Spectral Analysis for Comparing Bitcoin to Currencies and Assets

Maria Chiara Pocelli, Manuel L. Esquível () and Nadezhda P. Krasii
Additional contact information
Maria Chiara Pocelli: Department of Mathematics, School of Industrial and Information Engineering, Politecnico di Milano, Piazza Leonardo da Vinci, 32, 20133 Milano, Italy
Manuel L. Esquível: Department of Mathematics, Centre for Mathematics and Applications, NOVA School of Science and Technology, Quinta da Torre, 2829-516 Caparica, Portugal
Nadezhda P. Krasii: Department of Higher Mathematics, Faculty of Informatics and Computer Engineering, Don State Technical University, 344003 Rostov-on-Don, Russia

Mathematics, 2023, vol. 11, issue 8, 1-21

Abstract: 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—against the Swiss Franc—of 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.

Keywords: ARMA modelling; distance between power spectral densities; simulation-based testing; state-backed currencies; gold; exchange rate; bitcoin (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/8/1775/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/8/1775/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:11:y:2023:i:8:p:1775-:d:1118608

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().