Approaching Multifractal Complexity in Decentralized Cryptocurrency Trading

Abstract

Multifractality is a concept that helps compactly grasp the most essential features of financial dynamics. In its fully developed form, this concept applies to essentially all mature financial markets and even to more liquid cryptocurrencies traded on centralized exchanges. A new element that adds complexity to cryptocurrency markets is the possibility of decentralized trading. Based on the extracted tick-by-tick transaction data from the Universal Router contract of the Uniswap decentralized exchange, from 6 June 2023 to 30 June 2024, the present study using multifractal detrended fluctuation analysis (MFDFA) shows that even though liquidity on these new exchanges is still much lower compared to centralized exchanges, convincing traces of multifractality are already emerging in this new trading as well. The resulting multifractal spectra are, however, strongly left-side asymmetric, which indicates that this multifractality comes primarily from large fluctuations, and small ones are more of the uncorrelated noise type. What is particularly interesting here is the fact that multifractality is more developed for time series representing transaction volumes than rates of return. On the level of these larger events, a trace of multifractal cross-correlations between the two characteristics is also observed.