Fractional Transfer Entropy Networks: Short- and Long-Memory Perspectives on Global Stock Market Interactions

This study addresses the challenge of capturing both short-run volatility and long-run dependencies in global stock markets by introducing fractional transfer entropy (FTE), a new framework that embeds fractional calculus into transfer entropy. FTE allows analysts to tune memory parameters and thus observe how different temporal emphases reshape the network of directional information flows among major financial indices. Empirical evidence reveals that when short-memory effects dominate, markets swiftly incorporate recent news, creating networks that adapt quickly but remain vulnerable to transient shocks. In contrast, balanced memory parameters yield a more stable equilibrium, blending immediate reactions with persistent structural ties. Under long-memory configurations, historically entrenched relationships prevail, enabling established market leaders to remain central despite ongoing fluctuations. These findings demonstrate that FTE uncovers nuanced dynamics overlooked by methods focusing solely on either current events or deep-rooted patterns. Although the method relies on price returns and does not differentiate specific shock types, it offers a versatile tool for investors, policymakers, and researchers to gauge financial stability, evaluate contagion risk, and better understand how ephemeral signals and historical legacies jointly govern global market connectivity.