{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,19]],"date-time":"2026-03-19T02:33:52Z","timestamp":1773887632391,"version":"3.50.1"},"reference-count":44,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2025,5,22]],"date-time":"2025-05-22T00:00:00Z","timestamp":1747872000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"},{"start":{"date-parts":[[2025,5,22]],"date-time":"2025-05-22T00:00:00Z","timestamp":1747872000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Big Data"],"DOI":"10.1186\/s40537-025-01164-z","type":"journal-article","created":{"date-parts":[[2025,5,22]],"date-time":"2025-05-22T10:43:47Z","timestamp":1747910627000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Optimal Markowitz portfolio using returns forecasted with time series and machine learning models"],"prefix":"10.1186","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0009-0009-0593-4826","authenticated-orcid":false,"given":"Damian","family":"\u015alusarczyk","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5227-2014","authenticated-orcid":false,"given":"Robert","family":"\u015alepaczuk","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,5,22]]},"reference":[{"key":"1164_CR1","doi-asserted-by":"publisher","first-page":"27","DOI":"10.1016\/j.asoc.2014.05.028","volume":"23","author":"CN Babu","year":"2014","unstructured":"Babu CN, Reddy BE. A moving-average filter based hybrid arima-ann model for forecasting time series data. Appl Soft Comput. 2014;23:27\u201338.","journal-title":"Appl Soft Comput"},{"key":"1164_CR2","doi-asserted-by":"publisher","DOI":"10.1016\/j.engappai.2023.105843","volume":"120","author":"J Behera","year":"2023","unstructured":"Behera J, Pasayat AK, Behera H, Kumar P. Prediction based mean-value-at-risk portfolio optimization using machine learning regression algorithms for multi-national stock markets. Eng Appl Artif Intell. 2023;120: 105843.","journal-title":"Eng Appl Artif Intell"},{"issue":"5","key":"1164_CR3","doi-asserted-by":"publisher","first-page":"28","DOI":"10.2469\/faj.v48.n5.28","volume":"48","author":"F Black","year":"1992","unstructured":"Black F, Litterman R. Global portfolio optimization. Financ Anal J. 1992;48(5):28\u201343.","journal-title":"Financ Anal J"},{"issue":"3","key":"1164_CR4","doi-asserted-by":"publisher","first-page":"307","DOI":"10.1016\/0304-4076(86)90063-1","volume":"31","author":"T Bollerslev","year":"1986","unstructured":"Bollerslev T. Generalized autoregressive conditional heteroskedasticity. J Econometr. 1986;31(3):307\u201327.","journal-title":"J Econometr"},{"key":"1164_CR5","volume-title":"Time series analysis: forecasting and control","author":"GE Box","year":"2015","unstructured":"Box GE, Jenkins GM, Reinsel GC, Ljung GM. Time series analysis: forecasting and control. New York: Wiley; 2015."},{"key":"1164_CR6","doi-asserted-by":"publisher","first-page":"165","DOI":"10.1016\/j.eswa.2018.02.004","volume":"100","author":"C Chen","year":"2018","unstructured":"Chen C, Zhou Y-S. Robust multiobjective portfolio with higher moments. Expert Syst Appl. 2018;100:165\u201381.","journal-title":"Expert Syst Appl"},{"key":"1164_CR7","doi-asserted-by":"crossref","unstructured":"Chen T, Guestrin C. XGBoost: a scalable tree boosting system. In: Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. New York, NY, USA: ACM. 2016; pp. 785\u2013794.","DOI":"10.1145\/2939672.2939785"},{"key":"1164_CR8","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2020.106943","volume":"100","author":"W Chen","year":"2021","unstructured":"Chen W, Zhang H, Mehlawat MK, Jia L. Mean-variance portfolio optimization using machine learning-based stock price prediction. Appl Soft Comput. 2021;100: 106943.","journal-title":"Appl Soft Comput"},{"issue":"5","key":"1164_CR9","doi-asserted-by":"publisher","first-page":"1915","DOI":"10.1093\/rfs\/hhm075","volume":"22","author":"V DeMiguel","year":"2007","unstructured":"DeMiguel V, Garlappi L, Uppal R. Optimal versus naive diversification: how inefficient is the 1\/n portfolio strategy? Rev Financ Stud. 2007;22(5):1915\u201353. https:\/\/doi.org\/10.1093\/rfs\/hhm075.","journal-title":"Rev Financ Stud."},{"key":"1164_CR10","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4614-0391-3","volume-title":"Modern mathematical statistics with applications","author":"JL Devore","year":"2012","unstructured":"Devore JL, Berk KN, Carlton MA. Modern mathematical statistics with applications, vol. 285. Berlin: Springer; 2012."},{"key":"1164_CR11","doi-asserted-by":"publisher","DOI":"10.1016\/j.engappai.2022.105626","volume":"118","author":"A Dezhkam","year":"2023","unstructured":"Dezhkam A, Manzuri MT. Forecasting stock market for an efficient portfolio by combining xgboost and hilbert-huang transform. Eng Appl Artif Intell. 2023;118: 105626.","journal-title":"Eng Appl Artif Intell"},{"issue":"4","key":"1164_CR12","doi-asserted-by":"publisher","first-page":"157","DOI":"10.1257\/jep.15.4.157","volume":"15","author":"R Engle","year":"2001","unstructured":"Engle R. GARCH 101: the use of ARCH\/GARCH models in applied econometrics. J Econ Perspect. 2001;15(4):157\u201368.","journal-title":"J Econ Perspect"},{"key":"1164_CR13","doi-asserted-by":"crossref","unstructured":"Engle RF. Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometr J Econometr Soc. 1982;987\u20131007.","DOI":"10.2307\/1912773"},{"issue":"3","key":"1164_CR14","doi-asserted-by":"publisher","first-page":"7","DOI":"10.3905\/joi.2002.319510","volume":"11","author":"FJ Fabozzi","year":"2002","unstructured":"Fabozzi FJ, Gupta F, Markowitz HM. The legacy of modern portfolio theory. J Invest. 2002;11(3):7\u201322.","journal-title":"J Invest"},{"key":"1164_CR15","unstructured":"Ghalanos A. R package version 1.4-9; 2022."},{"key":"1164_CR16","doi-asserted-by":"publisher","DOI":"10.1016\/j.ribaf.2023.102052","volume":"66","author":"J Grudniewicz","year":"2023","unstructured":"Grudniewicz J, \u015alepaczuk R. Application of machine learning in algorithmic investment strategies on global stock markets. Res Int Bus Financ. 2023;66: 102052. https:\/\/doi.org\/10.1016\/j.ribaf.2023.102052.","journal-title":"Res Int Bus Financ"},{"key":"1164_CR17","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2019.105781","volume":"85","author":"P Gupta","year":"2019","unstructured":"Gupta P, Mehlawat MK, Yadav S, Kumar A. A polynomial goal programming approach for intuitionistic fuzzy portfolio optimization using entropy and higher moments. Appl Soft Comput. 2019;85: 105781.","journal-title":"Appl Soft Comput"},{"issue":"5","key":"1164_CR18","doi-asserted-by":"publisher","first-page":"469","DOI":"10.1080\/14697681003756877","volume":"10","author":"CR Harvey","year":"2010","unstructured":"Harvey CR, Liechty JC, Liechty MW, M\u00fcller P. Portfolio selection with higher moments. Quantitative Financ. 2010;10(5):469\u201385.","journal-title":"Quantitative Financ"},{"key":"1164_CR19","doi-asserted-by":"crossref","unstructured":"Jabeur SB, Mefteh-Wali S, Viviani J-L. Forecasting gold price with the XGBoost algorithm and SHAP interaction values. Ann Opera Res. 2021;1\u201321.","DOI":"10.1007\/s10479-021-04187-w"},{"issue":"4","key":"1164_CR20","doi-asserted-by":"publisher","first-page":"1651","DOI":"10.1111\/1540-6261.00580","volume":"58","author":"R Jagannathan","year":"2003","unstructured":"Jagannathan R, Ma T. Risk reduction in large portfolios: why imposing the wrong constraints helps. J Financ. 2003;58(4):1651\u201383. https:\/\/doi.org\/10.1111\/1540-6261.00580.","journal-title":"J Financ."},{"issue":"4","key":"1164_CR21","doi-asserted-by":"publisher","first-page":"1473","DOI":"10.1016\/j.ijforecast.2021.10.004","volume":"38","author":"T Januschowski","year":"2022","unstructured":"Januschowski T, Wang Y, Torkkola K, Erkkil\u00e4 T, Hasson H, Gasthaus J. Forecasting with trees. Int J Forecast. 2022;38(4):1473\u201381.","journal-title":"Int J Forecast"},{"issue":"3","key":"1164_CR22","doi-asserted-by":"publisher","first-page":"991","DOI":"10.1016\/j.ijforecast.2015.11.003","volume":"32","author":"J Jeon","year":"2016","unstructured":"Jeon J, Taylor JW. Short-term density forecasting of wave energy using ARMA-GARCH models and kernel density estimation. Int J Forecast. 2016;32(3):991\u20131004.","journal-title":"Int J Forecast"},{"key":"1164_CR23","unstructured":"Kry\u0144ska K, \u015alepaczuk R. Daily and intraday application of various architectures of the LSTM model in algorithmic investment strategies on Bitcoin and the S &P 500 Index. Working Papers of Faculty of Economic Sciences, University of Warsaw, 25\/2022 (401), Retrieved from https:\/\/www.wne.uw.edu.pl\/application\/files\/6416\/6601\/0304\/WNE_WP401.pdf; 2022."},{"issue":"4","key":"1164_CR24","doi-asserted-by":"publisher","first-page":"110","DOI":"10.3905\/jpm.2004.110","volume":"30","author":"O Ledoit","year":"2004","unstructured":"Ledoit O, Wolf M. Honey, i shrunk the sample covariance matrix. J Portf Manag. 2004;30(4):110.","journal-title":"J Portf Manag"},{"key":"1164_CR25","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2020.113973","volume":"165","author":"Y Ma","year":"2021","unstructured":"Ma Y, Han R, Wang W. Portfolio optimization with return prediction using deep learning and machine learning. Expert Syst Appl. 2021;165: 113973.","journal-title":"Expert Syst Appl"},{"key":"1164_CR26","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2023.120638","volume":"230","author":"Y Ma","year":"2023","unstructured":"Ma Y, Wang Y, Wang W, Zhang C. Prediction-based mean-variance portfolios with risk budgeting based on neural networks. Expert Syst Appl. 2023;230: 120638.","journal-title":"Expert Syst Appl"},{"issue":"2","key":"1164_CR27","doi-asserted-by":"publisher","first-page":"151","DOI":"10.1086\/257177","volume":"60","author":"H Markowitz","year":"1952","unstructured":"Markowitz H. The utility of wealth. J Polit Econ. 1952;60(2):151\u20138.","journal-title":"J Polit Econ"},{"issue":"3","key":"1164_CR28","doi-asserted-by":"publisher","first-page":"917","DOI":"10.3390\/s22030917","volume":"22","author":"J Micha\u0144k\u00f3w","year":"2022","unstructured":"Micha\u0144k\u00f3w J, Sakowski P, \u015alepaczuk R. LSTM in algorithmic investment strategies on BTC and S &P500 index. Sensors. 2022;22(3):917.","journal-title":"Sensors"},{"issue":"1","key":"1164_CR29","doi-asserted-by":"publisher","first-page":"31","DOI":"10.2469\/faj.v45.n1.31","volume":"45","author":"RO Michaud","year":"1989","unstructured":"Michaud RO. The markowitz optimization enigma: is \u201coptimized\u2019\u2019 optimal? Financ Anal J. 1989;45(1):31\u201342.","journal-title":"Financ Anal J"},{"issue":"5","key":"1164_CR30","doi-asserted-by":"publisher","first-page":"1001","DOI":"10.1016\/j.eneco.2010.04.009","volume":"32","author":"H Mohammadi","year":"2010","unstructured":"Mohammadi H, Su L. International evidence on crude oil price dynamics: applications of ARIMA-GARCH models. Energy Econ. 2010;32(5):1001\u20138.","journal-title":"Energy Econ"},{"key":"1164_CR31","doi-asserted-by":"publisher","DOI":"10.1088\/1742-6596\/1366\/1\/012130","volume":"1366","author":"FH Mustapa","year":"2019","unstructured":"Mustapa FH, Ismail MT. Modelling and forecasting S &P 500 stock prices using hybrid Arima-Garch Model. J Phys Conf Ser. 2019;1366: 012130.","journal-title":"J Phys Conf Ser"},{"issue":"8","key":"1164_CR32","doi-asserted-by":"publisher","first-page":"840","DOI":"10.3390\/e22080840","volume":"22","author":"M Nabipour","year":"2020","unstructured":"Nabipour M, Nayyeri P, Jabani H, Mosavi A, Salwana E. Deep learning for stock market prediction. Entropy. 2020;22(8):840.","journal-title":"Entropy"},{"key":"1164_CR33","doi-asserted-by":"publisher","first-page":"181","DOI":"10.1016\/j.eswa.2019.01.083","volume":"125","author":"J Nobre","year":"2019","unstructured":"Nobre J, Neves RF. Combining principal component analysis, discrete wavelet transform and XGBoost to trade in the financial markets. Expert Syst Appl. 2019;125:181\u201394.","journal-title":"Expert Syst Appl"},{"issue":"9","key":"1164_CR34","doi-asserted-by":"publisher","first-page":"2293","DOI":"10.1016\/j.csda.2004.12.008","volume":"50","author":"L Pascual","year":"2006","unstructured":"Pascual L, Romo J, Ruiz E. Bootstrap prediction for returns and volatilities in GARCH models. Comput Statis Data Anal. 2006;50(9):2293\u2013312.","journal-title":"Comput Statis Data Anal"},{"key":"1164_CR35","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2023.110939","volume":"149","author":"S Ray","year":"2023","unstructured":"Ray S, Lama A, Mishra P, Biswas T, Das SS, Gurung B. An arima-lstm model for predicting volatile agricultural price series with random forest technique. Appl Soft Comput. 2023;149: 110939.","journal-title":"Appl Soft Comput"},{"issue":"3","key":"1164_CR36","doi-asserted-by":"publisher","first-page":"78","DOI":"10.18559\/ebr.2016.3.6","volume":"2","author":"P Sakowski","year":"2016","unstructured":"Sakowski P, \u015alepaczuk R, Wywia\u0142 M. Can we invest on the basis of equity risk premia and risk factors from multi-factor models? Econ Bus Rev. 2016;2(3):78\u201398.","journal-title":"Econ Bus Rev"},{"key":"1164_CR37","doi-asserted-by":"publisher","DOI":"10.1002\/0471746193","volume-title":"Analysis of financial time series","author":"RS Tsay","year":"2005","unstructured":"Tsay RS. Analysis of financial time series. New York: Wiley; 2005."},{"issue":"1","key":"1164_CR38","doi-asserted-by":"publisher","first-page":"204","DOI":"10.1016\/j.jfineco.2010.08.013","volume":"99","author":"J Tu","year":"2011","unstructured":"Tu J, Zhou G. Markowitz meets talmud: a combination of sophisticated and naive diversification strategies. J Financ Econ. 2011;99(1):204\u201315. https:\/\/doi.org\/10.1016\/j.jfineco.2010.08.013.","journal-title":"J Financ Econ"},{"issue":"2","key":"1164_CR39","doi-asserted-by":"publisher","first-page":"158","DOI":"10.3390\/e24020158","volume":"24","author":"N Vo","year":"2022","unstructured":"Vo N, \u015alepaczuk R. Applying hybrid ARIMA-SGARCH in algorithmic investment strategies on S &P500 Index. Entropy. 2022;24(2):158. https:\/\/doi.org\/10.3390\/e24020158.","journal-title":"Entropy"},{"key":"1164_CR40","unstructured":"Wooldridge JM. Introductory econometrics: a modern approach. Cengage learning. 2015."},{"key":"1164_CR41","unstructured":"Wysocki M, Sakowski P. Investment portfolio optimization based on modern portfolio theory and deep learning models. In: Working Papers of Faculty of Economic Sciences, University of Warsaw, 12\/2022 (388). Retrieved from https:\/\/www.wne.uw.edu.pl\/application\/files\/2816\/5451\/1328\/WNE_WP388.pdf; 2022."},{"issue":"3","key":"1164_CR42","doi-asserted-by":"publisher","first-page":"3417","DOI":"10.1002\/ijfe.1968","volume":"26","author":"Q Xu","year":"2021","unstructured":"Xu Q, Zuo J, Jiang C, He Y. A large constrained time-varying portfolio selection model with dcc-midas: evidence from Chinese stock market. Int J Financ Econ. 2021;26(3):3417\u201335.","journal-title":"Int J Financ Econ"},{"key":"1164_CR43","unstructured":"Yaziz S, Azizan N, Zakaria R, Ahmad M. The performance of hybrid ARIMA-GARCH modeling in forecasting gold price. In: 20th international congress on modelling and simulation, Adelaide. 2013; pp. 1\u20136."},{"key":"1164_CR44","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2021.115716","volume":"186","author":"KK Yun","year":"2021","unstructured":"Yun KK, Yoon SW, Won D. Prediction of stock price direction using a hybrid GA-XGBoost algorithm with a three-stage feature engineering process. Expert Syst Appl. 2021;186: 115716.","journal-title":"Expert Syst Appl"}],"container-title":["Journal of Big Data"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/s40537-025-01164-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1186\/s40537-025-01164-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/s40537-025-01164-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,5,22]],"date-time":"2025-05-22T10:43:51Z","timestamp":1747910631000},"score":1,"resource":{"primary":{"URL":"https:\/\/journalofbigdata.springeropen.com\/articles\/10.1186\/s40537-025-01164-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,5,22]]},"references-count":44,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2025,12]]}},"alternative-id":["1164"],"URL":"https:\/\/doi.org\/10.1186\/s40537-025-01164-z","relation":{},"ISSN":["2196-1115"],"issn-type":[{"value":"2196-1115","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,5,22]]},"assertion":[{"value":"23 October 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 April 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 May 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"127"}}