Abstract

We develop spectral methods for clustering heterogeneous networks, in the setting of signed and directed networks, and demonstrate their benefits on networks arising from stochastic block models and financial multivariate time series data, where one is often interested in clustering assets that exhibit similar contemporaneous behaviour. Another task of interest is that of uncovering lead-lag relationships in high-dimensional multivariate time series. In such settings, certain groups of variables partially lead the evolution of the system, while other variables follow this evolution with a time delay, resulting in a lead-lag structure, which, at the pairwise level, can be encoded as edges of a directed network. Detecting clusters which exhibit a certain notion of pairwise flow imbalance amounts to identifying baskets of assets which lead-lag each other. We leverage graph clustering and ranking algorithms for the task of lead-lag detection in multivariate time series data, and demonstrate that our proposed methodology is able to detect statistically significant lead-lag clusters in the US equity market, and test their robustness on synthetically generated lagged multi-factor models. We study the composition of the uncovered lead-lag equity clusters, compare performance at different time frequencies and against established approaches from the lead-lag literature for portfolio construction.