{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,15]],"date-time":"2025-10-15T18:12:35Z","timestamp":1760551955507,"version":"build-2065373602"},"reference-count":34,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2023,4,7]],"date-time":"2023-04-07T00:00:00Z","timestamp":1680825600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"project of the Centro de Matem\u00e1tica e Aplica\u00e7\u00f5es","award":["UID\/MAT\/00297\/2020"],"award-info":[{"award-number":["UID\/MAT\/00297\/2020"]}]},{"name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia (Portuguese Foundation for Science and Technology)","award":["UID\/MAT\/00297\/2020"],"award-info":[{"award-number":["UID\/MAT\/00297\/2020"]}]},{"name":"Fidelidade-Companhia de Seguras, S.A.","award":["UID\/MAT\/00297\/2020"],"award-info":[{"award-number":["UID\/MAT\/00297\/2020"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematics"],"abstract":"<jats:p>We present an analysis on variability Bitcoin characteristics that help to quantitatively differentiate Bitcoin from the state-owned traditional currencies and the asset Gold. We provide a detailed study on returns of exchange rates\u2014against the Swiss Franc\u2014of several traditional currencies together with Bitcoin and Gold; for that purpose, we define a distance between currencies by means of the spectral densities of the ARMA models of the returns of the exchange rates, and we present the computed matrix of the distances between the chosen currencies. A statistical analysis of these matrix distances is further proposed, which shows that the distance between Bitcoin and any other currency or Gold is not comparable to any of the distances between currencies or between currencies and Gold and not involving Bitcoin. This result shows that Bitcoin is essentially different from the traditional currencies and from Gold, at least in what concerns the structure of its variance and auto-covariances.<\/jats:p>","DOI":"10.3390\/math11081775","type":"journal-article","created":{"date-parts":[[2023,4,10]],"date-time":"2023-04-10T03:19:54Z","timestamp":1681096794000},"page":"1775","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Spectral Analysis for Comparing Bitcoin to Currencies and Assets"],"prefix":"10.3390","volume":"11","author":[{"given":"Maria Chiara","family":"Pocelli","sequence":"first","affiliation":[{"name":"Department of Mathematics, School of Industrial and Information Engineering, Politecnico di Milano, Piazza Leonardo da Vinci, 32, 20133 Milano, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4991-7568","authenticated-orcid":false,"given":"Manuel L.","family":"Esqu\u00edvel","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Centre for Mathematics and Applications, NOVA School of Science and Technology, Quinta da Torre, 2829-516 Caparica, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4226-1658","authenticated-orcid":false,"given":"Nadezhda P.","family":"Krasii","sequence":"additional","affiliation":[{"name":"Department of Higher Mathematics, Faculty of Informatics and Computer Engineering, Don State Technical University, 344003 Rostov-on-Don, Russia"}]}],"member":"1968","published-online":{"date-parts":[[2023,4,7]]},"reference":[{"key":"ref_1","unstructured":"von Mises, L. 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