# Ensemble Deep Learning Models for Forecasting Cryptocurrency Time-Series
## 5 Numerical Experiments
\begin{table}
\begin{tabular}{l c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multicolumn{4}{c}{**BTC**} & \multicolumn{4}{c}{**ETH**} & \multicolumn{4}{c}{**XRP**} \\ \cline{2-13}  & **RMSE** & **Acc** & **AUC** & \(\mathbf{F_{1}}\) & **RMSE** & **Acc** & **AUC** & \(\mathbf{F_{1}}\) & **RMSE** & **Acc** & **AUC** & \(\mathbf{F_{1}}\) \\ \hline CNN-LSTM & 0.0124 & 51.19\% & 0.511 & 0.504 & 0.0140 & 53.49\% & 0.535 & 0.513 & 0.0140 & 53.43\% & 0.510 & 0.510 \\ \hline Averaging & 0.0122 & 54.12\% & **0.549** & 0.541 & 0.0138 & 53.86\% & 0.539 & 0.538 & 0.0138 & **53.94\%** & 0.502 & **0.538** \\ Bagging\({}_{7}^{(\text{DTR})}\) & 0.0123 & **54.29\%** & **0.549** & **0.543** & 0.0132 & **54.05\%** & **0.541** & **0.539** & 0.0093 & 52.97\% & 0.501 & 0.502 \\ Stacking\({}_{7}^{(\text{DRT})}\) & 0.0213 & 50.57\% & 0.510 & 0.504 & 0.0280 & 51.58\% & 0.509 & 0.511 & 0.0279 & 51.87\% & 0.514 & 0.514 \\ Stacking\({}_{11}^{(\text{LR})}\) & **0.0090** & 51.19\% & 0.530 & 0.503 & **0.0098** & 52.17\% & 0.525 & 0.503 & **0.0098** & 51.89\% & **0.524** & 0.506 \\ Stacking\({}_{7}^{(\text{SVR})}\) & 0.0168 & 50.54\% & 0.523 & 0.503 & 0.0203 & 51.94\% & 0.515 & 0.513 & 0.0203 & 51.86\% & 0.518 & 0.512 \\ Stacking\({}_{7}^{(\text{RNN})}\) & 0.0165 & 52.00\% & 0.525 & 0.509 & 0.0179 & 52.66\% & 0.526 & 0.487 & 0.0100 & 51.91\% & 0.521 & 0.522 \\ \hline Averaging\({}_{11}\) & 0.0122 & 54.25\% & **0.545** & **0.542** & 0.0136 & 54.02\% & **0.542** & **0.540** & 0.0136 & **54.03\%** & 0.501 & **0.539** \\ Bagging\({}_{11}\) & 0.0124 & **54.30\%** & **0.555** & **0.542** & 0.0134 & **54.11\%** & 0.541 & **0.540** & **0.0093** & 53.11\% & 0.502 & 0.509 \\ Stacking\({}_{11}^{(\text{DTR})}\) & 0.0209 & 50.43\% & 0.510 & 0.502 & 0.0271 & 51.69\% & 0.510 & 0.512 & 0.0274 & 51.85\% & 0.519 & 0.512 \\ Stacking\({}_{11}^{(\text{LR})}\) & **0.0087** & 50.99\% & 0.529 & 0.492 & **0.0095** & 52.43\% & 0.522 & 0.507 & 0.0096 & 52.11\% & 0.514 & 0.501 \\ Stacking\({}_{11}^{(\text{SVR})}\) & 0.0165 & 50.66\% & 0.520 & 0.504 & 0.0202 & 51.85\% & 0.512 & 0.512 & 0.0202 & 51.82\% & 0.517 & 0.511 \\ Stacking\({}_{11}^{(\text{RNN})}\) & 0.0165 & 52.13\% & 0.526 & 0.505 & 0.0179 & 52.19\% & 0.523 & 0.489 & 0.0100 & 52.49\% & **0.521** & 0.520 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Performance of ensemble models using CNN-LSTM as base learner for \(m=9\). \begin{table}
\begin{tabular}{l c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multicolumn{4}{c}{**BTC**} & \multicolumn{4}{c}{**ETH**} & \multicolumn{4}{c}{**XRP**} \\ \cline{2-13}  & **RMSE** & **Acc** & **AUC** & \(\mathbf{F_{1}}\) & **RMSE** & **Acc** & **AUC** & \(\mathbf{F_{1}}\) & **RMSE** & **Acc** & **AUC** & \(\mathbf{F_{1}}\) \\ \hline CNN-BiLSTM & 0.0107 & 53.93\% & 0.528 & 0.522 & 0.0116 & 53.56\% & 0.525 & 0.521 & 0.0099 & 53.72\% & 0.519 & 0.484 \\ \hline Averaging\({}_{7}^{(\text{DTR})}\) & 0.0104 & 54.15\% & 0.548 & 0.537 & 0.0114 & 53.87\% & 0.530 & **0.536** & 0.0096 & 54.73\% & 0.555 & **0.532** \\ Bagging\({}_{7}^{(\text{DTR})}\) & 0.0104 & **54.62  
Regarding the other two ensemble strategies, averaging and bagging, they exhibited slightly better regression performance compared to the single CNN-BiLSTM model. Nevertheless, both averaging and bagging reported the highest accuracy, AUC and \(F_{1}\)-score, which implies that they presented the best classification performance among all other models with bagging exhibiting slightly better classification performance. Furthermore, it is also worth mentioning that both ensembles slightly improved their performance in term of RMSE score and Accuracy, when the number of component classifiers increased from 7 to 11. In the follow-up, we provided a deeper insight classification performance of the forecasting models by presenting the confusion matrices of averaging\({}_{11}\), bagging\({}_{11}\), stacking\({}_{7}^{(\text{LR})}\) and stacking\({}_{11}^{(\text{kNN})}\) for \(m=4\), which exhibited the best overall performance.