## 6 Results
### Key Results  
The results indicate that RSQGAN learned a single joint representation of FTS behaviour over multiple regimes that is consistent with the performance of multiple QGAN representations each trained on data only from a single regime. RSQGAN outperformed QGAN for the minority 'crisis' regime class. Though RSQGAN SF test metrics in crisis environments show some improvement compared to QGAN trained only on 'crisis' data, it is not desirable to seek SF scores as close to zero as possible, which would indicate mode collapse. Tables 3 and 4 show the performance of RSQGAN versus QGAN across the range of SF test losses averaged over training stocks {WOW, BHP, WBC} and validation stocks {WES, RIO, ANZ}, respectively. In the first column, the SF test loss is bolded only if RSQGAN outperformed QGAN (lower is better). The second column shows in bold the outperforming model on that SF test loss. The third column shows the SF test loss averaged over all regimes for information purposes only. SF test losses are bolded for the crisis regime as the main class of interest. The key results demonstrated shown in this section suggest a choice of topology and training hyperparameters that may generalise well out of sample. Some other topological and training hyperparameter choices experimented on resulted in an extremely strong performance on the training stock set but relatively weaker results on the validation stock set. \begin{table}
\begin{tabular}{l l r r} \hline \hline  & & **All Regimes** & **Crisis Regime** \\ \hline
**acf** & **rsqgan** & 2.135 & **2.757** \\  & qgan & 2.030 & 3.197 \\ pdf & rsqgan & 0.641 & 0.770 \\  & **qgan** & 0.588 & **0.671** \\ vc\_acf* & rsqgan & 2.351 & 3.213 \\  & **qgan** & 2.566 & **3.111** \\
**vc\_pdf** & **rsqgan** & 0.396 & **0.479** \\  & qgan & 0.347 & 0.502 \\
**levf* & **rsqgan** & 1924.233 & **1463.868** \\  & qgan & 1607.904 & 1835.097 \\
**cfvol* & **rsqgan** & 4.749 & **6.202** \\  & qgan & 5.199 & 6.327 \\ cfvol\_diff & rsqgan & 2.430 & 3.886 \\  & **qgan** & 2.386 & **3.840** \\ gain\_cdf\_12\_5 & rsqgan & 21.826 & 19.622 \\  & **qgan** & 23.052 & **19.119** \\
**loss\_cdf\_12\_5* & **rsqgan** & 24.968 & **20.450** \\  & qgan & 24.259 & 21.305 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Single RSQGAN vs. multiple QGANs trained on single regime data. _Training set_. Hidden layer topology: 6 hidden layers and skip layers of 50 nodes each. Cosine annealing. \(z^{clip}=2.5\) (train), \(z^{clip}=2.3\) (generation). However, some caution should be exercised when interpreting these results:  
1. **Minimising crisis regime SF test losses toward zero is not desired. ** This outcome may be indicative of mode collapse. GANs are susceptible to mode collapse for reasons described in Section 2. High intra-class entropy (variability) is desirable and is a measure of GAN quality. The purpose of RSQGAN in risk management applications is to provide a rich, non-degenerate synthetic density distribution. Hence, hyperparameter choices should focus on the relative improvement over QGAN without aiming to drive crisis regime SF test losses to zero. An equivalent metric for Frechet joint distance [40] in the image domain that balances fidelity versus variety does not yet exist for the FTS domain. The investigation will be left for future work. 2. **GAN training is notoriously unstable, leading to performance variations sensitive to the number of training epochs. ** SF test losses can be unstable due to the instability of learned generator representations during training. Potential approaches to dealing with this were discussed in Section 3.1. Hence, the results shown in these tables do not include RSQGAN improvements that could be captured through the use of improved GAN objective loss functions or research into the calibration of early stopping criteria. This has been left for future work. Synthetic output samples for training and validation stocks are shown in Figures 12 and 13 below. Figures 14 and 15 show the quality of RSQGAN and QGAN fit to 'crisis-sensitive' SF test metrics.