IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i8p1775-d1118608.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/8/1775/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/8/1775/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Panagiotidis, Theodore & Stengos, Thanasis & Vravosinos, Orestis, 2018. "On the determinants of bitcoin returns: A LASSO approach," Finance Research Letters, Elsevier, vol. 27(C), pages 235-240.
    2. Nguyen, Linh Hoang & Chevapatrakul, Thanaset & Yao, Kai, 2020. "Investigating tail-risk dependence in the cryptocurrency markets: A LASSO quantile regression approach," Journal of Empirical Finance, Elsevier, vol. 58(C), pages 333-355.
    3. Corbet, Shaen & Meegan, Andrew & Larkin, Charles & Lucey, Brian & Yarovaya, Larisa, 2018. "Exploring the dynamic relationships between cryptocurrencies and other financial assets," Economics Letters, Elsevier, vol. 165(C), pages 28-34.
    4. Qiu, Yue & Wang, Zongrun & Xie, Tian & Zhang, Xinyu, 2021. "Forecasting Bitcoin realized volatility by exploiting measurement error under model uncertainty," Journal of Empirical Finance, Elsevier, vol. 62(C), pages 179-201.
    5. Tsang, Kwok Ping & Yang, Zichao, 2022. "Do connections pay off in the bitcoin market?," Journal of Empirical Finance, Elsevier, vol. 67(C), pages 1-18.
    6. Alexander Lipton, 2001. "Mathematical Methods for Foreign Exchange:A Financial Engineer's Approach," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 4694, February.
    7. Dyhrberg, Anne Haubo, 2016. "Bitcoin, gold and the dollar – A GARCH volatility analysis," Finance Research Letters, Elsevier, vol. 16(C), pages 85-92.
    8. Gronwald, Marc, 2019. "Is Bitcoin a Commodity? On price jumps, demand shocks, and certainty of supply," Journal of International Money and Finance, Elsevier, vol. 97(C), pages 86-92.
    9. Assaf, Ata & Mokni, Khaled & Yousaf, Imran & Bhandari, Avishek, 2023. "Long memory in the high frequency cryptocurrency markets using fractal connectivity analysis: The impact of COVID-19," Research in International Business and Finance, Elsevier, vol. 64(C).
    10. Cavicchioli, Maddalena, 2013. "Spectral density of Markov-switching VARMA models," Economics Letters, Elsevier, vol. 121(2), pages 218-220.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Pham, Son Duy & Nguyen, Thao Thac Thanh & Do, Hung Xuan, 2022. "Dynamic volatility connectedness between thermal coal futures and major cryptocurrencies: Evidence from China," Energy Economics, Elsevier, vol. 112(C).
    2. Aurelio F. Bariviera & Ignasi Merediz‐Solà, 2021. "Where Do We Stand In Cryptocurrencies Economic Research? A Survey Based On Hybrid Analysis," Journal of Economic Surveys, Wiley Blackwell, vol. 35(2), pages 377-407, April.
    3. Panagiotidis, Theodore & Papapanagiotou, Georgios & Stengos, Thanasis, 2024. "A Bayesian approach for the determinants of bitcoin returns," International Review of Financial Analysis, Elsevier, vol. 91(C).
    4. Flori, Andrea, 2019. "News and subjective beliefs: A Bayesian approach to Bitcoin investments," Research in International Business and Finance, Elsevier, vol. 50(C), pages 336-356.
    5. Kwon, Ji Ho, 2020. "Tail behavior of Bitcoin, the dollar, gold and the stock market index," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 67(C).
    6. Ciner, Cetin & Lucey, Brian & Yarovaya, Larisa, 2022. "Determinants of cryptocurrency returns: A LASSO quantile regression approach," Finance Research Letters, Elsevier, vol. 49(C).
    7. Sofiane Aboura, 2022. "A note on the Bitcoin and Fed Funds rate," Empirical Economics, Springer, vol. 63(5), pages 2577-2603, November.
    8. Panagiotidis, Theodore & Papapanagiotou, Georgios & Stengos, Thanasis, 2022. "On the volatility of cryptocurrencies," Research in International Business and Finance, Elsevier, vol. 62(C).
    9. Julián A. Parra & Carlos Arango - Joaquín Bernal & José E. Gómez - Javier Gómez & Carlos León - Clara Machado & Daniel Osorio - Daniel Rojas & Nicolás Suárez - Eduardo Yanquen, 2019. "Criptoactivos: análisis y revisión de literatura," Revista ESPE - Ensayos Sobre Política Económica, Banco de la República, issue 92, pages 1-37, November.
    10. Toan Luu Duc Huynh & Muhammad Shahbaz & Muhammad Ali Nasir & Subhan Ullah, 2022. "Financial modelling, risk management of energy instruments and the role of cryptocurrencies," Annals of Operations Research, Springer, vol. 313(1), pages 47-75, June.
    11. Adel Benhamed & Ahlem Selma Messai & Ghassen El Montasser, 2023. "On the Determinants of Bitcoin Returns and Volatility: What We Get from Gets?," Sustainability, MDPI, vol. 15(3), pages 1-21, January.
    12. Walther, Thomas & Klein, Tony & Bouri, Elie, 2019. "Exogenous drivers of Bitcoin and Cryptocurrency volatility – A mixed data sampling approach to forecasting," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 63(C).
    13. Ahmed, Walid M.A., 2022. "Robust drivers of Bitcoin price movements: An extreme bounds analysis," The North American Journal of Economics and Finance, Elsevier, vol. 62(C).
    14. Cagli, Efe Caglar, 2019. "Explosive behavior in the prices of Bitcoin and altcoins," Finance Research Letters, Elsevier, vol. 29(C), pages 398-403.
    15. Katsiampa, Paraskevi, 2019. "An empirical investigation of volatility dynamics in the cryptocurrency market," Research in International Business and Finance, Elsevier, vol. 50(C), pages 322-335.
    16. Yousaf, Imran & Pham, Linh & Goodell, John W., 2023. "Interconnectedness between healthcare tokens and healthcare stocks: Evidence from a quantile VAR approach," International Review of Economics & Finance, Elsevier, vol. 86(C), pages 271-283.
    17. Huynh, Toan Luu Duc & Hille, Erik & Nasir, Muhammad Ali, 2020. "Diversification in the age of the 4th industrial revolution: The role of artificial intelligence, green bonds and cryptocurrencies," Technological Forecasting and Social Change, Elsevier, vol. 159(C).
    18. Walther, Thomas & Klein, Tony & Bouri, Elie, 2018. "Exogenous Drivers of Bitcoin and Cryptocurrency Volatility – A Mixed Data Sampling Approach to Forecasting," QBS Working Paper Series 2018/02, Queen's University Belfast, Queen's Business School.
    19. Bedi, Prateek & Nashier, Tripti, 2020. "On the investment credentials of Bitcoin: A cross-currency perspective," Research in International Business and Finance, Elsevier, vol. 51(C).
    20. Syed Zwick, Hélène & Syed, Sarfaraz Ali Shah, 2019. "Bitcoin and gold prices: A fledging long-term relationship," MPRA Paper 92512, University Library of Munich, Germany.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:11:y:2023:i:8:p:1775-:d:1118608. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.