Exploring weak-form efficiency in global Islamic stock markets: evidence from machine learning and wavelet analysis

Purpose This study aims to comprehensively assess the weak-form efficiency of nine major global Islamic stock indices by employing a combination of advanced machine learning, wavelet coherence (WTC), and Fourier-based econometric methods. The research seeks to reveal both the persistence of market efficiency and the dynamic nature of volatility–return relationships, especially during crisis periods. Design/methodology/approach The analysis uses daily data for nine Dow Jones Islamic stock indices across regions (2004–2025). We combine Fourier-ADF unit root tests, MLP-based ANN forecasting, random-walk benchmarks, Fourier Granger causality, and wavelet coherence to assess return predictability and volatility–return dynamics across time–frequency domains. The ANN is a one-hidden-layer MLP (20 ReLU neurons) with a linear output and Adam optimization, trained for 200 epochs (batch size 32). Data are split chronologically into training and test sets (75:25), with tuning within the training sample. Performance is evaluated using RMSE, MAE, and R2. Findings Overall, the results support weak-form efficiency across all indices: neither the econometric tests nor the machine learning models point to persistent abnormal returns. WTC results show that volatility-return linkages become stronger during major crisis periods (2008, 2020, 2022–23), but these effects fade and do not turn into stable predictive power. The ANN model does outperform the random-walk benchmark in out-of-sample forecast errors, and the Diebold-Mariano test confirms that this difference is statistically significant. Still, near-zero and often negative out-of-sample R2 values show that the improvement remains modest in predictive terms. Practical implications For market regulators and investors, the study emphasizes the importance of maintaining transparency, robust information flows, and effective risk management, particularly during periods of heightened market volatility. The dynamic approach can help policymakers design timely interventions and investors develop more informed, long-term strategies, reducing the risk of overreaction to short-lived market shocks. Originality/value To the best of our knowledge, this is the first study to combine machine learning and wavelet coherence analysis with Fourier-based causality and unit root tests to evaluate weak-form efficiency in a broad set of global Islamic stock markets. The interdisciplinary approach offers new empirical insights into the time-varying efficiency of Islamic financial markets and provides methodological innovations relevant to both academic research and market practice.