{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,19]],"date-time":"2025-10-19T16:01:25Z","timestamp":1760889685370,"version":"build-2065373602"},"reference-count":24,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2018,8,22]],"date-time":"2018-08-22T00:00:00Z","timestamp":1534896000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100010687","name":"H2020 Euratom","doi-asserted-by":"publisher","award":["633053"],"award-info":[{"award-number":["633053"]}],"id":[{"id":"10.13039\/100010687","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Understanding the details of the correlation between time series is an essential step on the route to assessing the causal relation between systems. Traditional statistical indicators, such as the Pearson correlation coefficient and the mutual information, have some significant limitations. More recently, transfer entropy has been proposed as a powerful tool to understand the flow of information between signals. In this paper, the comparative advantages of transfer entropy, for determining the time horizon of causal influence, are illustrated with the help of synthetic data. The technique has been specifically revised for the analysis of synchronization experiments. The investigation of experimental data from thermonuclear plasma diagnostics proves the potential and limitations of the developed approach.<\/jats:p>","DOI":"10.3390\/e20090627","type":"journal-article","created":{"date-parts":[[2018,8,22]],"date-time":"2018-08-22T03:42:37Z","timestamp":1534909357000},"page":"627","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["On the Use of Transfer Entropy to Investigate the Time Horizon of Causal Influences between Signals"],"prefix":"10.3390","volume":"20","author":[{"given":"Andrea","family":"Murari","sequence":"first","affiliation":[{"name":"Consorzio RFX (CNR, ENEA, INFN, Universita\u2019 di Padova, Acciaierie Venete SpA), I-35127 Padova, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1500-363X","authenticated-orcid":false,"given":"Michele","family":"Lungaroni","sequence":"additional","affiliation":[{"name":"Associazione EUROfusion\u2014University of Rome \u201cTor Vergata\u201d, Via Orazio Raimondo, 18, 00173 Roma, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6829-2180","authenticated-orcid":false,"given":"Emmanuele","family":"Peluso","sequence":"additional","affiliation":[{"name":"Associazione EUROfusion\u2014University of Rome \u201cTor Vergata\u201d, Via Orazio Raimondo, 18, 00173 Roma, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0861-558X","authenticated-orcid":false,"given":"Pasquale","family":"Gaudio","sequence":"additional","affiliation":[{"name":"Associazione EUROfusion\u2014University of Rome \u201cTor Vergata\u201d, Via Orazio Raimondo, 18, 00173 Roma, Italy"}]},{"given":"Ernesto","family":"Lerche","sequence":"additional","affiliation":[{"name":"EUROfusion Programme Management Unit, JET, Culham Science Centre, Abingdon OX14 3DB, UK"},{"name":"LPP-ERM\/KMS, Association EUROFUSION-Belgian State, TEC partner, Brussels 1000, Belgium"}]},{"given":"Luca","family":"Garzotti","sequence":"additional","affiliation":[{"name":"EUROfusion Programme Management Unit, JET, Culham Science Centre, Abingdon OX14 3DB, UK"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5158-7292","authenticated-orcid":false,"given":"Michela","family":"Gelfusa","sequence":"additional","affiliation":[{"name":"Associazione EUROfusion\u2014University of Rome \u201cTor Vergata\u201d, Via Orazio Raimondo, 18, 00173 Roma, Italy"}]},{"name":"JET Contributors","sequence":"additional","affiliation":[]}],"member":"1968","published-online":{"date-parts":[[2018,8,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Bossomaier, T., Barnett, T., Harr\u00e9, M., and Lizier, J.T. 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