We present a method to test and monitor structural relationships between time variables. The distribution of the first eigenvalue for lagged correlation matrices (Tracy-Widom distribution) is used to test structural time relationships between variables against the alternative hypothesis (Independence). This distribution studies the asymptotic dynamics of the largest eigenvalue as a function of the lag in lagged correlation matrices. By analyzing the time series of the standard deviation of the greatest eigenvalue for $2\times 2$ correlation matrices with different lags we can analyze deviations from the Tracy-Widom distribution to test structural relationships between these two time variables. These relationships can be related to causality. We use the standard deviation of the explanatory power of the first eigenvalue at different lags as a proxy for testing and monitoring structural causal relationships. The method is applied to analyse causal dependencies between daily monetary flows in a retail brokerage business allowing to control for liquidity risks.

翻译：我们提出了一种检验和监测时间变量间结构关系的方法。利用滞后相关矩阵第一特征值的分布（Tracy-Widom分布），在备择假设（独立性）下检验变量间的结构性时间关系。该分布研究了滞后相关矩阵中最大特征值随滞后变化的渐近动态特征。通过分析不同滞后条件下$2\times 2$相关矩阵最大特征值标准差的时间序列，我们能够检测与Tracy-Widom分布的偏离，从而检验这两个时间变量间的结构关系。这些关系可关联至因果关系。我们采用不同滞后条件下第一特征值解释力的标准差作为代理指标，用于检验和监测结构性因果关系。该方法被应用于分析零售经纪业务中每日货币流动的因果依赖关系，从而实现对流动性风险的有效管控。