Figure 2.

(Top) Characteristic values of the Hölder exponent: ${\alpha }_{\min }$ (green line, bottom), ${\alpha }_0$ (red line, middle), and ${\alpha }_{\max }$ (blue line, top)—see Equation (9) in Section 2.2 and Figure 3—describing the singularity spectra $f\left(\alpha \right)$ for the index returns representing 8 the most capitalized cryptocurrencies, calculated in a 30-day-long moving window with a step of five days and for $-3\le q\le 3$. Each date represent a window that ends on that day. (Upper middle) The same quantities as in the top panel, but here calculated for the BTC/USDT exchange rate returns. Three interesting cases of small ${\alpha }_{\min }$ are indicated by dashed circles. (Lower middle) Scaling exponent $\gamma$ of the cumulative distribution function fitted to tails of the empirical cdf in each moving window position. Values equal or below $\gamma =2$ correspond to Lévy-stable distributions. (Bottom) Total cryptocurrency market capitalization and new Covid-19 cases in the world as function of time. Characteristic events are indicated by vertical dashed lines and Roman numerals: Start of a bull market in April 2019 (event I), its end in July 2019 (event II), the Covid-19 panic in March 2020 (event III), and start of the 2nd wave of the pandemic in May-June 2020 (event IV).