{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,16]],"date-time":"2026-03-16T00:54:25Z","timestamp":1773622465603,"version":"3.50.1"},"reference-count":33,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2019,7,22]],"date-time":"2019-07-22T00:00:00Z","timestamp":1563753600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001691","name":"Japan Society for the Promotion of Science","doi-asserted-by":"publisher","award":["JP18K11461"],"award-info":[{"award-number":["JP18K11461"]}],"id":[{"id":"10.13039\/501100001691","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We propose a method for generating surrogate data that preserves all the properties of ordinal patterns up to a certain length, such as the numbers of allowed\/forbidden ordinal patterns and transition likelihoods from ordinal patterns into others. The null hypothesis is that the details of the underlying dynamics do not matter beyond the refinements of ordinal patterns finer than a predefined length. The proposed surrogate data help construct a test of determinism that is free from the common linearity assumption for a null-hypothesis.<\/jats:p>","DOI":"10.3390\/e21070713","type":"journal-article","created":{"date-parts":[[2019,7,22]],"date-time":"2019-07-22T11:07:28Z","timestamp":1563793648000},"page":"713","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Surrogate Data Preserving All the Properties of Ordinal Patterns up to a Certain Length"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9245-2543","authenticated-orcid":false,"given":"Yoshito","family":"Hirata","sequence":"first","affiliation":[{"name":"Mathematics and Informatics Center, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan"},{"name":"Faculty of Engineering, Information and Systems, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573, Japan"}]},{"given":"Masanori","family":"Shiro","sequence":"additional","affiliation":[{"name":"Human Informatics Research Institute, National Institute of Advanced Industrial Science and Technology, Ibaraki 305-8568, Japan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1642-1171","authenticated-orcid":false,"given":"Jos\u00e9 M.","family":"Amig\u00f3","sequence":"additional","affiliation":[{"name":"Centro de Investigaci\u00f3n Operativa, Universidad Miguel Hern\u00e1ndez, Avda. de la Universidad s\/n, 03202 Elche, Spain"}]}],"member":"1968","published-online":{"date-parts":[[2019,7,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"635","DOI":"10.1103\/PhysRevLett.77.635","article-title":"Improved surrogate data for nonlinearity tests","volume":"77","author":"Schreiber","year":"1996","journal-title":"Phys. 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