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Spectral Analysis for Comparing Bitcoin to Currencies and Assets

Author

Listed:
  • Maria Chiara Pocelli

    (Department of Mathematics, School of Industrial and Information Engineering, Politecnico di Milano, Piazza Leonardo da Vinci, 32, 20133 Milano, Italy
    These authors contributed equally to this work.)

  • Manuel L. Esquível

    (Department of Mathematics, Centre for Mathematics and Applications, NOVA School of Science and Technology, Quinta da Torre, 2829-516 Caparica, Portugal
    These authors contributed equally to this work.)

  • Nadezhda P. Krasii

    (Department of Higher Mathematics, Faculty of Informatics and Computer Engineering, Don State Technical University, 344003 Rostov-on-Don, Russia
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Maria Chiara Pocelli & Manuel L. Esquível & Nadezhda P. Krasii, 2023. "Spectral Analysis for Comparing Bitcoin to Currencies and Assets," Mathematics, MDPI, vol. 11(8), pages 1-21, April.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:8:p:1775-:d:1118608
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    References listed on IDEAS

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    Cited by:

    1. Francisco Germán Badía & María D. Berrade, 2023. "Special Issue “Probability Theory and Stochastic Modeling with Applications”," Mathematics, MDPI, vol. 11(14), pages 1-3, July.

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