# Bitcoin as a Safe Haven during COVID-19 Disease
## 3 Data and Methods
### Regression and DCC Model  
Following the regression models proposed by [PERSON] (2007) and [PERSON] et al. (2016), we defined a multiple regression model with a dummy variable, called \"Covid\", equal to 1 in the _event windows_ described in the previous sections. The model is the following:  
\[retCrypto(t)=a_{0}+(b_{0}+b_{1}Covid)*Vol(t)+\\ \sum_{i}[(c_{0,i}+c_{1}Covid)*retIndex_{i}(t)]+\\ d_{0}retCrypto(t-1)+e_{0}Vol(t-1)+\sum_{i}[f_{0,i}retIndex_{i}(t-1)]+ \epsilon(t) \tag{1}\]  
where  
* \(retCrypto\) represents the daily Bitcoin/Ether returns;
* \(Vol\) represents the volatility in the FX market. It is the average daily volatility across the three currency pair _EUR-USD_, _IPY-USD_, _GBP-USD_ as in work (2016), (Let us underline \begin{table}
\begin{tabular}{l r r r r r r r r} \hline  & **retBTC** & **retETH** & **retDAX** & **retGSC** & **retFTSE** & **retN225** & **retSS** & **retMWL** \\ \hline mean & 0.002705 & 0.003129 & 0.000265 & 0.000450 & \(-\)0.000221 & 0.000543 & 0.000347 & 0.000317 \\ std & 0.039739 & 0.050453 & 0.015741 & 0.014854 & 0.012917 & 0.011302 & 0.009361 & 0.014131 \\ min & \(-\)0.464730 & -0.550732 & \(-\)0.120154 & \(-\)0.127652 & \(-\)0.115117 & \(-\)0.062736 & \(-\)0.080343 & \(-\)0.120786 \\
25\% & \(-\)0.013128 & \(-\)0.017409 & \(-\)0.001918 & \(-\)0.001468 & \(-\)0.003025 & \(-\)0.002149 & \(-\)0.001755 & \(-\)0.000990 \\
50\% & 0.001331 & 0.001802 & 0.00000 & 0.00000 & 0.00000 & 0.00000 & 0.00000 & 0.000000 \\
75\% & 0.017542 & 0.026513 & 0.005442 & 0.004696 & 0.003396 & 0.003434 & 0.003135 & 0.004058 \\ max & 0.171821 & 0.230695 & 0.092150 & 0.089683 & 0.086664 & 0.077314 & 0.055535 & 0.087061 \\ kurtosis & 33.512346 & 25.807796 & 15.162256 & 20.116052 & 17.408403 & 10.062584 & 13.570148 & 23.031934 \\ skewness & \(-\)2.479123 & \(-\)2.264091 & \(-\)1.426191 & \(-\)1.188401 & \(-\)1.338449 & 0.281258 & \(-\)1.123514 & \(-\)1.690548 \\ \hline \end{tabular}
\end{table} 
Table 1: Return statistics. \begin{table}
\begin{tabular}{l r r r r r r r} \hline  & **retEUFN** & **retIPAC** & **retDX** & **retGD** & **retBND** & **retBZ** & **retGC** \\ \hline mean & 0.000009 & 0.000319 & \(-\)0.000124 & 0.000031 & 0.000092 & \(-\)0.000234 & 0.00040 \\ std & 0.019565 & 0.012227 & 0.003238 & 0.015295 & 0.003994 & 0.031627 & 0.009929 \\ min & \(-\)0.162119 & \(-\)0.111030 & \(-\)0.016262 & \(-\)0.127625 & \(-\)0.055920 & \(-\)0.279761 & \(-\)0.051069 \\
25 \% & \(-\)0.003926 & \(-\)0.001580 & \(-\)0.001323 & \(-\)0.001786 & \(-\)0.000343 & \(-\)0.004974 & \(-\)0.001366 \\
50\% & 0.000000 & 0.000000 & 0.000000 & 0.000000 & 0.000000 & 0.000000 & 0.000000 \\
75\% & 0.004352 & 0.003943 & 0.000953 & 0.003769 & 0.000953 & 0.006553 & 0.004037 \\ max & 0.113003 & 0.072607 & 0.015786 & 0.073011 & 0.041335 & 0.190774 & 0.057775 \\ kurtosis & 20.573739 & 22.246038 & 5.062571 & 21.876907 & 89.795265 & 25.313214 & 8.024764 \\ skewness & \(-\)1.757299 & \(-\)1.690733 & 0.432049 & \(-\)2.033562 & \(-\)3.179314 & \(-\)1.577847 & \(-\)0.249648 \\ \hline \end{tabular}
\end{table} 
Table 2: Return statistics. that as a measure of volatility for each currency pair we computed the logarithmic returns and then we applied the moving standard deviation calculated using the rolling method of a pandas DataFrame with a window equal to five days as in [23]);
* \(r_{i}\) represents the returns of the \(i\)-th index, with \(i\) varying from 1 to 13, that is the number of indexes downloaded from the Yahoo finance website as already described (\(i=1\) for \(retGSP\), \(i=2\) for \(retDAX\), \(i=3\) for \(retTSE\), \(i=4\) for \(retN225\), \(i=5\) for \(retSS\), \(i=6\) for \(retURTH\), \(i=7\) for \(retEUFN\), \(i=8\) for \(retDAC\), \(i=9\) for \(retDX\), \(i=10\) for \(retGD\), \(i=11\) for \(retBND\), \(i=12\) for \(retBZ\), and \(i=13\) for \(retGC\)). * _Covid_ is an indicator variable for days in the sample that correspond to the days within the _event window_. This is a multiple regression model in which Bitcoin/Ether returns (\(retBTC(t)/retETH\)) represent our dependent variable.