{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,4]],"date-time":"2025-11-04T23:48:47Z","timestamp":1762300127332,"version":"build-2065373602"},"reference-count":20,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2022,7,30]],"date-time":"2022-07-30T00:00:00Z","timestamp":1659139200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Predicting the values of a financial time series is mainly a function of its price history, which depends on several factors, internal and external. With this history, it is possible to build an \u220a-machine for predicting the financial time series. This work proposes considering the influence of a financial series through the transfer of entropy when the values of the other financial series are known. A method is proposed that considers the transfer of entropy for breaking the ties that occur when calculating the prediction with the \u220a-machine. This analysis is carried out using data from six financial series: two American, the S&amp;P 500 and the Nasdaq; two Asian, the Hang Seng and the Nikkei 225; and two European, the CAC 40 and the DAX. This work shows that it is possible to influence the prediction of the closing value of a series if the value of the influencing series is known. This work showed that the series that transfer the most information through entropy transfer are the American S&amp;P 500 and Nasdaq, followed by the European DAX and CAC 40, and finally the Asian Nikkei 225 and Hang Seng.<\/jats:p>","DOI":"10.3390\/e24081049","type":"journal-article","created":{"date-parts":[[2022,7,31]],"date-time":"2022-07-31T23:37:29Z","timestamp":1659310649000},"page":"1049","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Influence of Transfer Entropy in the Short-Term Prediction of Financial Time Series Using an \u220a-Machine"],"prefix":"10.3390","volume":"24","author":[{"given":"Jos\u00e9 Crisp\u00edn","family":"Zavala-D\u00edaz","sequence":"first","affiliation":[{"name":"Faculty of Accounting, Administration and Informatics, Universidad Aut\u00f3noma del Estado de Morelos, Cuernavaca 62209, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5138-7984","authenticated-orcid":false,"given":"Joaqu\u00edn","family":"P\u00e9rez-Ortega","sequence":"additional","affiliation":[{"name":"Tecnol\u00f3gico Nacional de M\u00e9xico\/CENIDET, Cuernavaca 62490, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5885-7635","authenticated-orcid":false,"given":"Nelva Nely","family":"Almanza-Ortega","sequence":"additional","affiliation":[{"name":"Tecnol\u00f3gico Nacional de M\u00e9xico\/IT de Tlalnepantla, Tlalnepantla de Baz 54070, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rodolfo","family":"Pazos-Rangel","sequence":"additional","affiliation":[{"name":"Tecnol\u00f3gico Nacional de M\u00e9xico\/IT de Cd. Madero, Ciudad Madero 89440, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jos\u00e9 Mar\u00eda","family":"Rodr\u00edguez-Lel\u00eds","sequence":"additional","affiliation":[{"name":"Tecnol\u00f3gico Nacional de M\u00e9xico\/CENIDET, Cuernavaca 62490, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,7,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Dunis, C.L., Laws, J., and Na\u00efm, P. (2003). Applied Quantitative Methods for Trading and Investment, John Wiley Sons. [1st ed.].","DOI":"10.1002\/0470013265"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"497","DOI":"10.1007\/s00500-013-1070-2","article-title":"Financial time series prediction by a random data-time effective RBF neural network","volume":"18","author":"Niu","year":"2014","journal-title":"Soft Comput."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"610","DOI":"10.1109\/LSP.2016.2542881","article-title":"Dispersion Entropy: A Measure for Time Series Analysis","volume":"23","author":"Rostaghi","year":"2016","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"5865","DOI":"10.1016\/j.physa.2013.07.075","article-title":"Modified multiscale entropy for short-term time series analysis","volume":"392","author":"Wua","year":"2013","journal-title":"Physica A"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"288","DOI":"10.1016\/j.cnsns.2017.05.003","article-title":"Permutation entropy analysis of financial time series based on Hill\u2019s diversity number","volume":"53","author":"Zhang","year":"2017","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1016\/j.physa.2017.12.116","article-title":"Refined composite multiscale weighted-permutation entropy of financial time series","volume":"496","author":"Zhang","year":"2018","journal-title":"Physica A"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"158","DOI":"10.1016\/j.physa.2006.10.077","article-title":"Revisiting sample entropy analysis","volume":"376","author":"Govindana","year":"2007","journal-title":"Physica A"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"967","DOI":"10.1016\/j.physa.2017.08.144","article-title":"Time series analysis of multiple foreign exchange rates using time-dependent pattern entropy","volume":"490","author":"Ishizaki","year":"2018","journal-title":"Physica A"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"414","DOI":"10.1088\/1469-7688\/1\/4\/302","article-title":"Conditional entropy and randomness in financial time series","volume":"1","author":"London","year":"2001","journal-title":"Quant. Financ."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1016\/j.physa.2015.12.124","article-title":"Foreign Exchange rate entropy evolution during financial crises","volume":"449","author":"Stosic","year":"2016","journal-title":"Physica A"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"123540","DOI":"10.1016\/j.physa.2019.123540","article-title":"Short-term prediction of the closing price of financial series using a \u03f5-machine model","volume":"545","year":"2020","journal-title":"Physica A"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1016\/j.physa.2016.11.061","article-title":"Transfer entropy coefficient: Quantifying level of information flow between financial time series","volume":"469","author":"Teng","year":"2017","journal-title":"Physica A"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"125121","DOI":"10.1016\/j.physa.2020.125121","article-title":"Transfer entropy calculation for short time sequences with application to stock markets","volume":"559","author":"Qiu","year":"2020","journal-title":"Physica A"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"392","DOI":"10.1016\/j.physa.2017.04.103","article-title":"Nonlinear transformation on the transfer entropy of financial time series","volume":"482","author":"Wu","year":"2017","journal-title":"Physica A"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"398","DOI":"10.1016\/j.physa.2016.10.085","article-title":"Financial time series analysis based on effective phase transfer entropy","volume":"468","author":"Yang","year":"2017","journal-title":"Physica A"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1002\/j.1538-7305.1948.tb01338.x","article-title":"A mathematical theory of communication","volume":"27","author":"Shannon","year":"1948","journal-title":"Bell Syst. Tech. J."},{"key":"ref_17","unstructured":"Cormen, T., Leiserson, C., and Rivest, R. (2000). Introduction to Algorithms, MIT Press. [24th ed.]."},{"key":"ref_18","unstructured":"(2021, October 30). Yahoo Finanzas. \u00cdndices Mundiales. Available online: https:\/\/es-us.finanzas.yahoo.com\/mercados\/indices-mundo\/."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1038\/nphys2190","article-title":"Between order and chaos","volume":"8","author":"Crutchfield","year":"2012","journal-title":"Nat. Phys."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1212","DOI":"10.1016\/j.physa.2019.04.029","article-title":"Multivariate generalized information entropy of financial time series","volume":"525","author":"Zhang","year":"2019","journal-title":"Physica A"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/8\/1049\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:59:51Z","timestamp":1760140791000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/8\/1049"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,7,30]]},"references-count":20,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2022,8]]}},"alternative-id":["e24081049"],"URL":"https:\/\/doi.org\/10.3390\/e24081049","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2022,7,30]]}}}