{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,14]],"date-time":"2026-04-14T22:40:47Z","timestamp":1776206447510,"version":"3.50.1"},"reference-count":80,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2020,4,16]],"date-time":"2020-04-16T00:00:00Z","timestamp":1586995200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Open Access Publikationsfonds","award":["20200310"],"award-info":[{"award-number":["20200310"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>This paper develops the generalized causality algorithm and applies it to a multitude of data from the fields of economics and finance. Specifically, our parameter-free algorithm efficiently determines the optimal non-linear mapping and identifies varying lead\u2013lag effects between two given time series. This procedure allows an elastic adjustment of the time axis to find similar but phase-shifted sequences\u2014structural breaks in their relationship are also captured. A large-scale simulation study validates the outperformance in the vast majority of parameter constellations in terms of efficiency, robustness, and feasibility. Finally, the presented methodology is applied to real data from the areas of macroeconomics, finance, and metal. Highest similarity show the pairs of gross domestic product and consumer price index (macroeconomics), S&amp;P 500 index and Deutscher Aktienindex (finance), as well as gold and silver (metal). In addition, the algorithm takes full use of its flexibility and identifies both various structural breaks and regime patterns over time, which are (partly) well documented in the literature.<\/jats:p>","DOI":"10.3390\/a13040095","type":"journal-article","created":{"date-parts":[[2020,4,16]],"date-time":"2020-04-16T13:01:39Z","timestamp":1587042099000},"page":"95","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["How to Identify Varying Lead\u2013Lag Effects in Time Series Data: Implementation, Validation, and Application of the Generalized Causality Algorithm"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8643-2768","authenticated-orcid":false,"given":"Johannes","family":"St\u00fcbinger","sequence":"first","affiliation":[{"name":"Department of Statistics and Econometrics, University of Erlangen-N\u00fcrnberg, Lange Gasse 20, 90403 N\u00fcrnberg, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Katharina","family":"Adler","sequence":"additional","affiliation":[{"name":"Department of Statistics and Econometrics, University of Erlangen-N\u00fcrnberg, Lange Gasse 20, 90403 N\u00fcrnberg, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,4,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"359","DOI":"10.1006\/enfo.2001.0061","article-title":"Detecting trends using Spearman\u2019s rank correlation coefficient","volume":"2","author":"Gauthier","year":"2001","journal-title":"Environ. 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