{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T14:31:19Z","timestamp":1762353079724,"version":"build-2065373602"},"reference-count":51,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2021,7,27]],"date-time":"2021-07-27T00:00:00Z","timestamp":1627344000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100011033","name":"Agencia Estatal de Investigaci\u00f3n","doi-asserted-by":"publisher","award":["PID2019-109094GB-C22"],"award-info":[{"award-number":["PID2019-109094GB-C22"]}],"id":[{"id":"10.13039\/501100011033","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Time-delayed interactions naturally appear in a multitude of real-world systems due to the finite propagation speed of physical quantities. Often, the time scales of the interactions are unknown to an external observer and need to be inferred from time series of observed data. We explore, in this work, the properties of several ordinal-based quantifiers for the identification of time-delays from time series. To that end, we generate artificial time series of stochastic and deterministic time-delay models. We find that the presence of a nonlinearity in the generating model has consequences for the distribution of ordinal patterns and, consequently, on the delay-identification qualities of the quantifiers. Here, we put forward a novel ordinal-based quantifier that is particularly sensitive to nonlinearities in the generating model and compare it with previously-defined quantifiers. We conclude from our analysis on artificially generated data that the proper identification of the presence of a time-delay and its precise value from time series benefits from the complementary use of ordinal-based quantifiers and the standard autocorrelation function. We further validate these tools with a practical example on real-world data originating from the North Atlantic Oscillation weather phenomenon.<\/jats:p>","DOI":"10.3390\/e23080969","type":"journal-article","created":{"date-parts":[[2021,7,27]],"date-time":"2021-07-27T22:35:02Z","timestamp":1627425302000},"page":"969","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Time-Delay Identification Using Multiscale Ordinal Quantifiers"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6140-8451","authenticated-orcid":false,"given":"Miguel C.","family":"Soriano","sequence":"first","affiliation":[{"name":"Instituto de F\u00edsica Interdisciplinar y Sistemas Complejos (IFISC, UIB-CSIC), Campus Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2852-3263","authenticated-orcid":false,"given":"Luciano","family":"Zunino","sequence":"additional","affiliation":[{"name":"Centro de Investigaciones \u00d3pticas (CONICET La Plata-CIC), C.C. 3, 1897 Gonnet, Argentina"},{"name":"Departamento de Ciencias B\u00e1sicas, Facultad de Ingenier\u00eda, Universidad Nacional de La Plata (UNLP), 1900 La Plata, Argentina"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,7,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Erneux, T. 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