On methods to assess the significance of community structure in networks of financial time series

Abstract

We consider the problem of determining whether the community structure found by a clustering algorithm applied to financial time series is statistically significant, when no other information than the observed values and a similarity measure among time series is available. We propose two raw-data based methods for assessing robustness of clustering algorithms on time-dependent data linked by a relation of similarity: One based on community scoring functions that quantify some topological property that characterizes ground-truth communities, the other based on random perturbations and quantification of the variation in the community structure. These methodologies are well-established in the realm of unweighted networks; our contribution are versions adapted to complete weighted networks. We reinforce our assessment of the accuracy of the clustering algorithm by testing its performance on synthetic ground-truth communities of time series built through Monte Carlo simulations of VARMA processes.