{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,17]],"date-time":"2026-03-17T04:09:36Z","timestamp":1773720576962,"version":"3.50.1"},"reference-count":36,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2026,1,5]],"date-time":"2026-01-05T00:00:00Z","timestamp":1767571200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Social Science Fund of China Program","award":["24BJY093"],"award-info":[{"award-number":["24BJY093"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>While deep learning models have demonstrated superior performance in cryptocurrency forecasting, their deployment is often hindered by a lack of interpretability and trustworthiness. To bridge this gap, this paper proposes the Cryptocurrency Counterfactual Explanation (CryptoForecastCF) model. Recognizing the inherent volatility and complex non-linear dynamics of cryptocurrency markets, we argue that understanding the sensitivity of model outputs to slight variations in historical conditions is fundamental to robust risk management. CryptoForecastCF employs a gradient-based optimization strategy to generate meaningful counterfactual explanations. Specifically, it identifies minimal modifications, defined as the optimal perturbations to historical market features such as price constrained by \u21131 or \u21132 norms, that are sufficient to steer the model\u2019s future predictions into user-specified target intervals. This approach not only elucidates the key driving factors and decision boundaries of opaque models but also equips traders and risk managers with actionable insights, enabling them to identify the specific market shifts required to navigate high-stakes scenarios and mitigate unfavorable predictive outcomes.<\/jats:p>","DOI":"10.3390\/e28010065","type":"journal-article","created":{"date-parts":[[2026,1,5]],"date-time":"2026-01-05T15:28:57Z","timestamp":1767626937000},"page":"65","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Counterfactual Explanation-Based Cryptocurrency Price Prediction"],"prefix":"10.3390","volume":"28","author":[{"given":"Xinxin","family":"Luo","sequence":"first","affiliation":[{"name":"School of Cyber Science and Engineering, Southeast University, No.2, Southeast University Road, Jiangning District, Nanjing 211189, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wei","family":"Yin","sequence":"additional","affiliation":[{"name":"School of Cyber Science and Engineering, Southeast University, No.2, Southeast University Road, Jiangning District, Nanjing 211189, China"},{"name":"School of Economics and Management, Southeast University, No.2, Southeast University Road, Jiangning District, Nanjing 211189, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,1,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1186\/s40854-021-00321-6","article-title":"Cryptocurrency trading: A comprehensive survey","volume":"8","author":"Fang","year":"2022","journal-title":"Financ. 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