Multiscale topological analysis of virtual currency price series

Abstract

We investigate multiscale topological characteristics of virtual currency series. By applying detrended fluctuation analysis, we find that for the virtual currency series of interest, they present almost identical long-range correlation behavior. Moreover, we map these time series into complex networks via visibility graph technique. We then construct consecutive graphs from these resultant networks by using the coarse-grained method. Instead of observing low-order interactions, we focus on examine high-order correlations in terms of algebraic topological statistics. Interestingly, we find that the number of a specific order of clique in the renormalized networks exhibits a clearly scaling behavior. Meanwhile, their growth patterns are almost similar for these seemingly different virtual currency series. Our work, for the first time, reveals the role of cliques in shaping topological structures of virtual currency series.