{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,28]],"date-time":"2026-10-28T00:45:41Z","timestamp":1793148341272,"version":"4.5.0"},"reference-count":51,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2020,5,10]],"date-time":"2020-05-10T00:00:00Z","timestamp":1589068800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>Nowadays, cryptocurrency has infiltrated almost all financial transactions; thus, it is generally recognized as an alternative method for paying and exchanging currency. Cryptocurrency trade constitutes a constantly increasing financial market and a promising type of profitable investment; however, it is characterized by high volatility and strong fluctuations of prices over time. Therefore, the development of an intelligent forecasting model is considered essential for portfolio optimization and decision making. The main contribution of this research is the combination of three of the most widely employed ensemble learning strategies: ensemble-averaging, bagging and stacking with advanced deep learning models for forecasting major cryptocurrency hourly prices. The proposed ensemble models were evaluated utilizing state-of-the-art deep learning models as component learners, which were comprised by combinations of long short-term memory (LSTM), Bi-directional LSTM and convolutional layers. The ensemble models were evaluated on prediction of the cryptocurrency price on the following 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). Additionally, the reliability of each forecasting model and the efficiency of its predictions is evaluated by examining for autocorrelation of the errors. Our detailed experimental analysis indicates that ensemble learning and deep learning can be efficiently beneficial to each other, for developing strong, stable, and reliable forecasting models.<\/jats:p>","DOI":"10.3390\/a13050121","type":"journal-article","created":{"date-parts":[[2020,5,11]],"date-time":"2020-05-11T10:01:18Z","timestamp":1589191278000},"page":"121","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":136,"title":["Ensemble Deep Learning Models for Forecasting Cryptocurrency Time-Series"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3996-3301","authenticated-orcid":false,"given":"Ioannis E.","family":"Livieris","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Patras, GR 265-00 Patras, Greece"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Emmanuel","family":"Pintelas","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Patras, GR 265-00 Patras, Greece"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Stavros","family":"Stavroyiannis","sequence":"additional","affiliation":[{"name":"Department of Accounting &amp; Finance, University of the Peloponnese, GR 241-00 Antikalamos, Greece"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Panagiotis","family":"Pintelas","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Patras, GR 265-00 Patras, Greece"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,5,10]]},"reference":[{"key":"ref_1","unstructured":"Nakamoto, S. (2020, February 20). Bitcoin: A Peer-to-Peer Electronic Cash System. Available online: https:\/\/git.dhimmel.com\/bitcoin-whitepaper\/."},{"key":"ref_2","unstructured":"Corazza, M., and Pizzi, C. (2004). A Skew-in-Mean GARCH Model for Financial Returns. Skew-Elliptical Distributions and Their Applications: A Journey Beyond Normality, CRC\/Chapman & Hall."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1113","DOI":"10.1080\/1351847X.2011.640342","article-title":"Modelling multivariate skewness in financial returns: A SGARCH approach","volume":"21","author":"Loperfido","year":"2015","journal-title":"Eur. J. Financ."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Weigend, A.S. (2018). Time Series Prediction: Forecasting the Future and Understanding the Past, Routledge.","DOI":"10.4324\/9780429492648"},{"key":"ref_5","unstructured":"Azoff, E.M. (1994). Neural Network Time Series Forecasting of Financial Markets, John Wiley & Sons, Inc."},{"key":"ref_6","unstructured":"Oancea, B., and Ciucu, \u015e.C. (2014). Time series forecasting using neural networks. arXiv."},{"key":"ref_7","unstructured":"Pintelas, E., Livieris, I.E., Stavroyiannis, S., Kotsilieris, T., and Pintelas, P. (2020). Fundamental Research Questions and Proposals on Predicting Cryptocurrency Prices Using DNNs, University of Patras. Available online: https:\/\/nemertes.lis.upatras.gr\/jspui\/bitstream\/10889\/13296\/1\/TR01-20.pdf."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Wen, Y., and Yuan, B. (2018, January 9\u201312). Use CNN-LSTM network to analyze secondary market data. Proceedings of the 2nd International Conference on Innovation in Artificial Intelligence, Shanghai, China.","DOI":"10.1145\/3194206.3194226"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Liu, S., Zhang, C., and Ma, J. (2017). CNN-LSTM neural network model for quantitative strategy analysis in stock markets. International Conference on Neural Information Processing, Springer.","DOI":"10.1007\/978-3-319-70096-0_21"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Livieris, I.E., Pintelas, E., and Pintelas, P. (2020, February 20). A CNN-LSTM model for gold price time-series forecasting. Available online: https:\/\/link.springer.com\/article\/10.1007\/s00521-020-04867-x.","DOI":"10.1007\/s00521-020-04867-x"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Pintelas, E., Livieris, I.E., Stavroyiannis, S., Kotsilieris, T., and Pintelas, P. (2020, January 5\u20137). Investigating the problem of cryptocurrency price prediction\u2014A deep learning approach. Proceedings of the 16th International Conference on Artificial Intelligence Applications and Innovations, Neos Marmaras, Greece.","DOI":"10.1007\/978-3-030-49186-4_9"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Yiying, W., and Yeze, Z. (2019, January 24\u201327). Cryptocurrency Price Analysis with Artificial Intelligence. Proceedings of the 2019 5th International Conference on Information Management (ICIM), Cambridge, UK.","DOI":"10.1109\/INFOMAN.2019.8714700"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"587","DOI":"10.1016\/j.physa.2018.07.017","article-title":"Bitcoin technical trading with artificial neural network","volume":"510","author":"Nakano","year":"2018","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"McNally, S., Roche, J., and Caton, S. (2018, January 21\u201323). Predicting the price of Bitcoin using Machine Learning. Proceedings of the 2018 26th Euromicro International Conference on Parallel, Distributed and Network-based Processing (PDP), Cambridge, UK.","DOI":"10.1109\/PDP2018.2018.00060"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Shintate, T., and Pichl, L. (2019). Trend prediction classification for high frequency bitcoin time series with deep learning. J. Risk Financ. Manag., 12.","DOI":"10.3390\/jrfm12010017"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Miura, R., Pichl, L., and Kaizoji, T. (2019). Artificial Neural Networks for Realized Volatility Prediction in Cryptocurrency Time Series. International Symposium on Neural Networks, Springer.","DOI":"10.1007\/978-3-030-22796-8_18"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Ji, S., Kim, J., and Im, H. (2019). A Comparative Study of Bitcoin Price Prediction Using Deep Learning. Mathematics, 7.","DOI":"10.3390\/math7100898"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Kumar, D., and Rath, S. (2020). Predicting the Trends of Price for Ethereum Using Deep Learning Techniques. Artificial Intelligence and Evolutionary Computations in Engineering Systems, Springer.","DOI":"10.1007\/978-981-15-0199-9_9"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1735","DOI":"10.1162\/neco.1997.9.8.1735","article-title":"Long short-term memory","volume":"9","author":"Hochreiter","year":"1997","journal-title":"Neural Comput."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1235","DOI":"10.1162\/neco_a_01199","article-title":"A review of recurrent neural networks: LSTM cells and network architectures","volume":"31","author":"Yu","year":"2019","journal-title":"Neural Comput."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Zhang, K., Chao, W.L., Sha, F., and Grauman, K. (2016). Video summarization with long short-term memory. European Conference on Computer Vision, Springer.","DOI":"10.1007\/978-3-319-46478-7_47"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Nowak, J., Taspinar, A., and Scherer, R. (2017). LSTM recurrent neural networks for short text and sentiment classification. International Conference on Artificial Intelligence and Soft Computing, Springer.","DOI":"10.1007\/978-3-319-59060-8_50"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Rahman, L., Mohammed, N., and Al Azad, A.K. (2016, January 22\u201324). A new LSTM model by introducing biological cell state. Proceedings of the 2016 3rd International Conference on Electrical Engineering and Information Communication Technology (ICEEICT), Dhaka, Bangladesh.","DOI":"10.1109\/CEEICT.2016.7873164"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"2673","DOI":"10.1109\/78.650093","article-title":"Bidirectional recurrent neural networks","volume":"45","author":"Schuster","year":"1997","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Graves, A., Mohamed, A.R., and Hinton, G. (2013, January 26\u201331). Speech recognition with deep recurrent neural networks. Proceedings of the 2013 IEEE International Conference on Acoustics, Speech and Signal Processing, Vancouver, BC, Canada.","DOI":"10.1109\/ICASSP.2013.6638947"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Lu, L., Wang, X., Carneiro, G., and Yang, L. (2019). Deep Learning and Convolutional Neural Networks for Medical Imaging and Clinical Informatics, Springer.","DOI":"10.1007\/978-3-030-13969-8"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"2352","DOI":"10.1162\/neco_a_00990","article-title":"Deep convolutional neural networks for image classification: A comprehensive review","volume":"29","author":"Rawat","year":"2017","journal-title":"Neural Comput."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Michelucci, U. (2019). Advanced Applied Deep Learning: Convolutional Neural Networks and Object Detection, Springer.","DOI":"10.1007\/978-1-4842-4976-5"},{"key":"ref_29","unstructured":"Ioffe, S., and Szegedy, C. (2015). Batch normalization: Accelerating deep network training by reducing internal covariate shift. arXiv."},{"key":"ref_30","first-page":"1929","article-title":"Dropout: A simple way to prevent neural networks from overfitting","volume":"15","author":"Srivastava","year":"2014","journal-title":"J. Mach. Learn. Res."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Rokach, L. (2019). Ensemble Learning: Pattern Classification Using Ensemble Methods, World Scientific Publishing Co Pte Ltd.","DOI":"10.1142\/11325"},{"key":"ref_32","unstructured":"Lior, R. (2019). Ensemble Learning: Pattern Classification Using Ensemble Methods, World Scientific."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Zhou, Z.H. (2012). Ensemble Methods: Foundations and Algorithms, Chapman & Hall\/CRC.","DOI":"10.1201\/b12207"},{"key":"ref_34","first-page":"103","article-title":"On diversity and accuracy of homogeneous and heterogeneous ensembles","volume":"4","author":"Bian","year":"2007","journal-title":"Int. J. Hybrid Intell. Syst."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Polikar, R. (2012). Ensemble learning. Ensemble Machine Learning, Springer.","DOI":"10.1007\/978-1-4419-9326-7_1"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1587","DOI":"10.1175\/JCLI-D-17-0197.1","article-title":"Ensemble averaging and the curse of dimensionality","volume":"31","author":"Christiansen","year":"2018","journal-title":"J. Clim."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1023\/B:MACH.0000027783.34431.42","article-title":"Bagging equalizes influence","volume":"55","author":"Grandvalet","year":"2004","journal-title":"Mach. Learn."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Livieris, I.E., Iliadis, L., and Pintelas, P. (2020). On ensemble techniques of weight-constrained neural networks. Evol. Syst., 1\u20133.","DOI":"10.1007\/s12530-019-09324-2"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1016\/S0893-6080(05)80023-1","article-title":"Stacked generalization","volume":"5","author":"Wolpert","year":"1992","journal-title":"Neural Netw."},{"key":"ref_40","unstructured":"Gulli, A., and Pal, S. (2017). Deep Learning with Keras, Packt Publishing Ltd."},{"key":"ref_41","unstructured":"Kingma, D.P., and Ba, J. (2015, January 7\u20139). Adam: A method for stochastic optimization. Proceedings of the 2015 International Conference on Learning Representations, San Diego, CA, USA."},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Wu, X., and Kumar, V. (2009). The Top Ten Algorithms in Data Mining, CRC Press.","DOI":"10.1201\/9781420089653"},{"key":"ref_43","unstructured":"Deng, N., Tian, Y., and Zhang, C. (2012). Support Vector Machines: Optimization Based Theory, Algorithms, and Extensions, Chapman and Hall\/CRC."},{"key":"ref_44","unstructured":"Kutner, M.H., Nachtsheim, C.J., Neter, J., and Li, W. (2005). Applied Linear Statistical Models, McGraw-Hill Irwin."},{"key":"ref_45","unstructured":"Aha, D.W. (2013). Lazy learning, Springer Science & Business Media."},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Breiman, L., Friedman, J., and Olshen, R. (2017). Classification and Regression Trees, Routledge.","DOI":"10.1201\/9781315139470"},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Brockwell, P.J., and Davis, R.A. (2016). Introduction to Time Series and Forecasting, Springer.","DOI":"10.1007\/978-3-319-29854-2"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"399","DOI":"10.1504\/IJEBR.2019.103093","article-title":"Can Bitcoin diversify significantly a portfolio?","volume":"18","author":"Stavroyiannis","year":"2019","journal-title":"Int. J. Econ. Bus. Res."},{"key":"ref_49","doi-asserted-by":"crossref","unstructured":"Stavroyiannis, S. (2017). Value-at-Risk and Expected Shortfall for the major digital currencies. arXiv.","DOI":"10.2139\/ssrn.3028625"},{"key":"ref_50","first-page":"55","article-title":"Stability of randomized learning algorithms","volume":"6","author":"Elisseeff","year":"2005","journal-title":"J. Mach. Learn. Res."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1017\/S0269888913000313","article-title":"Bagging and boosting variants for handling classifications problems: A survey","volume":"29","author":"Kotsiantis","year":"2014","journal-title":"Knowl. Eng. Rev."}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/13\/5\/121\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T09:27:26Z","timestamp":1760174846000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/13\/5\/121"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,5,10]]},"references-count":51,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2020,5]]}},"alternative-id":["a13050121"],"URL":"https:\/\/doi.org\/10.3390\/a13050121","relation":{},"ISSN":["1999-4893"],"issn-type":[{"value":"1999-4893","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,5,10]]}}}