-specific features (see the point above). 3. **The choice of early stopping criteria for training QGAN and RSQGAN is a significant area for further improvement. ** The original early stopping criteria in the open-source implementation by [PERSON] et al. [12] was used. The early stopping of QGAN and RSQGAN training occurred if the mean absolute deviation of the ACF of log-returns and the ACF of absolute returns both fell below preset thresholds. Figure 16 below shows that, during training for a given regime, none of the six possible stopping criteria uniformly converge for any of the three training stocks. This could be due to a number of causes--a topology without the sufficient capacity to simultaneously learn all SF behaviours and/or unstable training. Further, it is not necessarily desirable for convergence over all SF behaviours, as it may suggest mode collapse. No experiments were conducted to explore if there were reliable heuristics for setting early stopping conditions and understanding trade-offs between individual SF test metrics. This remains an open problem and is left for future work. 4. **A modest z-clipping of noise prior to \(z^{clip}=2.5\) in training and \(z^{clip}=2.3\) in generation appeared to improve the performance further. **  
Experiments with a 'crude' implementation of z-clipping and skip-z layers from the BigGAN paper by [PERSON] et al. [21] showed that modest z-clipping could produce synthetic data with higher initial fidelity to real data. The 'crude' RSQGAN implementation only applied skip-z layers to the first hidden layer of the generator and discriminator networks rather than learnable embeddings at all hidden layers. Further, it did not include the authors' suggestion to implement an orthogonal regularisation of the generator. Despite the crude implementation, modest but mixed performance improvements were observed across SF test losses when a modest z-clipping of \(z^{clip}=2.5\) in training and \(z^{clip}=2.3\) in generation were applied. However, an experiment that used a more extreme clipping parameter \(z^{clip}=1.5\) in training and \(z^{clip}=1.25\) in generation appeared to degrade the relative performance of RSQGAN relative to QGAN. A full implementation of z-clipping and skip-z layers and further experiments are left to future work. 5. **RSQGAN produced synthetic data from crisis regimes with improved SF evaluation measures. **  
It is reasonable to expect an RSQGAN outperformance for the minority crisis regime, as the RSQGAN training procedure corrects for regime class imbalance and enables shared parameter learning across all classes in a single model representation. This is a useful property for crisis risk management applications where fewer historical crisis data are observable. Improving simulations for the expected decay of the ACF of absolute returns or volatility could be useful for assessing the value of options instruments.