Batrancea Larissa M, Akgüller Ömer, Balcı Mehmet Ali, Altan Koç Dilara, Gaban Lucian
Department of Business, Babeş-Bolyai University, 7 Horea Street, 400174 Cluj-Napoca, Romania.
Faculty of Science, Deparment of Mathematics, Muğla Sıtkı Koçman University, 48000 Muğla, Turkey.
Entropy (Basel). 2025 May 26;27(6):560. doi: 10.3390/e27060560.
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.
本研究引入了一种新颖的方法，通过采用结合部分信息分解的卡普托分数阶费希尔信息框架来分析关键经济指标之间的动态相互作用。通过将分数阶导数整合到传统的费希尔信息度量中，我们的方法捕捉到了分别由利率（INTEREST）、信用违约互换（CDS）、波动率指数（VIX）、消费者物价指数（CPI）和生产者物价指数（PPI）所代表的货币政策、信用风险、市场波动和通货膨胀演变的长期记忆效应。我们使用滚动窗口估计进行全面的比较分析，以生成不同分数阶的卡普托分数阶费希尔信息值以及无记忆的普通费希尔信息值。随后的相关性、交叉相关性和转移熵分析揭示了历史依赖性如何影响指数之间独特的和协同的信息流。值得注意的是，我们的部分信息分解结果表明，深度历史交互显著放大了每个指标的信息贡献，特别是在长记忆条件下，而普通费希尔信息框架往往低估了这些协同效应。这些发现强调了将记忆效应纳入信息论模型以更好地理解金融指标之间复杂的、随时间变化的关系的重要性，这对预测和政策分析具有重要意义。
