# Ensemble Deep Learning Models for Forecasting Cryptocurrency Time-Series
## 5 Numerical Experiments
The use of the confusion matrix provides a compact and to the classification performance of each model, presenting complete information about mislabeled classes. Notice that each row of a confusion matrix represents the instances in an actual class while each column represents the instances in a predicted class. Additionally, both stacking ensembles utilizing DTR and SVM as meta-learners were excluded from the rest of our experimental analysis, since they presented the worst regression and classification performance, relative to all cryptocurrencies. Tables 7-9 present the confusion matrices of the best identified ensemble models using CNN-LSTM as base learner, regarding BTC, ETH and XRP datasets, respectively. The confusion matrices for BTC and ETH revealed that stacking\({}_{7}^{(\text{LR})}\) is biased, since most of the instances were misclassified as \"Down\", meaning that this model was unable to identify possible hidden patterns despite the fact that it exhibited the best regression performance. On the other hand, bagging\({}_{11}\) exhibited a balanced prediction distribution between \"Down\" or \"Up\" predictions, presenting its superiority over the rest forecasting models, followed by averaging\({}_{11}\) and stacking\({}_{11}^{(\text{kNN})}\). Regarding XRP dataset, bagging\({}_{11}\) and stacking\({}_{11}^{(\text{kNN})}\) presented the highest prediction accuracy and the best trade-off between true positive and true negative rate, meaning that these models may have identified some hidden patters. \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-BiLSTM & 0.0146 & 53.47\% & 0.529 & 0.526 & 0.0154 & 53.87\% & 0.531 & 0.529 & 0.0101 & 50.36\% & 0.506 & 0.394 \\ \hline Averaging\({}_{7}\) & 0.0146 & **53.58\%** & **0.547** & **0.535** & 0.0151 & 54.03\% & **0.540** & **0.539** & 0.0095 & 50.04\% & 0.537 & 0.428 \\ Bagging\({}_{7}\) & 0.0143 & 53.20\% & 0.541 & 0.528 & 0.0155 & **54.09\%** & **0.540** & **0.539** & 0.0095 & 51.11\% & **0.540** & 0.417 \\ Stacking\({}_{7}^{(\text{DTR})}\) & 0.0233 & 50.84\% & 0.521 & 0.507 & 0.0324 & 52.23\% & 0.522 & 0.517 & 0.0149 & 52.19\% & 0.519 & **0.521** \\ Stacking\({}_{7}^{(\text{LR})}\) & **0.0091** & 52.30\% & 0.518 & 0.516 & **0.0105** & 52.26\% & 0.525 & 0.512 & **0.0093** & 50.10\% & 0.522 & 0.488 \\ Stacking\({}_{7}^{(\text{SVR})}\) & 0.0109 & 52.30\% & 0.517 & 0.516 & 0.0235 & 52.10\% & 0.513 & 0.514 & 0.0112 & 51.28\% & 0.518 & 0.512 \\ Stacking\({}_{7}^{(\text{kNN})}\) & 0.0166 & 52.00\% & 0.522 & 0.508 & 0.0142 & 51.91\% & 0.529 & 0.475 & 0.0101 & **52.50\%** & 0.523 & 0.510 \\ \hline Averaging\({}_{11}\) & 0.0144 & **53.53\%** & **0.548** & **0.535** & 0.0151 & 54.02\% & 0.539 & 0.537 & 0.0093 & 50.22\% & 0.549 & 0.437 \\ Bagging\({}_{11}\) & 0.0143 & 53.32\% & 0.547 & 0.530 & 0.0155 & **54.20\%** & **0.539** & **0.539** & 0.0093 & 51.15\% & **0.551** & 0.470 \\ Stacking\({}_{11}^{(\text{DTR})}\) & 0.0235 & 50.76\% & 0.513 & 0.506 & 0.0305 & 52.41\% & 0.513 & 0.520 & 0.0152 & 51.72\% & 0.522 & **0.516** \\ Stacking\({}_{11}^{(\text{LR})}\) & **0.008** & 50.48\% & 0.527 & 0.489 & **0.0098** & 52.67\% & 0.524 & 0.515 & **0.0092** & 50.68\% & 0.529 & 0.505 \\ Stacking\({}_{11}^{(\text{SVR})}\) & 0.0108 & 50.48\% & 0.513 & 0.489 & 0.0235 & 52.12\% & 0.516 & 0.514 & 0.0110 & 51.68\% & 0.517 & **0.516** \\ Stacking\({}_{11}^{(\text{kNN})}\) & 0.0166 & 52.00\% & 0.526 & 0.496 & 0.0142 & 51.95\% & 0.517 & 0.475 & 0.0100 & **52.32\%** & 0.526 & 0.505 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Performance of ensemble models using convolutional neural network with CNN-BiLSTM as base learner for \(m=9\).