{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T04:23:20Z","timestamp":1772252600362,"version":"3.50.1"},"reference-count":190,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2021,8,29]],"date-time":"2021-08-29T00:00:00Z","timestamp":1630195200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004504","name":"Research Council of Lithuania","doi-asserted-by":"publisher","award":["09.3.3-LMT-K-712-19-0017"],"award-info":[{"award-number":["09.3.3-LMT-K-712-19-0017"]}],"id":[{"id":"10.13039\/501100004504","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In the face of the upcoming 30th anniversary of econophysics, we review our contributions and other related works on the modeling of the long-range memory phenomenon in physical, economic, and other social complex systems. Our group has shown that the long-range memory phenomenon can be reproduced using various Markov processes, such as point processes, stochastic differential equations, and agent-based models\u2014reproduced well enough to match other statistical properties of the financial markets, such as return and trading activity distributions and first-passage time distributions. Research has lead us to question whether the observed long-range memory is a result of the actual long-range memory process or just a consequence of the non-linearity of Markov processes. As our most recent result, we discuss the long-range memory of the order flow data in the financial markets and other social systems from the perspective of the fractional L\u00e8vy stable motion. We test widely used long-range memory estimators on discrete fractional L\u00e8vy stable motion represented by the auto-regressive fractionally integrated moving average (ARFIMA) sample series. Our newly obtained results seem to indicate that new estimators of self-similarity and long-range memory for analyzing systems with non-Gaussian distributions have to be developed.<\/jats:p>","DOI":"10.3390\/e23091125","type":"journal-article","created":{"date-parts":[[2021,8,29]],"date-time":"2021-08-29T21:45:16Z","timestamp":1630273516000},"page":"1125","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Understanding the Nature of the Long-Range Memory Phenomenon in Socioeconomic Systems"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0672-2288","authenticated-orcid":false,"given":"Rytis","family":"Kazakevi\u010dius","sequence":"first","affiliation":[{"name":"Institute of Theoretical Physics and Astronomy, Vilnius University, Sauletekio al. 3, 10257 Vilnius, Lithuania"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6365-0252","authenticated-orcid":false,"given":"Aleksejus","family":"Kononovicius","sequence":"additional","affiliation":[{"name":"Institute of Theoretical Physics and Astronomy, Vilnius University, Sauletekio al. 3, 10257 Vilnius, Lithuania"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3988-8599","authenticated-orcid":false,"given":"Bronislovas","family":"Kaulakys","sequence":"additional","affiliation":[{"name":"Institute of Theoretical Physics and Astronomy, Vilnius University, Sauletekio al. 3, 10257 Vilnius, Lithuania"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1859-1318","authenticated-orcid":false,"given":"Vygintas","family":"Gontis","sequence":"additional","affiliation":[{"name":"Institute of Theoretical Physics and Astronomy, Vilnius University, Sauletekio al. 3, 10257 Vilnius, Lithuania"}]}],"member":"1968","published-online":{"date-parts":[[2021,8,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"422","DOI":"10.1137\/1010093","article-title":"Fractional Brownian motions, fractional noises and applications","volume":"10","author":"Mandelbrot","year":"1968","journal-title":"SIAM Rev."},{"key":"ref_2","first-page":"103","article-title":"Flicker noises in astronomy and elsewhere","volume":"7","author":"Press","year":"1978","journal-title":"Comments Astrophys."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"497","DOI":"10.1103\/RevModPhys.53.497","article-title":"Low-frequency fluctuations in solids: 1\/f noise","volume":"53","author":"Dutta","year":"1981","journal-title":"Rev. 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