Signature-Based Community Detection for Time Series

Abstract: Community detection for time series without prior knowledge poses an open challenge within complex networks theory. Traditional approaches begin by assessing time series correlations and maximizing modularity under diverse null models. These methods suffer from assuming temporal stationarity and are influenced by the granularity of observation intervals. In this study, we propose an approach based on the signature matrix, a concept from path theory for studying stochastic processes. By employing a signature-derived similarity measure, our method overcomes drawbacks of traditional correlation-based techniques. Through a series of numerical experiments, we demonstrate that our method consistently yields higher modularity compared to baseline models, when tested on the Standard and Poor's 500 dataset. Moreover, our approach showcases enhanced stability in modularity when the length of the underlying time series is manipulated. This research contributes to the field of community detection by introducing a signature-based similarity measure, offering an alternative to conventional correlation matrices.