{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,22]],"date-time":"2026-01-22T22:20:19Z","timestamp":1769120419591,"version":"3.49.0"},"reference-count":60,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2022,7,21]],"date-time":"2022-07-21T00:00:00Z","timestamp":1658361600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Future Internet"],"abstract":"<jats:p>Unlike price fluctuations, the temporal structure of cryptocurrency trading has seldom been a subject of systematic study. In order to fill this gap, we analyse detrended correlations of the price returns, the average number of trades in time unit, and the traded volume based on high-frequency data representing two major cryptocurrencies: bitcoin and ether. We apply the multifractal detrended cross-correlation analysis, which is considered the most reliable method for identifying nonlinear correlations in time series. We find that all the quantities considered in our study show an unambiguous multifractal structure from both the univariate (auto-correlation) and bivariate (cross-correlation) perspectives. We looked at the bitcoin\u2013ether cross-correlations in simultaneously recorded signals, as well as in time-lagged signals, in which a time series for one of the cryptocurrencies is shifted with respect to the other. Such a shift suppresses the cross-correlations partially for short time scales, but does not remove them completely. We did not observe any qualitative asymmetry in the results for the two choices of a leading asset. The cross-correlations for the simultaneous and lagged time series became the same in magnitude for the sufficiently long scales.<\/jats:p>","DOI":"10.3390\/fi14070215","type":"journal-article","created":{"date-parts":[[2022,7,21]],"date-time":"2022-07-21T10:36:56Z","timestamp":1658399816000},"page":"215","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":28,"title":["Multifractal Cross-Correlations of Bitcoin and Ether Trading Characteristics in the Post-COVID-19 Time"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2131-7440","authenticated-orcid":false,"given":"Marcin","family":"W\u0105torek","sequence":"first","affiliation":[{"name":"Faculty of Computer Science and Telecommunications, Cracow University of Technology, ul. Warszawska 24, 31-155 Krak\u00f3w, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8813-9637","authenticated-orcid":false,"given":"Jaros\u0142aw","family":"Kwapie\u0144","sequence":"additional","affiliation":[{"name":"Complex Systems Theory Department, Institute of Nuclear Physics, Polish Academy of Sciences, Radzikowskiego 152, 31-342 Krak\u00f3w, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1613-6175","authenticated-orcid":false,"given":"Stanis\u0142aw","family":"Dro\u017cd\u017c","sequence":"additional","affiliation":[{"name":"Faculty of Computer Science and Telecommunications, Cracow University of Technology, ul. Warszawska 24, 31-155 Krak\u00f3w, Poland"},{"name":"Complex Systems Theory Department, Institute of Nuclear Physics, Polish Academy of Sciences, Radzikowskiego 152, 31-342 Krak\u00f3w, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,7,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"180643","DOI":"10.1098\/rsos.180643","article-title":"Dissection of Bitcoin\u2019s multiscale bubble history from January 2012 to February 2018","volume":"6","author":"Gerlach","year":"2019","journal-title":"R. Soc. Open Sci."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.physrep.2020.07.005","article-title":"COVID-19 and SARS-CoV-2. Modeling the present, looking at the future","volume":"869","author":"Estrada","year":"2020","journal-title":"Phys. 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