A Systematic Review of Innovative Financial Modeling for Weak-Form Market Efficiency Testing: From Classical Econometrics to AI-Driven Hybrid Frameworks

This systematic review investigates the development of testing procedures for weak-form market efficiency under the Efficient Market Hypothesis (EMH) from 2000 to 2025. We organize the literature into three categories of approaches: traditional linear statistical tests (e.g., Variance Ratio, runs and unit root tests), nonlinear and fractal methods (e.g., multifractal detrended fluctuation analysis, wavelet transforms, entropy measures), and emerging hybrid techniques incorporating artificial intelligence (AI). Using PRISMA guidelines, we identified 72 peer-reviewed empirical studies through Scopus, Web of Science, JSTOR, and Google Scholar. Over the past two decades, research on weak-form efficiency has shifted from simple linear tests to more complex nonlinear and AI-based frameworks, reflecting the growing complexity of financial markets amid volatility, crises, and technological disruptions. Fractal and entropy-based models have uncovered long-memory effects and market anomalies with greater robustness, while AI methods have improved predictive power at the cost of interpretability. Persistent weaknesses remain, including inadequate handling of structural breaks and limited analysis of specialized contexts such as Islamic finance and Environmental, Social, and Governance (ESG) investing. Our findings highlight the need for integrated models that combine statistical rigor with interpretability and adaptability to modern market dynamics