**1. Introduction**

From the physics point of view, the financial markets are considered as one of the most complex systems we observe in our world [1]. Not only they are characterised by all the properties such systems can typically show, but there is also an important intelligent component involved that is decisively responsible for their enormous complexity. Among the well-known features of the financial markets is their flexibility in the transition between the disordered and ordered phases. Such a transition is the key feature associated with the market crashes but it is also often observed on the level of whole markets when some so-far independent markets start to have their dynamics substantially coupled (or *vice-versa*). Exactly this kind of phenomenon has recently been experienced by the cryptocurrency market, which has lost its relative dynamical autonomy and become significantly tied to the traditional financial instruments. In this work, we present quantitative arguments in support of this statement.

Since the inception of Bitcoin in 2009, the cryptocurrency market has experienced a rapid surge. Although it used to be a niche and traded unofficially in its early years [2], trading takes place now 24/7 on more than 500 exchanges [3]. The current (October 2022) capitalization of the cryptocurrency market is approximately 1 trillion USD [3], which can

**Citation:** W ˛atorek, M.; Kwapie ´n, J.; Drozd˙ z, S. Cryptocurrencies Are ˙ Becoming Part of the World Global Financial Market. *Entropy* **2023**, *25*, 377. https://doi.org/10.3390/ e25020377

Academic Editors: Panos Argyrakis and José F. F. Mendes

Received: 9 November 2022 Revised: 5 December 2022 Accepted: 16 February 2023 Published: 18 February 2023

**Copyright:** © 2023 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/).

be compared to the largest US tech stocks. During these 12 years of Bitcoin history, there were bubbles and crashes [4–6]. In particular, the foundation of Ethereum in 2015, which allowed for a new application of the blockchain technology in the form of smart contracts, and the subsequent Initial Coin Offer bubble [7] in 2018 reshaped the cryptocurrency market and made it appear in the public eye. A recent bubble in 2021, which was related to the adoption of DeFi (Decentralized Finance) and DEX (Decentralized Exchanges) trading [8], ended with a peak in November 2021, when the total market capitalization was close to 3 trillion dollars. Although there are more than 10,000 cryptocurrencies [3], Bitcoin and Ethereum are currently the most recognizable, and their share in the capitalization of the entire market changed from over 80% in early 2021 to 60% in October 2022 [3].

During these 12 years of development, the characteristics of the cryptocurrency market have changed significantly [9,10]. The properties of the cryptocurrency price return time series are now close to those observed in mature financial markets such as Forex [11]. However, it has long been believed that the cryptocurrency market, which itself is strongly correlated [12–18], especially during the COVID-19 period [19–23], has dynamics that is separate from the traditional financial markets [24–28] and that bitcoin can even serve as a hedge or safe haven [29,30] with respect to the stock market, Forex or the commodity market. The hedging potential of bitcoin was even compared to gold [31–35]. However, the results of many recent studies have changed this paradigm [36–43]. They reported that during the COVID-19 pandemic outburst and the related crash in March 2020 [44,45] the cryptocurrency market and, in particular, bitcoin was highly correlated with the falling stock markets [46–52]. Some studies even noted that this connection still occurred in the market recovery phase in the second half of 2020 [15,53].

The studies referenced above brought therefore rather mixed results and have led to uncertainty as to whether cryptocurrencies can be used for hedging the financial investments. This uncertainty opens space for further research on this topic and our study proceeds exactly in this direction. Our aim is to clarify whether the loss of the cryptocurrency market independence was temporary and primarily caused by the pandemic turmoil or it was only a part of a more general trend towards coupling of this market with the traditional financial markets. We intend to determine how strongly the cryptocurrency price changes are associated with the price changes in the traditional financial markets. To achieve that, the detrended multiscale correlation of the two principal cryptocurrencies: bitcoin (BTC) and ethereum (ETH) versus the traditional financial instruments: stock indices, commodities and currency exchange rates are studied based on high frequency data covering the period from January 2020 to October 2022, which is an extension of the period before 2020 that was analyzed in our earlier study [47]. The year 2022 is particularly interesting, because since the BTC price peak in November 2021, there is a joint bear market on the US tech stocks and the cryptocurrencies for the first time in the existence of the latter. On the basis of this observation, it is likely that there will be some detectable correlation between both markets. The year 2022 is also unique in the history of cryptocurrencies due to the presence of high inflation in the world against which Bitcoin was intended to protect [54–57].

Compared to the other articles dealing with correlations between the cryptocurrency market and traditional financial markets, in our research, the main task is to measure these correlations quantitatively on various time scales and for the fluctuations of various size. It can broaden the market practitioners' perspective on the investing and hedging possibilities by incorporating the fluctuation size as an additional dimension that might be considered while making investment decisions.
