Abstract
Purpose
The encrypted money market has attracted the attention of investors all over the world. Among the encrypted currency, bitcoin is undoubtedly the most popular. Because blockchain technology is the crucial support of bitcoin, exploring the relationship between bitcoin and the blockchain index is necessary.
Design/methodology/approach
This paper uses the Granger causality test to explore the correlation between bitcoin and the blockchain index. Furthermore, their volatility is analyzed by a GARCHclass model.
Findings
The results show that no significant correlation exists between bitcoin and the blockchain index; external shocks aggravate the volatility of bitcoin and the blockchain index, and the volatility has a certain degree of sustainability; and blockchain index has obvious leverage, namely, its decline has a stronger impact.
Originality/value
The volatility of bitcoin and the blockchain index is crucial for investors.
Keywords
Citation
Qi, T., Wang, T., Zhu, J. and Bai, R. (2020), "The correlation and volatility between bitcoin and the blockchain index", International Journal of Crowd Science, Vol. 4 No. 2, pp. 103115. https://doi.org/10.1108/IJCS1120190036
Publisher
:Emerald Publishing Limited
Copyright © 2020, Tuotuo Qi, Tianmei Wang, Jianming Zhu and Ruyu Bai.
License
Published in International Journal of Crowd Science – Published by Emerald Publishing Limited. This article is published under the Creative Commons Attribution (CC BY 4.0) license. Anyone may reproduce, distribute, translate and create derivative works of this article (for both commercial and noncommercial purposes), subject to full attribution to the original publication and authors. The full terms of this license may be seen at http://creativecommons.org/licences/by/4.0/legalcode
1. Introduction
The electronic and virtualization of currency has accelerated the development of digital currency and bitcoin has attracted the attention of various industries. On June 18, 2019, the launch of the Libra White Paper, which is Facebook’s encrypted currency, triggered another boom in bitcoin investments. In addition, what worth noting is that blockchain technology is the underlying technology that ensures that bitcoins operate normally (Yuan and Wang, 2016). Blockchain technology combines peertopeer with block technology, enabling people to trust the cooperation between two sides without the supervision of a central authority (He et al., 2017). Blockchain technology has become the goal of enterprise informatization construction, resulting in investors gradually paying close attention to the blockchain concept stocks.
The stocks for businesses with a connection to blockchain are classified as blockchain concept stocks in the stock market. The blockchain index is composed of 50 of the most representative blockchain concept stocks, which not only reflects the overall appearance and operation of blockchain concept stocks but also is used as the scale and standard for investors. Because of the close relationship between the blockchain and bitcoin, we expect that the price fluctuations in bitcoin affect the stock price of the blockchain Index to some extent and vice versa.
This paper explores the correlation between bitcoin and the blockchain index. The demand in the bitcoin market is not affected by macroeconomic development and investment behavior cannot be explained by standard economic and financial theory. Because digital currency is not affected by the basic level of the macroeconomy, the supply function is either fixed or evolved according to an algorithm. Therefore, the price of digital currency is entirely driven by investors’ confidence in its sustainable growth. We expect that the blockchain index may become a crucial variable. Therefore, this paper puts forward the following research questions.
Is there a correlation between the logarithmic yields of bitcoin and the blockchain index?
In fact, bitcoin is mainly used as an asset rather than currency (Baek and Elbeck, 2015; Glaser et al., 2014). Compared with other currencies, the bitcoin market is highly speculative, less stable and more vulnerable when facing speculative bubbles (Cheah and Fry, 2015; Grinberg, 2011). Therefore, unlike other assets in the financial market, bitcoin creates new possibilities for stakeholders in risk management, portfolio analysis and consumer sentiment analysis (Dyhrberg, 2015, 2016). Therefore, studying its volatility is of great significance. In addition, the blockchain index is influenced by the new blockchain technology, making its volatility also worthy of attention.
Prior studies used various GARCH models. However, most such studies on the price fluctuation of bitcoin used a single conditional heteroskedasticity model, which model can better explain the relationship between bitcoin and the blockchain index is not clear. Therefore, this paper compares and analyses various GARCH models to obtain the best one to describe the volatility of bitcoin and the blockchain index. This paper puts forward the following research questions.
How is the volatility of the logarithmic yields of bitcoin and the blockchain index?
This paper studies the relationship between the logarithmic yields of bitcoin and the blockchain index and finds no significant correlation between them. In addition, through an analysis using the GARCH model, we found that external shocks aggravate the volatility of logarithmic yields of bitcoin and the blockchain index, and the volatility has a certain persistence. Additionally, the logarithmic yields of the blockchain index have leverage; namely, the decline of the logarithmic yields of the blockchain index has a stronger impact on the market.
The structure of this paper is as follows. Section 2 summarizes the relevant research literature on the factors affecting the price of bitcoin and the price volatility of bitcoin and blockchain concept stocks. Section 3 puts forward the main research hypothesis on.
2. Literature review
2.1 Literature reviews on influencing factors of bitcoin price
The analysis of bitcoin has received significant recent attention, which can be attributed to its innovation, simplicity, transparency and growing popularity (Urquhart, 2016). A large number of studies explored the relevant factors affecting the price of bitcoin, as shown in Table I. Kristoufek (2013) assumed that the volatility of encrypted currency is not related to basic macroeconomic factors, such as GDP, interest rates and inflation, but to investor sentiment. This result is contrary to the finding in van Wijk (2013), which holds that a significant relationship exists between the price of bitcoin and macroeconomic indicators. A statistically significant twoway relationship exists between bitcoin prices and Google trends, whereas the relationship between Wikipedia and bitcoin is not significant (Kristoufek, 2013). The page views of forum posts and Wikipedia have a significant impact on bitcoin prices (Ciaian et al., 2014). The amount and sentiment of news affect the bitcoin yield (Polasik et al., 2015). Dyhrberg (2015) used the GARCH model and found that the price of bitcoin is similar to that of the dollar and gold, and a significant correlation exists between bitcoin and the federal funds rate. Hayes (2016) applied a least squares regression model and found that the three main driving factors of the encrypted currency price are the competition level of miners, unit output, and the difficulty of encrypted currency mining algorithms. In addition, Bouoiyour and Selmi (2015) use the ADRL boundaries test to determine a series of factors affecting bitcoin trading prices, including the stock market. Moreover, factors such as speculation significantly affect prices during bitcoin trading under certain conditions (Kristoufek, 2014).
2.2 Literature review on bitcoin price volatility
Early literature focused on speculative bubbles related to bitcoin, as indicated in Table II. Cheah and Fry (2015) believed that a speculative bubble exists in the bitcoin market and that the basic price of bitcoin is zero. Kristoufek (2013) believed that the convenience of buying bitcoins and the lack of a need to conduct largescale transactions create the possibility of speculative bubbles. Glaser et al. (2014) used the ARCH and GARCH methods to find that bitcoin was mainly used for speculation and not to buy goods or services. Phillip et al. (2018) found that encrypted currency has the characteristics of long memory, a leverage effect, random fluctuations and thick tails. These results are consistent with the conclusions of Catania et al. (2018), who used the GARCH and GHSKT models and found that encrypted currencies exhibit a long memory and a leverage effect during the process of fluctuations.
2.3 Literature review on blockchain concept stocks
At present, little literature exists on blockchain concept stocks. Duan and Dong (2019) studied the impact of the network heat of blockchain on the volatility of blockchain concept stocks. The results show that the Baidu index of blockchain has a positive correlation with the volatility of blockchain concept stocks. Li and Sun (2018) used the BCCDEA method to measure the inputoutput efficiency of blockchain concept stocks and found that most enterprises have relatively low inputoutput efficiency given inefficient technology or scale. Table III summarizes the relevant literature of the blockchain concept unit.
Therefore, this paper aims to overcome the shortcomings of previous studies. First, considering the natural relationship between bitcoin and blockchain, the bitcoin market may have some influence on blockchain concept stocks. However, no scholars have studied the relationship between the price and volatility of the bitcoin market and blockchain concept stocks. Second, to the best of our knowledge, this study is the first on the volatility of the blockchain index. Because the volatility law of the blockchain index can provide useful guidance for investors, studying it is necessary. Finally, most studies on the volatility of bitcoin and the blockchain index are based on a single model. Therefore, this paper aims to compare the best models to analyze the relationship between bitcoin and the blockchain index. The purpose of this paper is to study the correlation between bitcoin and the blockchain index, as well as the volatility of their respective yields.
3. Research hypothesis
When the price of bitcoin increases or decreases, along with the propaganda effect of the network media, investors in the market for the short term may be highly concerned about some blockchain concept stocks and may affect their yield. For the blockchain sector, the blockchain application industry has been expanding, injecting new ideas into the traditional industry. Therefore, driven by the news of the bitcoin price increase, many investors have gradually begun to pay attention to the blockchain concept and generate speculative demand. However, given the uncertainty of blockchain technology, the news of bitcoin price declines has a negative impact on investors. In contrast, because the blockchain is the underlying technical support for bitcoin, we expect that the rise and fall of the blockchain index will also affect bitcoin price fluctuations. Therefore, the following assumptions are proposed.
A significant correlation exists between bitcoin and blockchain concept stocks.
In addition, external shocks, including the promulgation of policies, will have a strong impact on bitcoin and the blockchain index. For example, “the Notice on Preventing Bitcoin Risk” stipulates that bitcoin cannot and should not be used as a currency in the market, which limits its trading in China and affects the yield of the bitcoin market to a certain extent. Moreover, because of the longterm effectiveness of the policy, we believe that the shock has a sustained impact on the volatility of the bitcoin market. In addition, external shocks, such as blockchain support or control policies, will have the same effect. Therefore, we expect that external shocks will increase the volatility of the logarithmic yields of bitcoin and the blockchain index, and the volatility has a certain sustainability. Therefore, the following assumptions are proposed.
External shocks can exacerbate the volatility of bitcoin and the blockchain index.
External shocks have a sustainable impact on the volatility of bitcoin and the blockchain index.
4. Data source and preprocess
4.1 Data source
This paper takes December 31, 2013 to June 25, 2019, as the time interval and crawls all of the closing price data of the blockchain index. The data on bitcoin trading are similar to data on stock market trading. We also choose the closing price for the sample analysis. To explore the relationship with the blockchain index and compare it to its law of fluctuations, the interval for bitcoinrelated data is the same as that for the blockchain index. The data on the blockchain index and bitcoin are from the Wind database at http://coinmarketcap.com/website
4.2 Data preprocess
First, we drop data on holidays and weekends using the blockchain index as the standard to ensure the consistency and correspondence of the two series. Second, according to the GARCH model, directly using the closing price of bitcoin and the blockchain index is not appropriate. Therefore, this paper adopts the logarithmic difference method to address the closing price data of bitcoin and the blockchain index, that is
5. Data analysis and results
5.1 Basic description
The QQ plot of the logarithmic yields of bitcoin and the blockchain index show that both bitcoin and the blockchain index are not completely distributed on the straight line of the QQ plot (Figures 1 and 2). Therefore, a preliminary consideration is that the series does not conform to the normal distribution. Further, combined with the descriptive statistics of the sample data in Table IV and the histogram of the sample data in Figures 3 and 4, the distribution of the sample data can be preliminarily judged.
Table IV shows that, for a total of 1,335 samples, the skewness of the logarithmic yield series of bitcoin and the blockchain index are −0.385 and −0.448, respectively, indicating that the series has a longleft tail, and the left tail of the blockchain index series is more obvious. The kurtosis of the logarithmic yield series of bitcoin and the blockchain index is 8.549 and 5.420, respectively, indicating that the return series have peaks, and the peak of the bitcoin series is more obvious. Therefore, both series have the characteristics of a peak and a thick tail. In addition, the JarqueBera values were 1745.708 and 370.580, respectively and pvalues of 0.000. Therefore, the hypothesis that the logarithmic yield series of bitcoin and the blockchain index obeys a normal distribution is again rejected.
To more intuitively observe the fluctuation of bitcoin and the blockchain index over time, the fluctuation diagram is used for further analysis. Figure 5 indicates that the fluctuations of the logarithmic yield series display a “clustering” phenomenon, namely, alternating high and low fluctuations occur and last for a while.
5.2 Volatility relationships test
First, we observe the trend diagram of the closing price of bitcoin and the blockchain index (Figure 6). Combined with the original data, we observe that the closing price of bitcoin has been increasing continuously since January 2014, reaching its highest point on December 18, 2017, and then declined rapidly until 2019. The closing price of the blockchain index has been rising since January 2014, reached its peak on June 12, 2015, and then declined. Then, by observing the scatter plot of the logarithmic yields of bitcoin and the blockchain index (as shown in Figure 7), we find that no obvious relationship exists between these two variables.
Therefore, a preliminary determination is that a weak correlation exists between the two series; however, the relationship between the volatility of bitcoin and the blockchain index cannot be clearly observed in the figure. To test the causality between bitcoin and the blockchain index and to avoid a false regression, we use the Augmented Dickey–Fuller (ADF) method to test the stationarity of the logarithmic yield series of bitcoin and the blockchain index.
5.2.1 Stationarity test.
To avoid the pseudoregression problem, this paper uses the ADF method to test the stationarity of the logarithmic yield series of bitcoin and the blockchain index. The results are indicated in Table V. The tstatistics of the logarithmic yield series of bitcoin and the blockchain index are found to be −35.434 and −32.939, respectively. The pvalues are both 0; therefore, the series all satisfy the characteristics of stationarity. Therefore, bitcoin and the blockchain index series passed the stationarity test and can be further modeled and analyzed.
5.2.2 Granger causality test of series.
In this paper, the Granger causality test is used to explore the correlation, and the results are shown in Table VI. Table VI shows that no twoway Granger causality exists between bitcoin and the blockchain index. In other words, the bitcoin trend does not have a guiding effect on the blockchain index, and vice versa. Therefore, hypothesis H1 is rejected.
5.3 Construction of GARCHclass model
5.3.1 ARCH test.
First, in this paper, the ARCH effect is tested. Table VII shows that the autocorrelation coefficient AC and partial correlation coefficient PAC of the logarithmic yield of bitcoin and the blockchain index are not zero, indicating that the series have the ARCH effect. Therefore, the GARCHclass model can be established.
5.3.2 Construction of GARCHclass model.
Because ARCH effects exist, the GARCH model is used for further analysis. The commonly used GARCHclass models include the GARCH, EGARCH and TGARCH models. In this paper, three GARCHclass models are selected to build the model, and the specific formulas are provided in Table VIII.
By using Eviews, the GARCH (1,1), EGARCH (1,1) and TGARCH (1,1) models of bitcoin and the blockchain index are established, respectively. The parameters of each GARCH model are provided in Table IX.
We choose the optimal model of the bitcoin and the blockchain index series. Table IX shows the estimated results of the GARCHclass model based on two selection criteria, namely, AIC and Hannan–Quinn (HQ). Table IX shows that the AIC and HQ values of the EGARCH model are the smallest for the bitcoin logarithmic yield series, and each parameter is significant at the 1 per cent level. Therefore, the EGARCH model is chosen as the best one to describe the volatility of the bitcoin logarithmic yield. For the logarithmic yield series of the blockchain index, the AIC and HQ values of the EGARCH model are smaller, and the parameters of the EGARCH model are significant at the 1 per cent level. We also choose the EGARCH model to describe the volatility of the logarithmic yield of the blockchain index.
In addition, the results in Table IX indicate that for bitcoin and the blockchain index, the parameters of the EGARCH model are significant, which indicates that both bitcoin and the blockchain index series have leverage. In addition, the ARCH and GARCH parameters in the GARCH model are significant. The coefficients of ARCH are 0.150 and 0.063, and the coefficients of GARCH are 0.788 and 0.921, respectively. Both are positive, which satisfies the conditions of greater than zero, and the sum of α and β are less than 1. The ARCH coefficient α is greater than zero, indicating that external shocks aggravate the fluctuations in the logarithmic yield of bitcoin and the blockchain index, and these fluctuations have a strong impact. Therefore, hypothesis H2a is accepted. The GARCH coefficient β is less than 1, indicating that the fluctuations in the logarithmic yield of bitcoin and the blockchain index persist. Therefore, hypothesis H2b is accepted.
5.3.3 ARCHLM test.
The ARCHLM test is carried out on the residual series of the fitted bitcoin and the blockchain index to test the fitting effect of the EGARCH model. Take the lag of order 12 as an example. The results, shown in Table X, indicate that the Fstatistics of bitcoin and the blockchain index are not significant. Therefore, the EGARCH model has no ARCH effect.
6. Conclusions and discussions
6.1 Conclusions
First, this paper uses the Granger causality test to explore the correlation between bitcoin and the logarithmic yield of the blockchain index. Interestingly, the results of this study show that no significant correlation exists between bitcoin and the blockchain index, which does not support H1. This result indicates that although bitcoin is closely related to the blockchain index, the price trends of blockchain concept stocks in the bitcoin and stock markets are almost independent of each other – neither dominates the price trends of the other side. This lack of domination may be the result of the different influencing factors of investment decision making between the bitcoin market and the stock market. First, for blockchain concept stocks, the potential return on investment depends partly on the degree of application and implementation of blockchain technology and the development potential of enterprises. Second, because investments in blockchain concept stocks are at the enterprise level, investors need to have more comprehensive information to evaluate the returns and losses.
Second, this paper engages in a descriptive statistical analysis on the closing price series and logarithmic yield series of bitcoin and the blockchain index. The results make the following points.
The closing prices of bitcoin and the blockchain index fluctuate sharply, indicating that certain risks exist in the investment of bitcoin and blockchain concept stocks and, thus, investors should increase the awareness of risk prevention.
Heteroskedasticity and the characteristics of peak, a thick tail and agglomeration exist in the logarithmic yield series of bitcoin and the blockchain index, indicating that risk does not significantly affect this logarithmic yield.
Finally, the GARCHclass model is constructed to analyze the volatility of the logarithmic yield series of bitcoin and the blockchain index. The results make the following points. For both bitcoin and the blockchain index, the EGARCH model is the best one. In addition, by constructing the GARCH model, we find that external shocks aggravate the volatility of the logarithmic return of bitcoin and the blockchain index, and the volatility has a certain persistence. We accept the assumptions of H2a and H2b. By analyzing the EGARCH model, we find that the logarithmic yield series of the blockchain index has obvious leverage characteristics.
6.2 Discussion
At present, bitcoin fluctuates sharply, and its main demand is speculation. In addition, the decentralization of bitcoin makes effectively monitoring it difficult, and the investment risk increases accordingly. Therefore, investors need to be cautious about investing in the bitcoin market.
In addition, the application of blockchain technology in blockchain concept stocks is not yet mature. However, we predict that the investment value of blockchain concept stocks will be enhanced as blockchain technology matures. The enterprises represented by blockchain concept stocks deserve continuous attention. Therefore, although the blockchain concept stocks are rising well, they are not suitable for catching up with high positions. The investment opportunities should be judged by the maturity of medium and longterm technology, the driving force and the degree of benefit of the relevant enterprises.
Importantly, a threshold also exists for “blockchain concept stocks.” From bitcoin to blockchain, many public investors begin to invest in blockchain concept stocks before they have a clear understanding of them. Because blockchain is not the same as bitcoin, investors need to clarify the two concepts and rationally address the price trends in the two markets.
Figures
Literature review on influencing factors of bitcoin price
Author (Year)  Influencing factors  Main conclusions 

Kristoufek (2013)  Investor sentiment  A statistically significant twoway relationship exists between bitcoin prices and Google trends, whereas the relationship between Wikipedia and bitcoin is not significant 
van Wijk (2013)  Macroeconomic development indicators  A significant correlation exists between the price of bitcoin and macroeconomic indicators 
Ciaian et al. (2014)  Page view of forum posts and Wikipedia  The page views of forum posts and Wikipedia have a significant impact on bitcoin prices 
Polasik et al. (2015)  Amount and sentiment of news  The amount and sentiment of news affect the bitcoin yield 
Dyhrberg (2015)  Gold, dollar, federal funds rate  The price of bitcoin is similar to that of the dollar and gold, and a significant correlation exists between the price of bitcoin and the federal funds rate 
Hayes (2016)  Technical factors  The competition level of miners, unit output and the difficulty of encrypted currency mining algorithms affect the price of encrypted currency 
Bouoiyour and Selmi (2015)  Stock market, etc.  Factors such as the stock market influence the price of bitcoin 
Kristoufek (2014)  Speculation, etc.  Factors such as speculation have a significant impact on the bitcoin trading price under certain conditions 
Literature review on bitcoin price volatility
Author (Year)  Main conclusions 

Cheah and Fry (2015)  A speculative bubble exists in the bitcoin market, and the basic price of bitcoin is zero 
Kristoufek (2013)  The convenience of buying bitcoins and the lack of a need for largescale transactions have created the possibility of speculative bubbles 
Glaser et al. (2014)  Bitcoin is mainly used for speculation and not to buy goods or services 
Phillip et al. (2018)  Encrypted currency has the characteristics of a long memory, a leverage effect, random fluctuations, and a thick tail 
Catania et al. (2018)  Encrypted currency has a long memory and a leverage effect during the process of fluctuations 
Literature review on bitcoin price volatility
Author (Year)  Main conclusions 

Duan and Dong (2019)  The Baidu index of blockchain is positively correlated with the volatility of blockchain concept stocks 
Li and Sun (2018)  For the majority of enterprises, uneconomic scale and inefficient technology or scale are the main reasons for the relatively low inputoutput efficiency 
Descriptive statistical results of bitcoin and the blockchain index
Basic indicators  Logarithmic yields of bitcoin  Logarithmic yields of blockchain index 

Sample size  1,335  1,335 
Mean  0.001  0.001 
Mean  0.002  0.001 
Max  0.225  0.111 
Min  −0.238  −0.105 
Standard deviation  0.042  0.028 
Skewness  −0.385  −0.448 
Kurtosis  8.549  5.420 
JarqueBera Statistic  1,745.708***  370.580*** 
*** Indicates significant at the 1% level
ADF Test results of bitcoin and the blockchain index series
1%level  5%level  10%level  tstatistic  ADF  

bitcoin  −3.435  −2.863  −2.568  −35.434  0.000 
blockchain index  −3.435  −2.863  −2.568  −32.939  0.000 
Granger causality test results of logarithmic yield of bitcoin and the blockchain index
Lagged Rank  Bitcoin is not the Granger reason of blockchain index  Blockchain index is not the Granger reason for Bitcoin  

Fstat  pvalue  Fstat  pvalue  
Firstorder  0.29064  0.5899  1.09042  0.2966 
Secondorder  0.31709  0.7283  0.53833  0.5838 
Thirdorder  0.76134  0.5158  1.59780  0.1881 
Fourthorder  0.54558  0.7023  1.53877  0.1885 
Fifthorder  0.72259  0.6065  1.26486  0.2766 
Sixthorder  0.68656  0.6606  1.09871  0.3609 
Seventhorder  0.68477  0.6851  1.05751  0.3889 
Eighthorder  0.83566  0.5711  0.93679  0.4848 
ARCH test results of logarithmic yield of bitcoin and the blockchain index
Bitcoin  AC  PAC  QStat  Prob  Blockchain index  AC  PAC  QStat  Prob 

1  0.029  0.029  1.112  0.292  1  0.102  0.102  13.917  0 
2  −0.032  −0.033  2.4991  0.287  2  0.052  0.043  17.604  0 
3  0.018  0.02  2.9548  0.399  3  0.08  0.072  26.233  0 
4  0.062  0.059  8.0386  0.09  4  0.008  −0.009  26.314  0 
5  −0.036  −0.039  9.8004  0.081  5  0.008  0.001  26.396  0 
6  −0.013  −0.007  10.015  0.124  6  0.024  0.018  27.184  0 
7  −0.022  −0.026  10.677  0.153  7  0.03  0.026  28.372  0 
8  −0.013  −0.015  10.907  0.207  8  0.054  0.047  32.272  0 
9  0.003  0.007  10.918  0.281  9  −0.034  −0.05  33.857  0 
10  0.009  0.009  11.028  0.355  10  −0.059  −0.06  38.471  0 
11  −0.032  −0.029  12.372  0.336  11  0.078  0.088  46.736  0 
12  0.003  0.005  12.381  0.416  12  −0.01  −0.015  46.864  0 
Formulas of GARCHclass model
GARCHclass model  Formulas 

GARCH 

EGARCH 

TGARCH 

Estimation results of logarithmic yield of bitcoin and the blockchain index by GARCHclass model
Parameters  Bitcoin GARCHclass model  Blockchain index GARCHclass model  

GARCH  EGARCH  TGARCH  GARCH  EGARCH  TGARCH  
Const(ω)  0.000*** (0.000)  −0.860*** (0.067)  0.000*** (0.000)  0.000*** (0.000)  −0.221***(0.034)  0.000*** (0.000) 
ARCH(α)  0.150*** (0.014)  0.303*** (0.020)  0.145*** (0.018)  0.063*** (0.009)  0.139*** (0.018)  0.054*** (0.010) 
GARCH(β)  0.788*** (0.015)  0.899*** (0.009)  0.785*** (0.016)  0.921*** (0.010)  0.984*** (0.004)  0.917*** (0.010) 
EGARCH(δ)  –  −0.030*** (0.012)  –  –  −0.033***(0.010)  – 
TGARCH(γ)  –  –  0.010 (0.020)  –  –  0.029**(0.013) 
LL  2,456.616  2,467.650  2,456.662  3,055.453  3,067.586  3,057.114 
AIC  −3.676  −3.691  −3.674  −4.573  −4.590  −4.574 
HQ  −3.671  −3.685  −3.669  −4.569  −4.584  −4.568 
Formulas of GARCHclass model
Bitcoin  Blockchain index  

Fstatistic  0.384  0.403 
Prob. F (1, 1332)  0.970  0.963 
Obs * R^{2}  4.638  4.861 
Prob. Chisquare(1)  0.969  0.963 
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Acknowledgements
This work was supported by the National Key Research and Development Plan of China: Research on Fundamental Theories and Methods of Crowd Science (2017YFB1400100) and the Research Base Project of Beijing Social Science Foundation: Research on the Mechanism and Effectiveness of Public Network Participation in Public Decisionmaking (18JDGLB020).