Financial markets are considered to be one of the most complex systems that we observe in our world. Not only are they characterized by all the properties that such systems can typically exhibit, but there are also important intelligent components involved that are strictly responsible for their enormous complexity. Among the well-known features of financial markets is their flexibility in transitions between irregular and regular phases. Such transitions are a key feature associated with market crashes but are also frequently observed at the market-wide level when several so far independent markets begin to have their dynamics substantially merged (or vice versa). This kind of phenomenon has recently been experienced by the cryptocurrency market, which has lost its relative dynamic autonomy and become closely tied to traditional financial instruments. In this work, we present quantitative arguments to support this assertion.

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Since Bitcoin's inception in 2009, the cryptocurrency market has experienced a rapid surge. While it used to be niche and traded informally in its early years, trading now takes place 24/7 on over 500 exchanges. The current cryptocurrency market capitalization (October 2022) is around 1 trillion USD, which is comparable to the largest US technology stocks. Over Bitcoin's 12-year history, there have been bubbles and crashes. In particular, the foundation of Ethereum in 2015, which enabled new applications of blockchain technology in the form of smart contracts, and the subsequent Initial Coin Offering bubble in 2018 reshaped the cryptocurrency market and brought it into the public eye. The recent bubble in 2021, associated with the adoption of DeFi (Decentralized Finance) and DEX (Decentralized Exchange) trading, ended with a peak in November 2021, when the total market capitalization approached 3 trillion dollars. Although there are more than 10,000 cryptocurrencies [3], Bitcoin and Ethereum are currently the best known, and their share in the entire market capitalization went from more than 80% at the beginning of 2021 to 60% in October 2022.

Over these 12 years of development, the characteristics of the cryptocurrency market have changed significantly. The time series properties of cryptocurrency price returns are now close to those observed in mature financial markets such as Forex. However, it has long been believed that cryptocurrency markets, which themselves are highly correlated, especially during the COVID-19 period, have dynamics separate from traditional financial markets and that bitcoin can even serve as a hedge or safe haven with respect to stock markets, Forex or commodity markets. Bitcoin's hedging potential is even compared to gold. However, the results of many recent studies have changed this paradigm. They report that during the COVID-19 pandemic boom and related crash in March 2020, cryptocurrency markets and, in particular, bitcoin were highly correlated with stock market declines. Several studies even noted that this relationship still occurred in the market recovery phase in the second half of 2020.

The studies referenced above have brought somewhat mixed results and have led to uncertainty as to whether cryptocurrencies can be used to hedge financial investments. This uncertainty opens up space for further research on this topic and our research goes exactly in this direction. Our goal is to clarify whether the loss of independence of cryptocurrency markets is temporary and primarily caused by the turmoil of the pandemic or it is simply part of a more general trend towards merging these markets with traditional financial markets. We aim to determine how strongly cryptocurrency price changes are related to price changes in traditional financial markets. To achieve that, the perturbed multiscale correlation of two major cryptocurrencies: bitcoin $BTC and ethereum $ETH versus traditional financial instruments: stock indices, commodities and currency exchange rates is studied based on high-frequency data covering the period from January 2020 to October 2022, which is an extension of the pre-2020 period analyzed in our previous study. 2022 is particularly interesting, as since the BTC price peak in November 2021, there has been a concerted bear market in US technology stocks and cryptocurrencies for the first time in the latter's existence. Based on these observations, there will likely be some detectable correlation between the two markets. The year 2022 is also unique in cryptocurrency history because of the high inflation in the world intended to protect Bitcoin.

Compared to other articles dealing with the correlation between cryptocurrency markets and traditional financial markets, in our research the main task is to measure this correlation quantitatively on various time scales and for fluctuations of various sizes. This can broaden a market practitioner's perspective on investment and hedging possibilities by including a measure of fluctuation as an additional dimension that may be considered when making investment decisions.

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