Multiscale topological analysis of financial markets

We study financial systems via multiscale topological analysis based on algebraic topology. By mapping coarse-grained time series into complex networks, we find that a universal scaling law behavior emerges between the number of higher-order cliques and the temporal scale. Remarkably, we show that the associated exponents exhibit a monotonic growth pattern irrespective of the kinds of financial system. Furthermore, we show that the multiscale entropy of financial systems presents a uniform decreasing trend. Our work, for the first time, uncovers higher-order structural organization underlying financial markets from a multiscale perspective.