# Ensemble Deep Learning Models for Forecasting Cryptocurrency Time-Series
## 1 Introduction
After the model structure has been defined, function \(f(\cdot)\) can be determined by traditional time-series methods such as ARIMA (Auto-Regressive Integrated Moving Average) and GARCH-type models and their variations [2; 3; 4] or by machine learning methods such as Artificial Neural Networks (ANNs) [5; 6]. However, both mentioned approaches fail to depict the stochastic and chaotic nature of cryptocurrency time-series and be successfully effective for accurate forecasting [7]. To this end, more sophisticated algorithmic approaches have to be applied such as deep learning and ensemble learning methods. From the perspective of developing strong forecasting models, deep learning and ensemble learning constitute two fundamental learning strategies. The former is based on neural networks architectures and it is able to achieve state-of-the-art accuracy by creating and exploiting new more valuable features by filtering out the noise of the input data; while the latter attempts to generate strong prediction models by exploiting multiple learners in order to reduce the bias or variance of error. During the last few years, researchers paid special attention to the development of time-series forecasting models which exploit the advantages and benefits of deep learning techniques such as convolutional and long short-term memory (LSTM) layers. More specifically, [PERSON] and [PERSON] [8] and [PERSON] et al. [9] proposed Convolutional Neural Network (CNN) and LSTM prediction models for stock market forecasting. Along this line, [PERSON] et al. [10] and [PERSON] et al. [11] proposed CNN-LSTM models with various architectures for efficiently forecasting gold and cryptocurrency time-series price and movement, reporting some interesting results. Nevertheless, although deep learning models are tailored to cope with temporal correlations and efficiently extract more valuable information from the training set, they failed to generate reliable forecasting models [7; 11]; while in contrast ensemble learning models although they are an elegant solution to develop stable models and address the high variance of individual forecasting models, their performance heavily depends on the diversity and accuracy of the component learners. Therefore, a time-series prediction model, which exploits the benefits of both mentioned methodologies may significantly improve the prediction performance. The main contribution of this research is the combination of ensemble learning strategies with advanced deep learning models for forecasting cryptocurrency hourly prices and movement. The proposed ensemble models utilize state-of-the-art deep learning models as component learners which are based on combinations of Long Short-Term Memory (LSTM), Bi-directional LSTM (BiLSTM) and convolutional layers. An extensive experimental analysis is performed considering both classification and regression problems, to evaluate the performance of averaging, bagging and stacking ensemble strategies. More analytically, all ensemble models are evaluated on prediction of the cryptocurrency price on the next hour (regression) and also on the prediction if the price on the following hour will increase or decrease with respect to the current price (classification). It is worth mentioning that the information of predicting the movement of a cryptocurrency is probably more significant that the prediction of the price for investors and financial institutions. Additionally, the efficiency of the predictions of each forecasting model is evaluated by examining for autocorrelation of the errors, which constitutes a significant reliability test of each model. The remainder of the paper is organized as follows: Section 2 presents a brief review of state of the art deep learning methodologies for cryptocurrency forecasting. Section 3 presents the advanced deep learning models, while Section 4 presents the ensemble strategies utilized in our research.