## 2 Materials and Methods  
In this study, we analyse high-frequency data collected from Binance [34], which is the largest cryptocurrency trading platform in terms of daily volume [35]. We analyse time series representing the number of transactions in time unit \(N(t_{i})\), logarithmic price returns \(r(t_{i})\), and volume traded in time unit \(V(t_{i})\) for two major cryptocurrencies: BTC and ETH, which were sampled every \(\Delta t=10\) s with \(\Delta t=t_{i+1}-t_{i}\) and \(i=1,\ldots,T\). Since cryptocurrency trading is continuous 24/7, our time series that start on 1 April 2020 and end on 31 May 2022 (i.e., they cover the period that we call the post-COVID-19 period) consist of 791 trading days and their length equals \(T=6\),834,240 data points. Among a few available approaches to fractal analysis of time series, the multifractal detrended fluctuation analysis (MFDFA) has proven to be among the most reliable (see, e.g., [36]). The reliability of MFDFA was assessed by comparing its outcomes for a few model data sets with the respective theoretical values based on analytically derived formulas. The MFDFA performance was, in the majority of cases, much better than that of competitive methods. MFDFA was designed to deal with nonstationary data by independently removing trends on different time scales, and to examine the statistical properties of the residual fluctuations [37]. Its generalised version, the multifractal cross-correlation analysis (MFCCA [38]), is capable of detecting multiscale cross-correlations between two parallel nonstationary signals [39; 40; 41]. Here, we briefly sketch the MFCCA procedure. Let us consider two nonstationary time series \(\mathrm{X}=\{X_{i}\}_{i=1}^{T}\) and \(Y=\{Y_{i}\}_{i=1}^{T}\) of length \(T\), sampled uniformly with an interval \(\Delta t\). We start by dividing each time series into \(M_{\mathrm{s}}=2\lfloor T/s\rfloor\) disjointed segments of length \(s\), going from both its start (\(i=1\)) and its end (\(i=T\)), where \(\lfloor\cdot\rfloor\) denotes the floor value. Next, we integrate the time series within each segment \(\
u\) and remove a polynomial trend \(P_{\
u}^{m}(j)\) of degree \(m\) from the resulting integral signal:  
\[x_{j}(s,\
u)=\sum_{k=1}^{j}X_{j(\
u-1)+k}-P_{\
u}^{m}(j),\quad j=1,\ldots,s, \quad\
u=1,\ldots,M_{s}. \tag{1}\]  
Typically, a polynomial of degree \(m=2\) is used, because the results obtained for a few larger values of \(m\) were stable. In each segment, we calculate a detrended covariance:  
\[f_{\mathrm{XY}}^{2}(s,\
u)=\frac{1}{s}\sum_{j=1}^{s}\big{[}x_{j}(s,\
u)- \langle x_{j}(s,\
u)\rangle_{j}\big{]}\big{[}y_{j}(s,\
u)-\langle y_{j}(s,\
u )\rangle_{j}\big{]}, \tag{2}\]where \(\langle\cdot\rangle_{j}\) denotes the averaging over \(j\). We then use the covariances of all segments to calculate the signed moments of order \(q\), which are called the (bivariate) fluctuation functions of \(s\):  
\[F_{q}^{\rm XY}(s)=\{\frac{1}{M_{s}}\sum_{\
u=1}^{M_{s}}\text{sign}[f_{\rm XY}^{ 2}(s,\
u)|]f_{\rm XY}^{2}(s,\
u)|^{q/2}\}^{1/q}. \tag{3}\]  
Since covariances can be negative, their absolute value prevents \(F_{q}^{\rm XY}\) from being complex, while the sign function ensures the consistency of the results [38]. A possibly negative sign of the whole expression in the curly brackets also has to be preserved before the \(q\)th-degree root is calculated. A character of the functional dependence of \(F_{q}^{\rm XY}\) on \(s\) allows for distinguishing the fractal time series from those that do not show this property. The most interesting are those signals for which the fluctuation functions exhibit power-law scaling for some range of \(q\) and \(s\):  
\[F_{q}^{\rm XY}(s)\sim s^{\lambda(q)}, \tag{4}\]  
where \(\lambda(q)\) plays a role of the bivariate generalised Hurst exponent. If the cross-correlations are monofractal, then \(\lambda(q)=\text{const}\) for all \(q\). In contrast, a multifractal case is associated with a monotonically decreasing function \(\lambda(q)\).