*6.2. Discussion of Results*

All compared ensemble models were evaluated considering both regression and classification problems, namely for the prediction of the cryptocurrency price on the following hour (regression) and also for the prediction if the price will increase or decrease on the following hour (classification). Our experiments revealed that the incorporation of deep learning models into ensemble learning framework improved the prediction accuracy in most cases, compared to a single deep learning model.

Bagging exhibited the best overall score in terms of classification accuracy, closely followed by averaging and stacking(*<sup>k</sup>*NN); while stacking(LR) the best regression performance. The confusion matrices revealed that stacking(LR) as base learner was actually biased, since most of the instances were wrongly classified as "Down" while bagging and stacking(*k*NN) exhibited a balanced prediction distribution between "Down" or "Up" predictions. It is worth noticing that since bagging can be interpreted as a perturbation technique aiming at improving the robustness especially against outliers and highly volatile prices [37]. The numerical experiments demonstrated that averaging ensemble models trained on perturbed training dataset is a means to favor invariance to these perturbations and better capture the directional movements of the presented random walk processes. However, the ACF plots revealed that bagging ensemble models violate the assumption of no autocorrelation in the residuals, which implies that their predictions may be inefficient. In contrast, the ACF plots of stacking(*k*NN) revealed that the residuals have no or small (inconsiderable) autocorrelation. This is probably due to fact that the use of a meta-learner, which is trained on the errors of the base learners, is able to reduce the autocorrelation in the residuals and provide more reliable forecasts. Finally, it is worth mentioning that the increment of component learners had little or no effect to the regression performance of the ensemble algorithms, in most cases

Summarizing, stacking utilizing advanced deep learning base learner and *k*NN as meta-learner may considered to be the best forecasting model for the problem of cryptocurrency price prediction and movement, based on our experimental analysis. Nevertheless, further research has to be performed in order to improve the prediction performance of our prediction framework by creating even more innovative and sophisticated algorithmic models. Moreover, additional experiments with respect to the trading-investment profit returns based on such prediction frameworks have to be also performed.
