Approaching multifractal complexity in decentralized cryptocurrency trading

TL;DR

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.

Abstract

Multifractality is a concept that helps compactly grasping the most essential features of the financial dynamics. In its fully developed form, this concept applies to essentially all mature financial markets and even to more liquid cryptocurrencies traded on the 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 June 6, 2023, to June 30, 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 on 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.

Figures (8)

• Figure S1: The probability distribution (histogram) of the exchange rates ETH/USDT and ETH/USDC log-returns $R_{\Delta t=12s}$ on Uniswap liquidity pools -- versions 2 and 3 with different trading commissions: 0.3% (USDT Uv3_0.3, USDC Uv3_03, USDT Uv2, USDC Uv2) and 0.05% (USDT Uv3_0.05 and USDC Uv3_0.05).
• Figure S2: Complementary cumulative distribution functions for (a) absolute log-returns $|R_{\Delta \textrm{t=5min}}|$ and (b) volume $V_{\Delta \textrm{t=5min}}$ of ETH expressed in USDT and USDC on Binance and Uniswap. The estimated exponent, $\gamma$ with standard error, is shown in the insets.
• Figure S3: Autocorrelation function for a) absolute log-returns $|R_{\Delta \textrm{t=5min}}|$ and b) volume $V_{\Delta \textrm{t=5min}}$ of ETH expressed in USDT and USDC on Binance and Uniswap exchanges.
• Figure S4: Fluctuation functions $F_{RR}(q,s)$ with the range of $q \in [-4,4]$ ($\Delta q = 0.2$) calculated for ETH/USDT and ETH/USDC log-returns $R_{\Delta t=5\textrm{min}}$ from Binance (top), Uniswap v3 (middle), and Uniswap v2 (bottom). (Main) Thick green lines represent $F(q=2,s)$, from the slope of which the Hurst exponent $H$ is estimated together with its standard error. Vertical red dashed lines indicate a scale range, where the family of $F_{RR}(q,s)$ exhibits a power-law dependence for different values of $q$. (Insets) The generalized Hurst exponent $h(q)$ is estimated from the scaling of $F_{RR}(q,s)$. Error bars represent the standard error of linear regression.
• Figure S5: $F_{VV}(q,s)$ obtained in the same way as in Fig. \ref{['fig::Fq_R']} but for volume $V_{\Delta t=5\textrm{min}}$.