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<p>The aim of this study is to examine the fractal market hypothesis (FMH) using the multifractal detrended fluctuation analysis (MFDFA) method across cryptocurrency, commodity, foreign exchange, and stock markets. Bitcoin, Ethereum, crude oil, gold, EUR/USD, USD/JPY, S&amp;P 500, and BIST 100 were selected to represent these markets, with daily returns from January 1, 2018 to December 19, 2022. The findings reveal that all financial assets exhibit multifractality with Hurst exponents indicating that Bitcoin, Ethereum, oil, and BIST 100 possess long memory, whereas gold, EUR/USD, USD/JPY, and S&amp;P 500 display short memory. The results highlight inefficiencies in time series that deviate from a random walk, thereby validating the FMH. Multifractality is found to be low in the foreign exchange market and high in the cryptocurrency and commodity markets. In the stock market, S&amp;P 500 has low multifractality, while BIST 100 exhibits the highest degree of multifractality among all variables. The sources of multifractality are both long-range correlations and fat-tailed distributions. Hurst exponents change over time and fall significantly during periods of increased uncertainty. Time series graphs display self-similar patterns that repeat at different scales, suggesting that past returns can predict future returns. This suggests that past returns can be used to predict future returns, potentially allowing investors to beat the market and earn abnormal returns. This study contributes to the literature, particularly by addressing the gap in studies that test the FMH using the MFDFA method across multiple markets.</p>

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Testing the Fractal Market Hypothesis Using MFDFA Across Multiple Asset Classes

  • 期刊论文

  • 发表日期：

    2025年12月16日

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  • Faruk Temel,
  • Osman Tuğay

摘要

The aim of this study is to examine the fractal market hypothesis (FMH) using the multifractal detrended fluctuation analysis (MFDFA) method across cryptocurrency, commodity, foreign exchange, and stock markets. Bitcoin, Ethereum, crude oil, gold, EUR/USD, USD/JPY, S&P 500, and BIST 100 were selected to represent these markets, with daily returns from January 1, 2018 to December 19, 2022. The findings reveal that all financial assets exhibit multifractality with Hurst exponents indicating that Bitcoin, Ethereum, oil, and BIST 100 possess long memory, whereas gold, EUR/USD, USD/JPY, and S&P 500 display short memory. The results highlight inefficiencies in time series that deviate from a random walk, thereby validating the FMH. Multifractality is found to be low in the foreign exchange market and high in the cryptocurrency and commodity markets. In the stock market, S&P 500 has low multifractality, while BIST 100 exhibits the highest degree of multifractality among all variables. The sources of multifractality are both long-range correlations and fat-tailed distributions. Hurst exponents change over time and fall significantly during periods of increased uncertainty. Time series graphs display self-similar patterns that repeat at different scales, suggesting that past returns can predict future returns. This suggests that past returns can be used to predict future returns, potentially allowing investors to beat the market and earn abnormal returns. This study contributes to the literature, particularly by addressing the gap in studies that test the FMH using the MFDFA method across multiple markets.