Memory-Driven Dynamics: A Fractional Fisher Information Approach to Economic Interdependencies

This study introduces a novel approach for analyzing the dynamic interplay among key economic indicators by employing a Caputo Fractional Fisher Information framework combined with partial information decomposition. By integrating fractional derivatives into traditional Fisher Information metrics, our methodology captures long-range memory effects that govern the evolution of monetary policy, credit risk, market volatility, and inflation, represented by INTEREST, CDS, VIX, CPI, and PPI, respectively. We perform a comprehensive comparative analysis using rolling-window estimates to generate Caputo Fractional Fisher Information values at different fractional orders alongside the memoryless Ordinary Fisher Information. Subsequent correlation, cross-correlation, and transfer entropy analyses reveal how historical dependencies influence both unique and synergistic information flows between indices. Notably, our partial information decomposition results demonstrate that deep historical interactions significantly amplify the informational contribution of each indicator, particularly under long-memory conditions, while the Ordinary Fisher Information framework tends to underestimate these synergistic effects. The findings underscore the importance of incorporating memory effects into information-theoretic models to better understand the intricate, time-dependent relationships among financial indicators, with significant implications for forecasting and policy analysis.