The market nanostructure origin of asset price time reversal asymmetry
We introduce a method to infer lead-lag networks between the states of elements of complex systems, determined at different timescales. As such networks encode a causal structure of a system, inferring lead-lag networks for many pairs of timescales provides a global picture of the mutual influence between timescales. We apply our method to two trader-resolved FX data sets and document a strong and complex asymmetric influence of timescales on the structure of lead-lag networks. This asymmetry extends to the propagation of trader activity between timescales. For both retail and institutional traders, we find that historical activity over longer timescales has a greater correlation with future activity over shorter timescales (Zumbach effect), for sufficiently large timescales both in the past and future (about one hour for retail traders and two hours for institutional traders); remarkably the effect is opposite for smaller timescales, and much weaker for retail traders.