标题： 映射危机驱动的市场动态：一种转移熵和克雷默-莫伊尔方法在金融网络中的应用 显示英文标题

标题： Mapping Crisis-Driven Market Dynamics: A Transfer Entropy and Kramers-Moyal Approach to Financial Networks

摘要： 金融市场是动态的、相互关联的系统，局部冲击可能引发广泛不稳定，这对投资组合经理和政策制定者构成挑战。 传统的相关性分析往往忽略了信息流动的方向性和时间动态性。 为了解决这个问题，我们提出一个统一的框架，将传递熵（TE）和N维Kramers-Moyal（KM）展开相结合，以映射四个主要指数之间的静态和时间分辨耦合：纳斯达克综合指数（^IXIC）、WTI原油（WTI）、黄金（GC=F）和美元指数（DX-Y.NYB）。 TE捕捉方向性信息流动。 KM模型非线性随机动力学，揭示了线性方法常被忽视的相互作用。 使用2014年8月11日至2024年9月8日的每日数据，我们计算收益率，通过导出滑动窗口TE和KM分析确认非平稳性。 我们发现，在新冠疫情（2020年3月至6月）和俄乌危机（2022年2月至4月）期间，平均TE分别增加了35%和28%，表明方向性流动增强。 漂移系数突显了黄金与美元之间的相互作用作为持续的避险渠道，而石油与股票的联系显示出制度转变，在压力下减弱并在快速反弹。 我们的结果暴露了线性度量的不足，并强调了结合信息理论和随机漂移方法的价值。 这种方法为适应性对冲提供了可操作的见解，并通过揭示系统性风险演变的架构，为宏观审慎政策提供了依据。 显示英文摘要

摘要： Financial markets are dynamic, interconnected systems where local shocks can trigger widespread instability, challenging portfolio managers and policymakers. Traditional correlation analysis often miss the directionality and temporal dynamics of information flow. To address this, we present a unified framework integrating Transfer Entropy (TE) and the N-dimensional Kramers-Moyal (KM) expansion to map static and time-resolved coupling among four major indices: Nasdaq Composite (^IXIC), WTI crude oil (WTI), gold (GC=F), and the US Dollar Index (DX-Y.NYB). TE captures directional information flow. KM models non-linear stochastic dynamics, revealing interactions often overlooked by linear methods. Using daily data from August 11, 2014, to September 8, 2024, we compute returns, confirm non-stationary using a conduct sliding-window TE and KM analyses. We find that during the COVID-19 pandemic (March-June 2020) and the Russia-Ukraine crisis (Feb-Apr 2022), average TE increases by 35% and 28%, respectively, indicating heightened directional flow. Drift coefficients highlight gold-dollar interactions as a persistent safe-haven channel, while oil-equity linkages show regime shifts, weakening under stress and rebounding quickly. Our results expose the shortcomings of linear measures and underscore the value of combining information-theoretic and stochastic drift methods. This approach offers actionable insights for adaptive hedging and informs macro-prudential policy by revealing the evolving architecture of systemic risk.