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In multivariate time series systems, it has been observed that certain groupsof variables partially lead the evolution of the system, while other variablesfollow this evolution with a time delay; the result is a lead-lag structureamongst the time series variables. In this paper, we propose a method for thedetection of lead-lag clusters of time series in multivariate systems. Wedemonstrate that the web of pairwise lead-lag relationships between time seriescan be helpfully construed as a directed network, for which there existsuitable algorithms for the detection of pairs of lead-lag clusters with highpairwise imbalance. Within our framework, we consider a number of choices forthe pairwise lead-lag metric and directed network clustering components. Ourframework is validated on both a synthetic generative model for multivariatelead-lag time series systems and daily real-world US equity prices data. Weshowcase that our method is able to detect statistically significant lead-lagclusters in the US equity market. We study the nature of these clusters in thecontext of the empirical finance literature on lead-lag relations anddemonstrate how these can be used for the construction of predictive financialsignals.

Lead-lag detection and network clustering for multivariate time series with an application to the US equity market