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

P. Gatabazi, J. C. Mba, E. Pindza

Research output: Contribution to journalArticlepeer-review


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).

Original languageEnglish
Pages (from-to)327-341
Number of pages15
JournalDecisions in Economics and Finance
Issue number1
Publication statusPublished - Jun 2022
Externally publishedYes


  • Continuous time model
  • Discrete time model
  • Grey model
  • Malthus model
  • Mean absolute percentage error
  • Verhulst model

ASJC Scopus subject areas

  • Finance
  • Economics, Econometrics and Finance (all)


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