Exploring multifractality in African stock markets: A multifractal detrended fluctuation analysis approach

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This paper investigates the multifractal behavior of the six largest African stock markets, including the Johannesburg, Casablanca, Botswana, Nigerian, Egyptian, and Regional Stock Exchanges. Despite the growing significance of these markets in the global economy, there is limited understanding of their underlying dynamics, particularly regarding their multifractal properties. This lack of knowledge raises concerns about the informational efficiency of these markets, as traditional models may not adequately capture the complexities of price movements. To achieve the goals of the study, the Multifractal Detrended Fluctuation Analysis (MF-DFA) method is applied to capture the multifractal dynamics, and shuffling and phase randomization techniques are performed to identify the sources of the multifractality of the six African stock markets. The empirical results, derived from the generalized Hurst exponents, Rényi exponents, and Singularity spectrum, show that all six stock markets display multifractal behavior, characterized by irregular and complex price movements that vary across different scales and timeframes. Additionally, the study finds that both long-term correlations and heavy-tailed distributions contribute to the observed multifractality. Long-term correlations lead to persistent price trends, challenging the Efficient Market Hypothesis (EMH), while heavy tails increase market unpredictability by raising the likelihood of extreme events like crashes or booms. The findings have significant practical implications for stakeholders in African stock markets, enabling investors and portfolio managers to enhance risk assessment and develop effective trading strategies while helping market regulators improve efficiency and stability through appropriate policies. Financial institutions can also refine risk management frameworks to better account for extreme events.

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    • Figure 1. Graphs of the daily prices (1st column) and returns of the six indices (2nd column)
    • Figure 2. Plots of vs. for the six index returns
    • Figure 3. Plots of vs. for the six index returns
    • Figure 4. Degrees of multifractality based on the generalized Hurst exponent
    • Figure 5. Plots of vs. for the six index returns
    • Figure 6. Plots of vs. for the six index returns
    • Figure 7. Degrees of multifractality based on the singularity spectrum
    • Figure 8. Plots of vs. for the original, surrogate, and shuffled series
    • Figure 9. Plots of vs. for the original, surrogate and shuffled series
    • Table 1. Descriptive statistics of logarithmic returns for the six indices
    • Table 2. ADF test applied to daily prices and logarithmic returns of the six indices
    • Table 3. Degrees of multifractality based on the generalized Hurst exponent
    • Table 4. Degrees of multifractality based on the singularity spectrum
    • Table 5. Degrees of multifractality of original, surrogate and shuffled series based on the generalized Hurst exponent
    • Table 6. Degrees of multifractality of original, surrogate, and shuffled series based on the singularity spectrum
    • Conceptualization
      Benbachir Soufiane
    • Data curation
      Benbachir Soufiane
    • Formal Analysis
      Benbachir Soufiane
    • Investigation
      Benbachir Soufiane
    • Methodology
      Benbachir Soufiane
    • Project administration
      Benbachir Soufiane
    • Resources
      Benbachir Soufiane
    • Software
      Benbachir Soufiane
    • Supervision
      Benbachir Soufiane
    • Validation
      Benbachir Soufiane
    • Visualization
      Benbachir Soufiane
    • Writing – original draft
      Benbachir Soufiane
    • Writing – review & editing
      Benbachir Soufiane
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Investment Management and Financial Innovations
Investment Management and Financial Innovations