Lempel-Ziv Complexity and Crises of Cryptocurrency Market

Abstract

The informational (Kolmogorov) measure of complexity in accordance with the Lempel-Ziv algorithm (LZC) is calculated for the logarithmic returns of daily Bitcoin/$ values. The calculations were carried out for a moving window with a variation in its size (50–250 days) in increments of one day in the framework of the implemented coarse graining procedure. It is shown that in both mono-and multi-scaling versions, LZC is sensitive to noticeable fluctuations in the Bitcoin price that occur as a result of critical events in the cryptocurrency market. In equilibrium, stable state, having a relatively low value, LZC rapidly increases immediately before the crisis, which proves the dominance of the chaotic component of the time series. The classification and periodization of crisis phenomena in the cryptocurrency market for the period 2010–2020 has been carried out. The results demonstrate the possibility of using the LZC measure as an indicator-precursor of crisis phenomena in the cryptocurrency market.