# 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{2-11}  & **RMSE** & **Acc** & **AUC** & \(\boldsymbol{F_{1}}\) & **RMSE** & **Acc** & **AUC** & \(\boldsymbol{F_{1}}\) & **RMSE** & **Acc** & **AUC** & \(\boldsymbol{F_{1}}\) \\ \hline CNN-LSTM & 0.0101 & 52.80\% & 0.521 & 0.530 & 0.0111 & 53.39\% & 0.533 & 0.525 & 0.0110 & 53.82\% & 0.510 & 0.530 \\ \hline Averaging & 0.0096 & 54.39\% & 0.543 & 0.536 & 0.0107 & 53.73\% & 0.539 & **0.536** & 0.0108 & **54.12\%** & 0.552 & **0.536** \\ Bagging\({}_{7}\) & 0.0097 & **54.52\%** & **0.549** & **0.545** & 0.0107 & **53.95\%** & **0.541** & 0.530 & 0.0095 & 53.29\% & **0.560** & 0.483 \\ Stacking\({}_{7}^{(\text{DTR})}\) & 0.0168 & 49.96\% & 0.510 & 0.498 & 0.0230 & 50.13\% & 0.506 & 0.497 & 0.0230 & 49.67\% & 0.530 & 0.492 \\ Stacking\({}_{7}^{(\text{LR})}\) & **0.0085** & 52.57\% & 0.530 & 0.524 & **0.0093** & 52.44\% & 0.513 & 0.515 & **0.0095** & 52.32\% & 0.537 & 0.514 \\ Stacking\({}_{7}^{(\text{SVR})}\) & 0.0128 & 49.82\% & 0.523 & 0.497 & 0.0145 & 51.24\% & 0.501 & 0.508 & 0.0146 & 51.27\% & 0.515 & 0.508 \\ Stacking\({}_{7}^{(\text{NNN})}\) & 0.0113 & 52.64\% & 0.525 & 0.511 & 0.0126 & 52.85\% & 0.537 & 0.473 & 0.0101 & 52.87\% & 0.536 & 0.514 \\ \hline Averaging\({}_{11}\) & 0.0096 & 54.16\% & 0.545 & 0.534 & 0.0107 & 53.77\% & 0.542 & 0.535 & 0.0107 & 54.12\% & 0.531 & **0.537** \\ Bagging\({}_{11}\) & 0.0098 & **54.31\%** & **0.546** & **0.542** & 0.0107 & **53.95\%** & **0.548** & **0.536** & 0.0094 & **54.32\%** & **0.532** & 0.515 \\ Stacking\({}_{11}^{(\text{DTR})}\) & 0.0169 & 49.66\% & 0.510 & 0.495 & 0.0224 & 50.42\% & 0.512 & 0.500 & 0.0229 & 50.63\% & 0.519 & 0.501 \\ Stacking\({}_{13}^{(\text{LR})}\) & **0.0085** & 51.05\% & 0.529 & 0.475 & **0.0093** & 51.95\% & 0.514 & 0.514 & **0.0094** & 52.35\% & 0.529 & 0.512 \\ Stacking\({}_{13}^{(\text{LR})}\) & 0.0128 & 50.03\% & 0.520 & 0.499 & 0.0145 & 51.10\% & 0.510 & 0.506 & 0.0145 & 51.11\% & 0.511 & 0.506 \\ Stacking\({}_{11}^{(\text{ANN})}\) & 0.0112 & 52.66\% & 0.526 & 0.511 & 0.0126 & 52.65\% & 0.538 & 0.481 & 0.0101 & 53.05\% & 0.530 & 0.512 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Performance of ensemble models using convolutional neural network and long short-term memory (CNN-LSTM) as base learner for \(m=4\). Tables 5 and 6 present the performance of all ensemble models utilizing CNN-BiLSTM as base learner for \(m=4\) and \(m=9\), respectively. Firstly, it is worth noticing that stacking model using LR as meta-learner exhibited the best regression performance, regarding to all cryptocurrencies. Stacking\({}_{97}^{(\text{LR})}\) and Stacking\({}_{11}^{(\text{LR})}\) presented almost identical RMSE score Moreover, stacking\({}_{7}^{(\text{LR})}\) presented slightly higher accuracy, AUC and \(F_{1}\)-score than stacking\({}_{11}^{(\text{LR})}\), for ETH and XRP datasets, while for BTC dataset Stacking\({}_{11}^{(\text{LR})}\) reported slightly better classification performance. This implies that the increment of component learners from 7 to 11 did not considerably improved and affected the regression and classification performance of the stacking ensemble algorithm. Stacking ensemble reported the worst (highest) RMSE score utilizing DTR, SVR and \(k\)NN as meta-learners. It is also worth mentioning that it exhibited the worst performance among all ensemble models and also worst than that of the single model CNN-BiLSTM. However, stacking ensemble reported the highest classification performance using \(k\)NN as meta-learner. Additionally, it presented slightly better classification performance using DTR or SVR than LR as meta-learners for ETH and XRP datasets, while for BTC dataset it presented better performance using LR as meta-learner as meta-learner.