**1. Introduction**

Over the past few years, two processes have had a particularly strong impact on financial markets: the emergence of the cryptocurrency market [1–5] and the COVID-19 pandemic [6–12]. Each of these processes alone has already been a topic in numerous pieces of the scientific literature, but they also were studied together [5,13–21]. Of particular interest in this context is how the ongoing pandemic is changing the cryptocurrency market and how this market position among the other financial and commodity markets undergoes an accelerated evolution. The cryptocurrency market is an interesting object for analysis from the perspective of complex systems, as it is a unique financial market whose establishment and evolution was entirely spontaneous with no intervening governmen<sup>t</sup> or other regulatory institution. Thus, a process of the market's self-organization can be traced from the very beginning until the present.

As the cryptocurrency market properties are constantly evolving and they are still far from being fully identified and understood, there is heavy ongoing related research that points in various directions (see, for example, [4] for comprehensive literature listing and pointing out several significant research voids). On the general level, the cryptocurrency markets are studied at an angle of trading security, the vulnerability to improper trading practices [22], and the formation of demand [23]. On the asset level, the fundamental aspects of the market processes that drive price discovery [24,25], price fluctuations [26–28], asset liquidity [29], and asset–asset correlations [30,31] are studied from the investor's perspective in order to facilitate the optimal portfolio construction both inside the cryptocurrency market and across different markets, including the cryptocurrency one. An

**Citation:** Kwapie ´n J.; W ˛atorek, M.; Drozd˙ z, S. Cryptocurrency Market ˙ Consolidation in 2020–2021. *Entropy* **2021**, *23*, 1674. https://doi.org/ 10.3390/e23121674

Academic Editors: Ryszard Kutner, H. Eugene Stanley and Christophe Schinckus

Received: 18 November 2021 Accepted: 9 December 2021 Published: 13 December 2021

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**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

associated important direction of research is the possibility of market forecasting, which includes the approach developed in econophysics that is based on a search for evidence of the exogeneous and endogeneous market shocks, speculative bubbles, crashes, and their precursors [32]. Among the voids, one can count the sparse analyses based on highfrequency data, the exaggerated focus on bitcoin (BTC) alone, and the insufficient attention paid to how different mining protocols can affect the related asset properties and how various legal regulations being (actually or potentially) imposed on the cryptocurrency markets can perturb both the mining and the trade [4].

From a perspective of their statistical and dynamical properties, the cryptocurrencies neither resemble regular currencies, like the US dollar (USD) or Chinese yuan (CNH), nor commodities, like gold or oil [33–35]. Among the major problems associated with cryptocurrencies is their significant volatility. In consequence, even the largest and the most capitalized cryptocurrency, BTC, is considered an asset that resides at the interface between a standard financial asset and a speculative one [36]. Most studies of the cryptocurrency market relations with the traditional markets reported in the literature point to relative independence of the cryptocurrencies (see, for example, [13,31,37]). However, there were also some reports concluding that there are temporary or stable cross-correlations or even causality between the major cryptocurrencies and some regular currencies, like TRY [34] and some Asian currencies, like BHT, CNH, and TWD [38], as well as between the cryptocurrencies and commodities [37].

As a new system, it took several years for the cryptocurrency market to reveal any signatures of maturity, like the market efficiency [39,40]. However, already prior to the crash of April 2018, its statistical properties became similar to the properties of the other markets, among which there were the financial stylized facts (the power-law tails of the return distributions, volatility clustering, etc.) [5,28,40] and some other complexity traits, like multifractality [26], and, in some aspects, it started to resemble Forex [26,41]. On the other hand, one of the interesting facts about the cryptocurrency market's inner structure is that, unlike other financial markets where, typically, the highly capitalized assets have spillover effects on the less capitalized ones, here the less capitalized assets are able to influence the evolution of the highly capitalized ones. This can lead to more a complex structure than a typical structure of the other markets, where causality is unidirectional [42–45].

These and other similarities and differences opened space for a concern, whether bitcoin and other cryptocurrencies may be considered as a safe haven during market turmoils or whether they may be used to hedge against the traditional assets. Although the literature on this issue is growing, the conclusions are mixed: BTC and the other major cryptocurrencies are sometimes indicated as good candidates for a safe haven [15,16,18,46,47] but the opposite can also be suggested [15,17,36,48–52], depending on the analyzed data. Sometimes the answer can even be conditional: "yes" to a safe haven, "no" to a hedge [53]. An important risk factor of BTC and other cryptocurrencies that acts against their use for hedging is their possible lack of fundamental value [54].

As regards the asset–asset correlations among the cryptocurrencies, it was shown that, besides a trend going towards the stronger market cross-correlations, the cryptocurrencies reveal a cyclic amplification of volatility connectedness during periods of economic instability or external shocks. However, BTC does not play a central role in driving market volatility [42]. A different study applying different methodologies (principal component analysis, cross-sectional dependence, and vector autoregression framework) confirmed this finding and extended it from volatility to returns [45]. Another work reported the increased cross-correlations among the cryptocurrencies after the bubble of 2017 as compared to the earlier period by using the detrended fluctuation analysis [44]. The highly capitalized cryptocurrencies show statistically significant time-lagged autocorrelations that may indicate substantial market inefficiency (although not necessarily usable for profit-making) [35]. All these works analyzed very small sets of assets, however, which significantly limited the market insight they were able to provide. A more comprehensive study, which considered over 50 cryptocurrencies, also brought more diversified results, and identified some assets

that were statistically and dynamically different than the others (these were tether, holo, maker, NEM, and nexo) [20].

In our former publications we thoroughly analyzed the cryptocurrency market evolution from its early stages of development to the current, relatively mature phase. In the Ref. [55] we reported that the cryptocurrency dynamics over the years 2016–2019 displayed signatures of decoupling from dynamics of the regular currencies [55]. In the Refs. [5,13] we analyzed the cryptocurrency market properties during the pandemic onset (January 2019–October 2020). We showed that before the pandemic, over the years 2018–2019, the evolution of the cryptocurrency market was largely independent from the evolution of the traditional markets. We interpreted this independence as a consequence of a quiet period on the traditional markets and a disparity in the market capitalization: the cryptocurrency market was too small to perturb other markets, while they were too tranquil then to induce any turmoil among the cryptocurrencies. However, in the second half of January 2020, at the moment when the first COVID-19 case was reported in the United States, some cryptocurrencies responded and thus lost their independence. For example, BTC gained positive cross-correlation with JPY, CHF, and gold, which are considered as a financial safe haven, and negative cross-correlation with other major assets, while ETH preserved its independent dynamics longer. Later, during the outburst of the first wave of COVID-19 in April 2020, the cryptocurrencies underwent a crash together with all the major markets, except for a few regular currencies like JPY. This state of cross-market coupling continued in the months that followed, both at the moments of the subsequent pandemic waves and the market rallies. Our analyses ended in the middle of the third pandemic wave before the introduction of anti-COVID vaccines, thus we could not report on how the markets would respond to a decreased pandemic risk. From this angle, our present analysis can be viewed inter alia as a continuation of those previous works based on a new data set.

In the following, we will report on our study of a set of the most liquid cryptocurrencies whose high-frequency price quotes cover the last 21 months. We will apply the generalized detrended cross-correlation analysis [56–59] and study the spectral properties of a detrended correlation matrix, as well as the topological properties of its network representation. In the context of the current cryptocurrency research, our main objectives are (1) to look into the most recent data that have not been covered by other works yet, and compare results with the earlier ones, (2) to consider a set of assets that is wide as possible provided the available data quality, and (3) to apply a methodology that is rarely used in this context, that is, the *q*-dependent cross-correlation analysis that is able to filter data according to its magnitude. In Section 2 we will briefly recollect the related formalism, in Section 3 we present and discuss the main results, and in Section 4 we will present the summary and conclusions.
