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 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之间结构关系的方法。利用滞后相关矩阵第一特征值的分布（Tracy-Widom分布）来检验变量间的结构性时间关系是否与备择假设（独立性）相悖。该分布研究滞后相关矩阵中最大特征值随滞后变化的渐近动态特性。通过分析不同滞后下$2\times 2$相关矩阵最大特征值的标准差时间序列，可量化偏离Tracy-Widom分布的程度，从而检验这两个时间变量间的结构关系。这种关系可与因果关系相关联。我们采用不同滞后下第一特征值的标准差作为代理指标，检验并监测结构性因果依赖关系。将该方法应用于零售经纪业务中日度货币流动的因果依赖分析，可有效控制流动性风险。