# Cryptocurrencies Are Becoming Part of the World Global Financial Market

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## Abstract

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## 1. Introduction

## 2. Data and Methodology

#### 2.1. Data Sources and Preprocessing

#### 2.2. The q-Dependent Detrended Correlation Coefficient

## 3. Results and Discussion

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Evolution of the cumulative log-returns of the cryptocurrencies ${R}_{\mathrm{cum}}$ (

**a**), the stock market indices (

**b**), the fiat currencies (

**c**), and the commodities (

**d**) over a period from 1 January 2020 to 28 October 2022. Periods for which significant correlations between the cryptocurrencies and the US stock indices are distinguished by grey vertical strips. The most characteristic periods are denoted by Roman numerals: a COVID-19-related crash in March 2020 and a quick bounce in April–May 2020 (period I), new all-time highs of NQ100 and S&P500 and a September 2021 correction (period II), a bear phase in the cryptocurrency and stock markets since November 2021 (period III), and another downward wave of US stock indices after holiday upward correction along with the appreciating USD and inflation fears (period IV).

**Figure 2.**Correlation matrix of Pearson coefficients calculated for all possible pairs of the time series considered in this study (January to October 2022). All the values are statistically significant with p-value < 0.00001, except DAX vs. JPY, where $p=0.1$.

**Figure 3.**The q-dependent detrended cross-correlation coefficient ${\rho}_{q}\left(s\right)$ between BTC/USD (

**right**) and ETH/USD (

**left**) versus selected traditional financial instruments for $q=1$, which does not favor any specific amplitude range. ${\rho}_{q}\left(s\right)$ for a range of time scales from $s=12$ (2 min) to $s=32,000$ (∼4 trading days) is presented based on data from January to October 2022. The statistically insignificant correlation region (dotted green line) is given as ± standard deviation of ${\rho}_{q}\left(s\right)$ calculated from 100 independent realizations of the shuffled time series.

**Figure 4.**The q-dependent detrended cross-correlation coefficient ${\rho}_{q}\left(s\right)$ between BTC/USD (

**right**) and ETH/USD (

**left**) versus selected traditional financial instruments for $q=4$, which amplifies the large return contributions. ${\rho}_{q}\left(s\right)$ for a range of time scales from $s=12$ (2 min) to $s=32,000$ (∼4 trading days) is presented based on data from January to October 2022. The statistically insignificant correlation region (dotted green line) is given as ± standard deviation of ${\rho}_{q}\left(s\right)$ calculated from 100 independent realizations of the shuffled time series.

**Figure 5.**Evolution of the q-dependent detrended cross-correlation coefficient ${\rho}_{q}\left(s\right)$ with $q=1$ and $s=2$ min calculated in a 5-day rolling window with a 1-day step between 1 January 2020 and 28 October 2022 for the price returns of BTC/USD (

**left**) and ETH/USD (

**right**) versus the selected traditional assets: AUD, CAD, CHF, CL, DAX, EUR, HG, JPY, MXN, NIKKEI, NQ100, S&P500, XAG, and XAU. The statistically insignificant correlations are in the region ${\rho}_{q}\left(s\right)=0\pm 0.001$.

**Figure 6.**Evolution of the q-dependent detrended cross-correlation coefficient ${\rho}_{q}\left(s\right)$ with $q=1$ and $s=60$ min calculated in a 5-day rolling window with a 1-day step between 1 January 2020 and 28 October 2022 for the price returns of BTC/USD (

**left**) and ETH/USD (

**right**) versus the selected traditional assets: AUD, CAD, CHF, CL, DAX, EUR, HG, JPY, MXN, NIKKEI, NQ100, S&P500, XAG, and XAU. The statistically insignificant correlations are in the region ${\rho}_{q}\left(s\right)=0\pm 0.01$.

**Figure 7.**Evolution of the q-dependent detrended cross-correlation coefficient ${\rho}_{q}\left(s\right)$ with $q=4$ and $s=2$ min calculated in a 5-day rolling window with a 1-day step between 1 January 2020 and 28 October 2022 for the price returns of BTC/USD (

**left**) and ETH/USD (

**right**) versus the selected traditional assets: AUD, CAD, CHF, CL, DAX, EUR, HG, JPY, MXN, NIKKEI, NQ100, S&P500, XAG, and XAU. Higher levels of cross-correlations, associated with the Consumer Price Index (CPI) readings, are marked (see the event description in Figure 9). The statistically insignificant correlations are in the region ${\rho}_{q}\left(s\right)=0\pm 0.001$.

**Figure 8.**Evolution of the q-dependent detrended cross-correlation coefficient ${\rho}_{q}\left(s\right)$ with $q=4$ and $s=60$ min calculated in a 5-day rolling window with a 1-day step between 1 January 2020 and 28 October 2022 for the price returns of BTC/USD (

**left**) and ETH/USD (

**right**) versus the selected traditional assets: AUD, CAD, CHF, CL, DAX, EUR, HG, JPY, MXN, NIKKEI, NQ100, S&P500, XAG, and XAU. Higher levels of cross-correlations, associated with the Consumer Price Index (CPI) readings, are marked (see the event description in Figure 9. The statistically insignificant correlations are in the region ${\rho}_{q}\left(s\right)=0\pm 0.01$.

**Figure 9.**Evolution of the cumulative logarithmic returns ${R}_{\mathrm{cum}}$ of selected financial instruments: BTC, ETH, AUD, CAD, CHF, CL, DAX, EUR, HG, JPY, MXN, NIKKEI, NQ100, S&P500, XAG, and XAU on specific dates, around the publication time of the Consumer Price Index (CPI) report in the US.

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**MDPI and ACS Style**

Wątorek, M.; Kwapień, J.; Drożdż, S.
Cryptocurrencies Are Becoming Part of the World Global Financial Market. *Entropy* **2023**, *25*, 377.
https://doi.org/10.3390/e25020377

**AMA Style**

Wątorek M, Kwapień J, Drożdż S.
Cryptocurrencies Are Becoming Part of the World Global Financial Market. *Entropy*. 2023; 25(2):377.
https://doi.org/10.3390/e25020377

**Chicago/Turabian Style**

Wątorek, Marcin, Jarosław Kwapień, and Stanisław Drożdż.
2023. "Cryptocurrencies Are Becoming Part of the World Global Financial Market" *Entropy* 25, no. 2: 377.
https://doi.org/10.3390/e25020377