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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.
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