**3. Conclusions**

The statistical properties of price log-returns and the volume of the cryptocurrencies were the central points of the present study. The existence of the so-called financial stylized facts in the cryptocurrency market during the last 3 years was investigated and compared with the stylized facts observed in the traditional financial markets. Several characteristics were of particular interest: a tail behavior of the probability distribution functions for the log-returns and volume traded, the functional form of price impact, volatility autocorrelations, multiscaling, cross-correlations among the cryptocurrencies, and cross-correlations between the principal cryptocurrencies and selected traditional market assets. Almost all the analyzed characteristics of the cryptocurrency market were found to be in qualitative agreement with their counterparts from the traditional markets. It allows one to conclude that, from this particular perspective, the cryptocurrency market does not differ from the mature markets.

Despite such a positive conclusion, one still has to be cautious. First, the level of the maturity of the cryptocurrencies depends on their trading frequency. The most liquid ones, such as BTC and ETH, to a greater extent, have characteristics corresponding to mature financial markets, and the least liquid ones do not. Second, the price impact function, while also of a power-law form, results in being substantially different from its counterparts reported in the traditional markets (linear or convex here vs. concave there [21]). Third, while the statistical properties are important from a practical point of view as they can be exploited in various investment strategies, there are nevertheless many other important indicators of market maturity that were not investigated here. For example, the number of cryptocurrencies traded on the largest platforms, such as Binance, is so large that it already matches the world's largest markets, such as the New York Stock Exchange and NASDAQ. On the other hand, even the most recognized cryptocurrencies, such as BTC and ETH, show extreme volatility, which means that the market is still rather illiquid, and this property can question its maturity. There is another problem associated with the fact that the cryptocurrencies are often viewed as speculation toys rather than full-scale investment instruments. There are also numerous issues related to the limited reliability of the cryptocurrencies, their weak supply elasticity, etc. These problems, while important, were beyond the scope of this analysis, which one has to keep in mind when thinking about the given conclusions. Repeating this kind of analysis in future in order to follow how the cryptocurrency market changes seems to be a straightforward direction of potential future studies.

**Author Contributions:** Individual contributions of the authors are as follows. Conceptualization, S.D. and M.W.; methodology, S.D., J.K. and M.W.; software, M.W.; validation, S.D., J.K. and M.W.; formal analysis, S.D. and M.W.; investigation, S.D., J.K. and M.W.; resources, M.W.; data curation, M.W.; writing—original draft preparation, J.K.; writing—review and editing, S.D., J.K. and M.W.; visualization, M.W.; supervision, S.D. and J.K.; project administration, S.D. and M.W. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Data Availability Statement:** The data used in the article are freely available on Binance and Dukascopy platforms.

**Conflicts of Interest:** The authors declare no conflict of interest.
