{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,17]],"date-time":"2026-04-17T03:40:05Z","timestamp":1776397205816,"version":"3.51.2"},"reference-count":27,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2025,11,13]],"date-time":"2025-11-13T00:00:00Z","timestamp":1762992000000},"content-version":"vor","delay-in-days":316,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2025,1]]},"abstract":"<jats:p>\n                    This study evaluates the performance of deep learning models and a traditional econometric approach in forecasting cryptocurrency price movements using the BTC and BNB datasets. Four models are compared: recurrent neural network (RNN), long short\u2010term memory (LSTM), transformer, and GARCH, under two loss functions: log\u2010likelihood and mean squared error (MSE). The results show that BTC and BNB datasets exhibit similar stability, with only minor differences in predictive accuracy. Models trained with log\u2010likelihood loss consistently outperform those using MSE, achieving lower MAE and RMSE, higher\n                    <jats:italic>R<\/jats:italic>\n                    <jats:sup>2<\/jats:sup>\n                    , and improved probabilistic modeling. Among all models, RNN\u2010loglik delivers the best performance, accurately capturing both short\u2010term volatility and long\u2010term trends, while LSTM and transformer perform moderately well and GARCH underperforms significantly. These findings demonstrate the effectiveness of deep learning combined with probabilistic loss functions for cryptocurrency forecasting, supporting applications in algorithmic trading, portfolio optimization, and risk management.\n                  <\/jats:p>","DOI":"10.1155\/jama\/9089827","type":"journal-article","created":{"date-parts":[[2025,11,13]],"date-time":"2025-11-13T12:16:06Z","timestamp":1763036166000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Analysis and Forecasting of Bitcoin Price Volatility: A Deep Learning Approach Using DNN, LSTM, Transformers, and the ARMA\u2010GARCH Model"],"prefix":"10.1155","volume":"2025","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7594-9814","authenticated-orcid":false,"given":"Phung Duy","family":"Quang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0009-3270-1104","authenticated-orcid":false,"given":"Nguyen Khanh","family":"Huyen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0007-3982-6810","authenticated-orcid":false,"given":"Hoang Nam","family":"Quyen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2025,11,13]]},"reference":[{"key":"e_1_2_10_1_2","doi-asserted-by":"publisher","DOI":"10.14569\/IJACSA.2023.0140837"},{"key":"e_1_2_10_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2022.119233"},{"key":"e_1_2_10_3_2","doi-asserted-by":"publisher","DOI":"10.1186\/s40854-021-00321-6"},{"key":"e_1_2_10_4_2","doi-asserted-by":"publisher","DOI":"10.54691\/bcpbm.v34i.3163"},{"key":"e_1_2_10_5_2","doi-asserted-by":"publisher","DOI":"10.22161\/ijaers.4.11.20"},{"key":"e_1_2_10_6_2","volume-title":"Bitcoin Short-Term Price Prediction Using Time Series Analysis","author":"Alkamali A.","year":"2024"},{"key":"e_1_2_10_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.future.2017.08.033"},{"key":"e_1_2_10_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(86)90063-1"},{"key":"e_1_2_10_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.knosys.2021.107393"},{"key":"e_1_2_10_10_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10614-019-09928-5"},{"key":"e_1_2_10_11_2","doi-asserted-by":"publisher","DOI":"10.32604\/cmc.2022.020823"},{"key":"e_1_2_10_12_2","article-title":"Predicting Price of Cryptocurrency \u2013 A Deep Learning Approach","volume":"9","author":"Marne S.","year":"2021","journal-title":"International Journal of Engineering Research & Technology (IJERT)"},{"key":"e_1_2_10_13_2","doi-asserted-by":"publisher","DOI":"10.54254\/2754-1169\/79\/20241747"},{"key":"e_1_2_10_14_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.heliyon.2024.e28415"},{"key":"e_1_2_10_15_2","doi-asserted-by":"publisher","DOI":"10.5281\/zenodo.14264144"},{"key":"e_1_2_10_16_2","doi-asserted-by":"publisher","DOI":"10.1109\/MLSP52302.2021.9596429"},{"key":"e_1_2_10_17_2","doi-asserted-by":"publisher","DOI":"10.3390\/e21060589"},{"key":"e_1_2_10_18_2","volume-title":"Proceedings of the 15th National Conference on Basic Research and Applications of Information Technology (FAIR)","author":"Tung H.","year":"2022"},{"key":"e_1_2_10_19_2","volume-title":"Proceedings of the 12th National Conference on Basic Research and Applications of Information Technology (FAIR)","author":"Vinh L. 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