Dynamic market efficiency assessment in sustainability indices: Rolling fractional integration analysis with multiple estimators

This study develops a comprehensive econometric framework for assessing market efficiency in sustainability indices through rolling fractional integration analysis. We employ four fractional integration estimators (Andrews-Guggenberger, Robinson GSE, GPH, and FELW) with formal statistical testing, addressing critical methodological gaps including single estimator dependency and static analysis approaches. Applied to 17 sustainability indices across 13 countries, our results reveal significant heterogeneity in market efficiency evolution. Developed markets exhibit timevarying efficiency patterns with periodic inefficiencies driven by institutional rebalancing dynamics, while emerging markets demonstrate superior efficiency characteristics. The Turkey BIST Sustainability Index exhibits exceptional efficiency, while the SP 500 ESG Screened Index shows the highest inefficiency levels among developed markets. The convergent validity between fractional integration and traditional unit root tests provides robust methodological validation. Our findings establish unprecedented robustness in sustainability market efficiency research while providing policy implications for financial regulators and investment managers. • Develops first comprehensive rolling fractional integration framework with multiple estimators and formal statistical testing for sustainability indices. • Analyzes 17 sustainability indices across 13 countries revealing significant heterogeneity in efficiency evolution between developed and emerging markets. • Documents superior efficiency in emerging markets (Turkey BIST) compared to developed markets (S&P 500 ESG) challenging conventional market development assumptions. • Establishes convergent validity between fractional integration and traditional unit root tests providing unprecedented robustness in efficiency conclusions. • Demonstrates superior performance of asymmetric AESTAR models in capturing institutional investment patterns characteristic of ESG markets. • Provides dynamic policy implications for financial regulators and actionable insights for ESG investment strategy optimization.