*3.3. ADCC-GARCH Estimation Results*

The mean equation of the GARCH model was set to be AR(1) with the intercept term included, and the parameters of the intercept term and AR(1) were denoted by *μ* and *ϕ*, respectively. The variance equation was set to be GARCH(1,1), and the parameters of its intercept term, ARCH term and GARCH term were denoted by *ω*, *α* and *β*, respectively. The dynamic correlation parameters of the ADCC model were denoted by *a*, *b* and *g*, and υ denoted the joint distribution parameter of the model. Since all return series were not normally distributed, the multivariate joint t-distribution was selected for the distribution function.

Table 4 reports the ADCC-GARCH estimation results for the daily frequency sample of bitcoin and each asset price. In the variance equation, the coefficients of the ARCH and GARCH terms for all assets were significantly positive at least at the 5% level, indicating that the GARCH(1,1) setting was plausible. The coefficients of the GARCH term for all assets were much larger than the coefficients of the ARCH term, indicating that the conditional variance was more influenced by its prior period value and less sensitive to the previous period's return volatility, which showed that the price movements of these assets exhibited volatility clustering. From the ADCC estimation results, *a* was not negative, indicating that the standardized residuals with one lag had a positive effect on the dynamic correlation coefficient; *b* was close to 1, indicating that the dynamic correlation between bitcoin and other assets had strong persistence; and the sum of *a* and *b* was less than 1, ensuring that the conditional covariance matrix was positive definite and mean-reverting. ARCH tests were further performed on the residual terms of the ADCC-GARCH estimation results, and the results showed no significant ARCH effect. The above results indicated that the ADCC-GARCH estimation results were reliable. In addition to the daily frequency sample, we also performed ADCC-GARCH modeling for the weekly and semi-monthly frequency samples.


**Table 4.** Results of ADCC-GARCH estimation.


**Table 4.** *Cont.*

Note: This table reports the results of ADCC-GARCH estimation for the daily frequency sample. The *p* values are in parentheses. \*\*\*, \*\* and \* indicate significance at the 1%, 5% and 10% levels, respectively.

Figure 2 shows the trend of dynamic correlation coefficients between bitcoin and various assets, including daily, weekly and semi-monthly frequencies. The correlation coefficients between bitcoin and each asset all exhibited significant time variability, suggesting that using an ADCC-GARCH approach was necessary to capture the dynamic correlation between bitcoin and each asset. We classified these assets into stock, bond, commodity and currency to further analyze the dynamic correlation between bitcoin and different classes of assets.

**Figure 2.** Daily, weekly and semi-monthly dynamic correlation coefficients between bitcoin and other assets.

Figure 2, panels (1)–(6), show the trend of dynamic correlation coefficients between bitcoin and representative stock indices. Firstly, in the daily frequency dimension, the correlation coefficients between bitcoin and all stock indices were low and largely fluctuated around 0, showing no sustained positive or negative correlation. The reason for this may be that bitcoin's high short-term volatility undermines its short-term correlation with other assets. Secondly, as the frequency changed from high to low, bitcoin began to show a significant positive correlation with most stock indices. In both the weekly and semimonthly frequency dimensions, the correlation coefficients between bitcoin and global, U.S., U.K., German and Japanese stock indices were consistently positive in most periods, and the magnitude of the coefficients was also significantly higher. In particular, the dynamic correlation coefficients of bitcoin with global, U.S. and U.K. stock indices showed a clear "semimonthly frequency > weekly frequency > daily frequency". This showed that bitcoin had a weak correlation with major stock prices in the short term, but a more stable positive correlation in the long term. Thirdly, bitcoin's linkage with SSEC had different characteristics from its linkage with stock indices of developed countries. While the correlation between bitcoin and SSEC in the daily frequency dimension fluctuated around 0 over the full sample interval, the daily frequency correlation between the two was negative for most periods before 2017, which was consistent with the findings of Wang et al. [28]. Furthermore, the dynamic correlation coefficient between bitcoin and SSEC in the semi-monthly frequency dimension was negative in most periods, indicating that bitcoin and SSEC are negatively correlated in the long term. Unlike developed countries, China's financial markets have long been subject to capital controls, resulting in relatively limited channels for investors to invest abroad. In this context, when there is a long-term downward trend in the Chinese stock market, investors tend to enter the cryptocurrency (e.g., bitcoin) market to hedge their domestic stock investment losses, which is a possible reason for the negative correlation between bitcoin and the SSEC index in the long run. Fourth, the bitcoin-stock linkage increased sharply when subjected to exogenous extreme shocks. This observation was consistent with Kwapie ´n et al. [3], who also found that the level of correlation between the cryptocurrency market and the stock market becomes higher during turbulent periods. Following the outbreak of COVID-19 in early 2020, the dynamic correlation coefficients between bitcoin and all stock indices rose rapidly, with the weekly frequency correlation coefficients of bitcoin with global, U.S., Japanese and Chinese stock indices rising sharply to approximately 0.5, 0.35, 0.7 and 0.25, respectively, and the semi-monthly frequency correlation coefficients with the U.K. and German stock indices both rising sharply to levels close to 0.8. The epidemic shock has led to a rapid rise in uncertainty and a sudden drop in investor risk appetite, causing investors to be less willing to hold not only traditional risk assets such as stocks, but also bitcoin, which has led to a sharp decline in both bitcoin and stock markets and a sharp increase in the positive linkage between bitcoin and the underlying stock indices.

Figure 2, panels (7)–(9), show the trend of dynamic correlation coefficients between bitcoin and representative bond indices. Firstly, similar to the dynamic correlation coefficient between bitcoin and stock prices, the dynamic correlation coefficient between bitcoin and bond prices exhibited a gradual increase from the short term (high frequency) to the long term (low frequency). In the daily frequency dimension, the dynamic correlation coefficients between bitcoin and the U.S. bond index, the non-U.S. bond index and the emerging markets bond index all fluctuated in a small range around 0; however, in the weekly and semi-monthly frequency dimensions, the coefficients were not only consistently positive but also significantly higher in magnitude. In particular, the dynamic correlation coefficients between bitcoin and both the non-U.S. bond index and emerging markets bond index showed a clear "semimonthly frequency > weekly frequency > daily frequency". Secondly, in the comparable time-frequency dimension, the correlation between bitcoin and bond prices was lower than its correlation with stock prices, indicating that bitcoin is more closely linked to the stock market than its linkage to the bond market. Thirdly, the linkage between bitcoin and bond prices also exhibited a sharp enhancement in response to extreme

shocks. The outbreak of COVID-19 in early 2020 caused both bitcoin and bond prices to fall significantly, resulting in the weekly frequency correlation coefficients of bitcoin with the U.S. bond index, the daily frequency correlation coefficients with the non-U.S. bond index and the semi-monthly frequency correlation coefficients with the emerging markets bond index rising sharply to over 0.5, 0.3 and 0.6, respectively.

Figure 2, panels (10)–(13), show the trend of dynamic correlation coefficients between bitcoin and representative commodity prices. Firstly, with the exception of gold, the dynamic correlation coefficients between bitcoin prices and the S&P GSCI, CRB commodity index and oil prices were positive for all periods and all time-frequency dimensions, indicating a persistent positive linkage between bitcoin and major commodity prices. Secondly, similar to the dynamic correlation coefficient between bitcoin and stocks/bonds, the dynamic correlation coefficients between bitcoin and the three commodities other than gold showed a gradual increase from the short term (high frequency) to the long term (low frequency). In the daily frequency dimension, the dynamic correlation coefficients between bitcoin and the three commodities, although consistently positive, were at a low level of below 0.1 for most periods, while in the weekly and semi-monthly frequency dimensions, the positive correlation coefficients were significantly higher. The correlation between bitcoin and gold on both daily and weekly frequencies fluctuated basically in a small range around 0. However, the correlation between the two on semi-monthly frequencies, increased. Thirdly, the bitcoin–commodity market linkage also exhibited a sharp increase in response to extreme shocks, which was consistent with Kwapie ´n et al. [3], who showed that the level of correlation between the cryptocurrency market and the commodity market becomes higher during turbulent periods. Following the outbreak of COVID-19 in early 2020, both bitcoin and commodity prices fell rapidly, with bitcoin's semi-monthly frequency correlation coefficients with the S&P GSCI, oil prices and gold prices rising sharply to over 0.6, 0.5 and 0.6, respectively, and its weekly frequency correlation coefficient with the CRB commodity index rising rapidly to approximately 0.35.

Figure 2, panel (14), shows the trend of the dynamic correlation coefficient between bitcoin and the U.S. dollar index. At all frequencies, the dynamic correlation coefficient between bitcoin and the U.S. dollar index was negative in most periods, indicating that bitcoin price has an inverse linkage to the U.S. dollar index and that bitcoin can be used as an effective hedge against dollar depreciation. Bitcoin had a weak negative correlation with the U.S. dollar index on the daily and weekly frequencies, but showed a strong negative correlation for most periods on the semi-monthly frequency, peaking at nearly −0.4. The reason for the negative correlation between bitcoin and the dollar index may be interpreted in two ways. First, since bitcoin is denominated in USD, a dollar depreciation will cause bitcoin to become cheaper, thus, increasing demand for bitcoin and driving its price upward. Second, as deduced from the previous results regarding the predominantly positive correlation between bitcoin and stock/bond/commodity prices, bitcoin is closer in nature to a risk asset, while the U.S. dollar is typically a safe-haven asset, so the two prices naturally exhibit a negative correlation.

In summary, the linkage between bitcoin and various assets varies by asset class and time frequency, and can undergo significant structural changes in response to exogenous shocks in international financial markets. In terms of asset classes, bitcoin was positively correlated with risk assets including stock, commodity and bond, and bitcoin's positive correlation with stock or commodity was stronger than its positive correlation with bond; bitcoin had a significant negative correlation with the U.S. dollar, a typical safe-haven asset. As such, bitcoin is closer in nature to a risk asset than a safe-haven asset. In terms of time frequency, the long-term correlation between bitcoin and various asset prices was significantly stronger than the short-term correlation, mainly because the short-term high volatility and speculative nature of the bitcoin market undermine its short-term correlation with other assets. Finally, the linkage between bitcoin and the risk assets can increase sharply in response to exogenous extreme shocks. For example, after the outbreak of COVID-19 in early 2020, the plunge in investor risk appetite led to a sharp decline in the

prices of bitcoin and risk assets (including stocks, bonds and commodities), at which point the positive linkage between bitcoin and those risk assets rose rapidly. This also suggests that the outbreak of the COVID-19 pandemic has accelerated the integration of bitcoin with traditional financial markets, transforming it into part of a global market that is increasingly correlated with traditional assets [4].
