IDEAS home Printed from https://ideas.repec.org/a/spr/decfin/v45y2022i1d10.1007_s10203-022-00368-9.html
   My bibliography  Save this article

Grey Verhulst model and its chaotic behaviour with application to Bitcoin adoption

Author

Listed:
  • P. Gatabazi

    (University of Johannesburg
    University of Rwanda)

  • J. C. Mba

    (University of Johannesburg)

  • E. Pindza

    (Tshwane University of Technology
    University of Pretoria)

Abstract

The study applies the grey model (GM(1,1)) to the Verhulst differential equation for forecasting the Bitcoin transaction counts. The grey Verhulst model (GVM) is based on the data set of Bitcoin as recorded along 10 years from the 1st August 2010. The model accuracy is checked by the mean absolute percentage error (MAPE), while the model predictability is assessed by analysing a plot of the Verhulst model constructed upon the parameters provided by the GVM. The MAPE criterion suggests the reasonable accuracy of the overall GVM forecasting values and high accuracy by considering the last 400 forecasting values. Furthermore, the Verhulst model plot suggests that the GVM is potential on predictability as the plot is not chaotic. The GVM forecasting values suggest a slight future decline in transacting Bitcoin; this may be due to its competition with the other emerging cryptocurrencies. The GVM suggests a relatively high performance as compared to the usual one-variable forecasting model GM(1,1).

Suggested Citation

  • P. Gatabazi & J. C. Mba & E. Pindza, 2022. "Grey Verhulst model and its chaotic behaviour with application to Bitcoin adoption," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 45(1), pages 327-341, June.
    • Handle: RePEc:spr:decfin:v:45:y:2022:i:1:d:10.1007_s10203-022-00368-9
    DOI: 10.1007/s10203-022-00368-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10203-022-00368-9
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10203-022-00368-9?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Joshua R. Hendrickson & Thomas L. Hogan & William J. Luther, 2016. "The Political Economy Of Bitcoin," Economic Inquiry, Western Economic Association International, vol. 54(2), pages 925-939, April.
    2. Urquhart, Andrew, 2016. "The inefficiency of Bitcoin," Economics Letters, Elsevier, vol. 148(C), pages 80-82.
    3. Adrian Blundell-Wignall, 2014. "The Bitcoin Question: Currency versus Trust-less Transfer Technology," OECD Working Papers on Finance, Insurance and Private Pensions 37, OECD Publishing.
    4. Gatabazi, P. & Mba, J.C. & Pindza, E., 2019. "Modeling cryptocurrencies transaction counts using variable-order Fractional Grey Lotka-Volterra dynamical system," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 283-290.
    Full references (including those not matched with items on IDEAS)

    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. Gatabazi, P. & Mba, J.C. & Pindza, E. & Labuschagne, C., 2019. "Grey Lotka–Volterra models with application to cryptocurrencies adoption," Chaos, Solitons & Fractals, Elsevier, vol. 122(C), pages 47-57.
    2. Gatabazi, P. & Mba, J.C. & Pindza, E., 2019. "Modeling cryptocurrencies transaction counts using variable-order Fractional Grey Lotka-Volterra dynamical system," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 283-290.
    3. Paul Gatabazi & Gaëtan Kabera & Jules Clement Mba & Edson Pindza & Sileshi Fanta Melesse, 2022. "Cryptocurrencies and Tokens Lifetime Analysis from 2009 to 2021," Economies, MDPI, vol. 10(3), pages 1-14, March.
    4. Christie Smith & Aaron Kumar, 2018. "Crypto‐Currencies – An Introduction To Not‐So‐Funny Moneys," Journal of Economic Surveys, Wiley Blackwell, vol. 32(5), pages 1531-1559, December.
    5. Parthajit Kayal & Purnima Rohilla, 2021. "Bitcoin in the economics and finance literature: a survey," SN Business & Economics, Springer, vol. 1(7), pages 1-21, July.
    6. 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.
    7. Zhou, Siwen, 2018. "Exploring the Driving Forces of the Bitcoin Exchange Rate Dynamics: An EGARCH Approach," MPRA Paper 89445, University Library of Munich, Germany.
    8. Lennart Ante, 2020. "A place next to Satoshi: foundations of blockchain and cryptocurrency research in business and economics," Scientometrics, Springer;Akadémiai Kiadó, vol. 124(2), pages 1305-1333, August.
    9. Jalan, Akanksha & Matkovskyy, Roman & Urquhart, Andrew & Yarovaya, Larisa, 2023. "The role of interpersonal trust in cryptocurrency adoption," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 83(C).
    10. de la Horra, Luis P. & de la Fuente, Gabriel & Perote, Javier, 2019. "The drivers of Bitcoin demand: A short and long-run analysis," International Review of Financial Analysis, Elsevier, vol. 62(C), pages 21-34.
    11. Parthajit Kayal & G. Balasubramanian, 2021. "Excess Volatility in Bitcoin: Extreme Value Volatility Estimation," IIM Kozhikode Society & Management Review, , vol. 10(2), pages 222-231, July.
    12. Al Mamun, Md & Uddin, Gazi Salah & Suleman, Muhammad Tahir & Kang, Sang Hoon, 2020. "Geopolitical risk, uncertainty and Bitcoin investment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    13. Gina Christelle Pieters, 2017. "Bitcoin Reveals Exchange Rate Manipulation and Detects Capital Controls," 2017 Papers ppi307, Job Market Papers.
    14. Afees A. Salisu & Aviral Kumar Tiwari & Ibrahim D. Raheem, 2018. "Analysing the distribution properties of Bitcoin returns," Working Papers 058, Centre for Econometric and Allied Research, University of Ibadan.
    15. Bildirici, Melike E. & Sonustun, Bahri, 2021. "Chaotic behavior in gold, silver, copper and bitcoin prices," Resources Policy, Elsevier, vol. 74(C).
    16. Ata Assaf & Luis Alberiko Gil-Alana & Khaled Mokni, 2022. "True or spurious long memory in the cryptocurrency markets: evidence from a multivariate test and other Whittle estimation methods," Empirical Economics, Springer, vol. 63(3), pages 1543-1570, September.
    17. Kakinaka, Shinji & Umeno, Ken, 2021. "Exploring asymmetric multifractal cross-correlations of price–volatility and asymmetric volatility dynamics in cryptocurrency markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 581(C).
    18. Corbet, Shaen & Cumming, Douglas J. & Lucey, Brian M. & Peat, Maurice & Vigne, Samuel A., 2020. "The destabilising effects of cryptocurrency cybercriminality," Economics Letters, Elsevier, vol. 191(C).
    19. White, Reilly & Marinakis, Yorgos & Islam, Nazrul & Walsh, Steven, 2020. "Is Bitcoin a currency, a technology-based product, or something else?," Technological Forecasting and Social Change, Elsevier, vol. 151(C).
    20. Jiang, Yonghong & Nie, He & Ruan, Weihua, 2018. "Time-varying long-term memory in Bitcoin market," Finance Research Letters, Elsevier, vol. 25(C), pages 280-284.

    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:spr:decfin:v:45:y:2022:i:1:d:10.1007_s10203-022-00368-9. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.