  In multivariate time series systems, it has been observed that certain groups
of variables partially lead the evolution of the system, while other variables
follow this evolution with a time delay; the result is a lead-lag structure
amongst the time series variables. In this paper, we propose a method for the
detection of lead-lag clusters of time series in multivariate systems. We
demonstrate that the web of pairwise lead-lag relationships between time series
can be helpfully construed as a directed network, for which there exist
suitable algorithms for the detection of pairs of lead-lag clusters with high
pairwise imbalance. Within our framework, we consider a number of choices for
the pairwise lead-lag metric and directed network clustering components. Our
framework is validated on both a synthetic generative model for multivariate
lead-lag time series systems and daily real-world US equity prices data. We
showcase that our method is able to detect statistically significant lead-lag
clusters in the US equity market. We study the nature of these clusters in the
context of the empirical finance literature on lead-lag relations and
demonstrate how these can be used for the construction of predictive financial
signals.
