This paper presents a method to identify causal interactions between two time series. The largest eigenvalue follows a Tracy-Widom distribution, derived from a Coulomb gas model. This defines causal interactions as the pushing and pulling of the gas, measurable by the variability of the largest eigenvalue's explanatory power. The hypothesis that this setup applies to time series interactions was validated, with causality inferred from time lags. The standard deviation of the largest eigenvalue's explanatory power in lagged correlation matrices indicated the probability of causal interaction between time series. Contrasting with traditional methods that rely on forecasting or window-based parametric controls, this approach offers a novel definition of causality based on dynamic monitoring of tail events. Experimental validation with controlled trials and historical data shows that this method outperforms Granger's causality test in detecting structural changes in time series. Applications to stock returns and financial market data show the indicator's predictive capabilities regarding average stock return and realized volatility. Further validation with brokerage data confirms its effectiveness in inferring causal relationships in liquidity flows, highlighting its potential for market and liquidity risk management.

翻译：本文提出了一种识别两个时间序列间因果交互作用的方法。最大特征值遵循由库仑气体模型导出的Tracy-Widom分布。该方法将因果交互定义为气体的推拉作用，可通过最大特征值解释力的变异性进行测量。验证了该框架适用于时间序列交互的假设，并通过时间滞后推断因果关系。滞后相关矩阵中最大特征值解释力的标准差指示了时间序列间因果交互的概率。与传统依赖预测或基于窗口参数控制的方法不同，该方法基于尾部事件的动态监测提出了新颖的因果定义。通过控制试验和历史数据的实验验证表明，该方法在检测时间序列结构变化方面优于Granger因果检验。应用于股票收益率和金融市场数据时，该指示器显示出对平均股票收益率和已实现波动率的预测能力。基于经纪商数据的进一步验证证实了其在推断流动性流动中因果关系的有效性，凸显了其在市场与流动性风险管理中的应用潜力。