**6. Discussion**

In this section, we perform a discussion regarding the proposed ensemble models, the experimental results and the main finding of this work.

### *6.1. Discussion of Proposed Methodology*

Cryptocurrency prediction is considered a very challenging forecasting problem, since the historical prices follow a random walk process, characterized by large variations in the volatility, although a few hidden patterns may probably exist [48,49]. Therefore, the investigation and the development of a powerful forecasting model for assisting decision making and investment policies is considered essential. In this work, we incorporated advanced deep learning models as base learners into three of the most popular and widely used ensembles methods, namely averaging, bagging and stacking for forecasting cryptocurrency hourly prices.

The motivation behind our approach is to exploit the advantages of ensemble learning and advanced deep learning techniques. More specifically, we aim to exploit the effectiveness of ensemble learning for reducing the bias or variance of error by exploiting multiple learners and the ability of deep learning models to learn the internal representation of the cryptocurrency data. It is worth mentioning that since the component deep learning learners are initialized with different weight states, this leads to the development of deep learning models each of which focuses on different identified patterns. Therefore, the combination of these learners via an ensemble learning strategy may lead to stable and robust prediction model.

In general, deep learning neural networks are powerful prediction models in terms of accuracy, but are usually unstable in sense that variations in their training set or in their weight initialization may significantly affect their performance. Bagging strategy constitutes an effective way of building efficient and stable prediction models, utilizing unstable and diverse base learners [50,51], aiming to reduce variance and avoid overfitting. In other words, bagging stabilizes the unstable deep learning base learners and exploits their prediction accuracy focusing on building an accurate and robust final prediction model. However, the main problem of this approach is that since bagging averages the predictions of all models, redundant and non-informative models may add too much noise on the final prediction result and therefore, possible identified patterns, by some informative and valuable models, may disappear.

On the other hand, stacking ensemble learning utilizes a meta-learner in order to learn the prediction behavior of the base learners, with respect to the final target output. Therefore, it is able to identify the redundant and informative base models and "weight them" in a nonlinear and more intelligent way in order to filter out useless and non-informative base models. As a result, the selection of the meta-learner is of high significance for the effectiveness and efficiency of this ensemble strategy.
