Multiscale topological analysis of cryptocurrency price series

We introduce multiscale topological analysis for studying cryptocurrency price series in the time domain. This is achieved by first performing a coarse-grained procedure on the volatility series at multiple temporal scales, and then constructing consecutive visibility graphs from the resulting coarse-grained series. We show that their degree distribution presents a likely power-law behavior. This scaling characteristics keeps invariant even varying time scale factor. Interestingly, we find that the number of cliques that capturing higher-order relations, presents a clear power-law behavior with the time scale factor. Their associated scaling exponent shows a monotonically decreasing pattern. Our work reveals the function of higher-order topological structure underlying cryptocurrency time series.