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

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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).

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Data availability

The data sets analysed in the current study are available from anyone of the authors on request.

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Acknowledgements

We thank Josiane M. Gatabazi for proofreading and editing the text. The research was supported by the University of Johannesburg via the Global Excellence and Stature Fellowship.

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Authors and Affiliations

  1. Department of Mathematics and Applied Mathematics, University of Johannesburg, P.O. Box 524, Auckland Park, 2006, South Africa

    P. Gatabazi

  2. Department of Applied Statistics, School of Economics, College of Business and Economics, University of Rwanda, P.O. Box 124, Huye, Rwanda

    P. Gatabazi

  3. School of Economics, College of Business and Economics, University of Johannesburg, P.O. Box 524, Auckland Park, 2006, Johannesburg, South Africa

    J. C. Mba

  4. Department of Mathematics and Statistics, Tshwane University of Technology, 175 Nelson Mandela Drive OR Private Bag X680, Pretoria, 0001, South Africa

    E. Pindza

  5. Department of Mathematics and Applied Mathematics, University of Pretoria, Lynnwood Rd, Hatfield, Pretoria, 0002, South Africa

    E. Pindza

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  1. P. Gatabazi
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  2. J. C. Mba
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Correspondence to P. Gatabazi.

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Gatabazi, P., Mba, J.C. & Pindza, E. Grey Verhulst model and its chaotic behaviour with application to Bitcoin adoption. Decisions Econ Finan 45, 327–341 (2022). https://doi.org/10.1007/s10203-022-00368-9

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  • DOI: https://doi.org/10.1007/s10203-022-00368-9

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