  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.
