{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,23]],"date-time":"2026-07-23T02:02:23Z","timestamp":1784772143753,"version":"3.55.0"},"reference-count":35,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2026,5,27]],"date-time":"2026-05-27T00:00:00Z","timestamp":1779840000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"},{"start":{"date-parts":[[2026,7,23]],"date-time":"2026-07-23T00:00:00Z","timestamp":1784764800000},"content-version":"vor","delay-in-days":57,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Int J Comput Intell Syst"],"DOI":"10.1007\/s44196-026-01382-0","type":"journal-article","created":{"date-parts":[[2026,5,27]],"date-time":"2026-05-27T04:25:53Z","timestamp":1779855953000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Wasserstein Distance-Based Feature Engineering for Enhancing Forecasting and Asset Allocation Insights"],"prefix":"10.1007","volume":"19","author":[{"given":"Insu","family":"Choi","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,5,27]]},"reference":[{"key":"1382_CR1","doi-asserted-by":"publisher","DOI":"10.1002\/9781119319030","volume-title":"Real-Time Risk: What Investors Should Know about FinTech, High-Frequency Trading, and Flash Crashes","author":"I Aldridge","year":"2017","unstructured":"Aldridge, I., Krawciw, S.: Real-Time Risk: What Investors Should Know about FinTech, High-Frequency Trading, and Flash Crashes. John Wiley & Sons, Hoboken, NJ (2017)"},{"issue":"5","key":"1382_CR2","doi-asserted-by":"publisher","first-page":"458","DOI":"10.1090\/noti1105","volume":"61","author":"DH Bailey","year":"2014","unstructured":"Bailey, D.H., Borwein, J.M., de Prado, M.L., Zhu, Q.J.: Pseudo-mathematics and financial charlatanism: The effects of backtest overfitting on out-of-sample performance. Notices Am. Mathemat. Soc. 61(5), 458\u2013471 (2014)","journal-title":"Notices Am. Mathemat. Soc."},{"issue":"9","key":"1382_CR3","doi-asserted-by":"publisher","first-page":"6382","DOI":"10.1287\/mnsc.2021.4155","volume":"68","author":"J Blanchet","year":"2022","unstructured":"Blanchet, J., Chen, L., Zhou, X.Y.: Distributionally robust mean-variance portfolio selection with Wasserstein distances. Manage. Sci. 68(9), 6382\u20136410 (2022)","journal-title":"Manage. Sci."},{"key":"1382_CR4","doi-asserted-by":"crossref","unstructured":"Bouchaud, J.-P., Potters, M.: Theory of Financial Risk and Derivative Pricing: From Statistical Physics to Risk Management, Cambridge University Press (2003). (2nd edition)","DOI":"10.1017\/CBO9780511753893"},{"issue":"1","key":"1382_CR5","doi-asserted-by":"publisher","first-page":"5","DOI":"10.1023\/A:1010933404324","volume":"45","author":"L Breiman","year":"2001","unstructured":"Breiman, L.: Random forests. Mach. Learn. 45(1), 5\u201332 (2001)","journal-title":"Mach. Learn."},{"issue":"4","key":"1382_CR6","doi-asserted-by":"publisher","first-page":"559","DOI":"10.1017\/S1365100598009092","volume":"2","author":"JY Campbell","year":"1998","unstructured":"Campbell, J.Y., Lo, A.W., MacKinlay, A.C., Whitelaw, R.F.: The econometrics of financial markets. Macroeco. Dyn. 2(4), 559\u2013562 (1998)","journal-title":"Macroeco. Dyn."},{"issue":"2","key":"1382_CR7","doi-asserted-by":"publisher","first-page":"783","DOI":"10.1007\/s10898-022-01171-x","volume":"87","author":"D Chen","year":"2023","unstructured":"Chen, D., Wu, Y., Li, J., Ding, X., Chen, C.: Distributionally robust mean-absolute deviation portfolio optimization using Wasserstein metric. J. Global Optim. 87(2), 783\u2013805 (2023)","journal-title":"J. Global Optim."},{"key":"1382_CR8","doi-asserted-by":"crossref","unstructured":"Cont, R., Schaanning, E.F.: Fire sales, indirect contagion and systemic stress testing, (2017). (SSRN preprint)","DOI":"10.2139\/ssrn.2955646"},{"key":"1382_CR9","doi-asserted-by":"publisher","first-page":"182","DOI":"10.1016\/j.irfa.2018.09.003","volume":"62","author":"S Corbet","year":"2019","unstructured":"Corbet, S., Lucey, B., Urquhart, A., Yarovaya, L.: Cryptocurrencies as a financial asset: A systematic analysis. Int. Rev. Financ. Anal. 62, 182\u2013199 (2019)","journal-title":"Int. Rev. Financ. Anal."},{"issue":"9","key":"1382_CR10","doi-asserted-by":"publisher","first-page":"929","DOI":"10.3390\/e22090929","volume":"22","author":"R Cumings-Menon","year":"2020","unstructured":"Cumings-Menon, R., Shin, M.: Probability forecast combination via entropy regularized Wasserstein distance. Entropy 22(9), 929 (2020)","journal-title":"Entropy"},{"issue":"4","key":"1382_CR11","doi-asserted-by":"publisher","first-page":"59","DOI":"10.3905\/jpm.2016.42.4.059","volume":"42","author":"ML de Prado","year":"2016","unstructured":"de Prado, M.L.: Building diversified portfolios that outperform out of sample. The J. Portfolio Manage. 42(4), 59\u201369 (2016)","journal-title":"The J. Portfolio Manage."},{"key":"1382_CR12","volume-title":"Advances in Financial Machine Learning","author":"ML de Prado","year":"2018","unstructured":"de Prado, M.L.: Advances in Financial Machine Learning. John Wiley & Sons, Hoboken, NJ (2018)"},{"key":"1382_CR13","doi-asserted-by":"publisher","DOI":"10.1017\/9781108883658","volume-title":"Machine Learning for Asset Managers","author":"ML de Prado","year":"2020","unstructured":"de Prado, M.L.: Machine Learning for Asset Managers. Cambridge University Press, Cambridge (2020)"},{"issue":"5","key":"1382_CR14","doi-asserted-by":"publisher","first-page":"1915","DOI":"10.1093\/rfs\/hhm075","volume":"22","author":"V DeMiguel","year":"2009","unstructured":"DeMiguel, V., Garlappi, L., Uppal, R.: Optimal versus naive diversification: How inefficient is the $$1\/n$$ portfolio strategy? The Rev. Financ. Stud. 22(5), 1915\u20131953 (2009)","journal-title":"The Rev. Financ. Stud."},{"issue":"5","key":"1382_CR15","doi-asserted-by":"publisher","first-page":"425","DOI":"10.1002\/jae.683","volume":"17","author":"R Engle","year":"2002","unstructured":"Engle, R.: New frontiers for ARCH models. J. Appl. Economet. 17(5), 425\u2013446 (2002)","journal-title":"J. Appl. Economet."},{"issue":"2","key":"1382_CR16","doi-asserted-by":"publisher","first-page":"603","DOI":"10.1287\/moor.2022.1275","volume":"48","author":"R Gao","year":"2023","unstructured":"Gao, R., Kleywegt, A.: Distributionally robust stochastic optimization with Wasserstein distance. Math. Oper. Res. 48(2), 603\u2013655 (2023)","journal-title":"Math. Oper. Res."},{"key":"1382_CR17","doi-asserted-by":"publisher","first-page":"102052","DOI":"10.1016\/j.ribaf.2023.102052","volume":"66","author":"J Grudniewicz","year":"2023","unstructured":"Grudniewicz, J., \u015alepaczuk, R.: Application of machine learning in quantitative investment strategies on global stock markets. Res. Int. Bus. Financ. 66, 102052 (2023)","journal-title":"Res. Int. Bus. Financ."},{"key":"1382_CR18","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-84858-7","volume-title":"The Elements of Statistical Learning: Data Mining, Inference, and Prediction","author":"T Hastie","year":"2009","unstructured":"Hastie, T., Tibshirani, R., Friedman, J.H.: The Elements of Statistical Learning: Data Mining, Inference, and Prediction, 2nd edition Springer, New York (2009)","edition":"2nd edition"},{"key":"1382_CR19","doi-asserted-by":"publisher","first-page":"103735","DOI":"10.1016\/j.frl.2023.103735","volume":"54","author":"Z Hosseini-Nodeh","year":"2023","unstructured":"Hosseini-Nodeh, Z., Khanjani-Shiraz, R., Pardalos, P.M.: Portfolio optimization using robust mean absolute deviation model: wasserstein metric approach. Financ. Res. Lett. 54, 103735 (2023)","journal-title":"Financ. Res. Lett."},{"key":"1382_CR20","doi-asserted-by":"crossref","unstructured":"Kashif, K., \u015alepaczuk, R.: LSTM-ARIMA as a hybrid approach in algorithmic investment strategies, (arXiv preprint), (2024).","DOI":"10.2139\/ssrn.4877100"},{"key":"1382_CR21","doi-asserted-by":"crossref","unstructured":"Kijewski, M., \u015alepaczuk, R., Wysocki, M.: Predicting prices of S&P 500 index using classical methods and recurrent neural networks. In Proceedings of the 32nd International Conference on Information Systems Development (ISD 2024) (2024)","DOI":"10.62036\/ISD.2024.89"},{"key":"1382_CR22","doi-asserted-by":"publisher","DOI":"10.3905\/jpm.2024.1.639","author":"Y Lee","year":"2024","unstructured":"Lee, Y., Kim, J.H., Kim, W.C., Fabozzi, F.J.: An overview of machine learning for portfolio optimization. The J. Portfolio Manage. (2024). https:\/\/doi.org\/10.3905\/jpm.2024.1.639","journal-title":"The J. Portfolio Manage."},{"key":"1382_CR23","unstructured":"Li, F.: Feature selection based on Wasserstein distance, (arXiv preprint), (2024).\u00a0"},{"key":"1382_CR24","unstructured":"Lundberg, S.M., Erion, G.G., Lee, S.-I.: Consistent individualized feature attribution for tree ensembles, (arXiv preprint), (2018)."},{"key":"1382_CR25","unstructured":"Lundberg, S.M., Lee, S.-I.: A unified approach to interpreting model predictions. In Adv. Neural. Inf. Process. Syst., 30, (2017)"},{"issue":"1","key":"1382_CR26","first-page":"77","volume":"7","author":"H Markowitz","year":"1952","unstructured":"Markowitz, H.: Portfolio selection. The J. Finan. 7(1), 77\u201391 (1952)","journal-title":"The J. Finan."},{"issue":"1","key":"1382_CR27","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1146\/annurev-financial-011110-134602","volume":"2","author":"HM Markowitz","year":"2010","unstructured":"Markowitz, H.M.: Portfolio theory: As i still see it. Annual Rev. Financ. Eco. 2(1), 1\u201323 (2010)","journal-title":"Annual Rev. Financ. Eco."},{"key":"1382_CR28","doi-asserted-by":"crossref","unstructured":"Micha\u0144k\u00f3w, J., Sakowski, P., \u015alepaczuk, R.: Hedging properties of algorithmic investment strategies using LSTM and ARIMA-GARCH models for equity indices. In: Proceedings of the 32nd International Conference on Information Systems Development, (2024) . (ISD 2024)","DOI":"10.62036\/ISD.2024.57"},{"key":"1382_CR29","unstructured":"Nguyen, T.T.G., \u015alepaczuk, R.: The efficiency of various types of input layers of LSTM model in investment strategies on S&P 500 index. Technical Report WP No. 29\/2022 (405), Faculty of Economic Sciences, University of Warsaw (2022)"},{"issue":"1","key":"1382_CR30","doi-asserted-by":"publisher","first-page":"405","DOI":"10.1146\/annurev-statistics-030718-104938","volume":"6","author":"VM Panaretos","year":"2019","unstructured":"Panaretos, V.M., Zemel, Y.: Statistical aspects of Wasserstein distances. Annual Rev. Stat. Its Appl. 6(1), 405\u2013431 (2019)","journal-title":"Annual Rev. Stat. Its Appl."},{"key":"1382_CR31","doi-asserted-by":"crossref","unstructured":"Ribeiro, M. T., Singh, S., Guestrin, C.: \"Why should I trust you?\" explaining the predictions of any classifier. In Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 1135\u20131144 (2016)","DOI":"10.1145\/2939672.2939778"},{"issue":"1","key":"1382_CR32","doi-asserted-by":"publisher","first-page":"119","DOI":"10.1086\/294846","volume":"39","author":"WF Sharpe","year":"1966","unstructured":"Sharpe, W.F.: Mutual fund performance. The J. Bus. 39(1), 119\u2013138 (1966)","journal-title":"The J. Bus."},{"key":"1382_CR33","doi-asserted-by":"crossref","unstructured":"Souto, H.G., Moradi, A.: Wasserstein distance loss function for financial time series deep learning, (2024)","DOI":"10.1016\/j.simpa.2024.100639"},{"key":"1382_CR34","doi-asserted-by":"publisher","DOI":"10.1002\/0471746193","volume-title":"Analysis of Financial Time Series","author":"RS Tsay","year":"2005","unstructured":"Tsay, R.S.: Analysis of Financial Time Series, 2nd edition John Wiley & Sons, Hoboken, NJ (2005)","edition":"2nd edition"},{"issue":"3","key":"1382_CR35","first-page":"64","volume":"5","author":"LN Wasserstein","year":"1969","unstructured":"Wasserstein, L.N.: Markov processes over denumerable products of spaces, describing large systems of automata. Problemy Peredachi Informatsii 5(3), 64\u201372 (1969)","journal-title":"Problemy Peredachi Informatsii"}],"container-title":["International Journal of Computational Intelligence Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s44196-026-01382-0","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s44196-026-01382-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s44196-026-01382-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,7,23]],"date-time":"2026-07-23T01:30:50Z","timestamp":1784770250000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s44196-026-01382-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,5,27]]},"references-count":35,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2026,12]]}},"alternative-id":["1382"],"URL":"https:\/\/doi.org\/10.1007\/s44196-026-01382-0","relation":{},"ISSN":["1875-6883"],"issn-type":[{"value":"1875-6883","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,5,27]]},"assertion":[{"value":"21 January 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"28 April 2026","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 May 2026","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 May 2026","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The authors declare no competing interests.","order":1,"name":"Ethics","label":"Competing Interests","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no known competing financial interests or personal relationships that could appear to influence the work reported in this paper.","order":2,"name":"Ethics","label":"Conflicts of Interest","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"During the preparation of this manuscript, the authors used an AI-based writing assistant for language editing and manuscript formatting. After using this tool, the authors reviewed and edited the content as needed and take full responsibility for the content of the publication. AI tools were not used for data collection, data analysis, verification of empirical results, or formulation of interpretive or theoretical conclusions.","order":3,"name":"Ethics","label":"Declaration of Generative AI and AI-assisted Technologies in the Writing Process","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"This article does not contain any studies with human participants or animals performed by any of the authors.","order":4,"name":"Ethics","label":"Ethical Approval","group":{"name":"EthicsHeading","label":"Declarations"}}],"article-number":"286"}}