# Bitcoin as a Safe Haven during COVID-19 Disease
## 3 Data and Methods
### Results
#### 3.2.2 DCC Model Results: Dynamic Conditional Correlations  
Before proceeding with the results analysis of the DCC model let us describe all the performed tests and analyses to resolve such a model. First of all we performed normality tests to confirm that the returns were non-normal and heteroscedastic data needed to be handled through GARCH models. Specifically, the Henze-Zirkler test, which is a multivariate normality test, and the Anderson-Darling test, which is a univariate normality test, were run. Both the first test statistics on the entire sample and the second test statistics on the univariate series concluded that the null hypothesis was rejected. So both the univariate samples and the multivariate sample are not normally distributed as expected from the financial time series. In addition, a test to evaluate the presence of a dynamic structure in the correlations was performed. The test confirmed the presence of a dynamic structure, so a DCC-GARCH model was estimated. The DCC-GARCH model chosen was a DCC-eGARCH(1,1), where eGARCH stands for exponentional GARCH. In this model the volatility is computes as follows:  
\[ln(h_{t})=\omega+\beta ln(h_{t-1})+\alpha\left(\frac{|\epsilon_{t-i}|}{\sqrt{h _{t-1}}}-\sqrt{\frac{2}{\pi}}\right)+\gamma\frac{\epsilon_{t-1}}{\sqrt{h_{t- 1}}})). \tag{4}\]  
The choice was based on the AIC and BIC scores varying the order of the ARMA-GARCH model and the type of GARCH model. For the DCC-eGARCH(1,1) model the most of the parameters are significant, therefore we can conclude that the chosen model accurately captures both the univariate structure of the indexes and their interactions (see Table 9). \begin{table}
\begin{tabular}{c c c c c} \hline  & **Estimate** & **Std. Error** & **t Value** & **Pr (>|t|)** \\ \hline \([000002.SS].\omega\) & \(-1.542860\) & \(1.443807\) & \(-1.0686\) & \(0.285248\) \\ \([000002.SS].\alpha 1\) & \(-0.068448\) & \(0.128806\) & \(-5.3141\times 10^{-1}\) & \(0.595138\) \\ \([000002.SS].\beta 1\) & \(0.819270\) & \(0.167389\) & \(4.8944\) & \(0.000001\) \\ \([000002.SS].\gamma 1\) & \(0.493105\) & \(0.295964\) & \(1.6661\) & \(0.095693\) \\ \([EUFN].\omega\) & \(-0.245042\) & \(0.096110\) & \(-2.5496\) & \(0.010785\) \\ \([EUFN].\beta 1\) & \(-0.107970\) & \(0.056476\) & \(-3.0241\) & \(0.002494\) \\ \([EUFN].\beta 1\) & \(0.966439\) & \(0.012148\) & \(7.9557\times 10^{1+1}\) & \(0.000000\) \\ \([EUFN].\gamma 1\) & \(0.234274\) & \(0.052733\) & \(4.4426\) & \(0.000009\) \\ \([IPAC].\omega\) & \(-0.210337\) & \(0.068830\) & \(-3.0559\) & \(0.002244\) \\ \([IPAC].\alpha 1\) & \(-0.125786\) & \(0.049631\) & \(-2.5344\) & \(0.011264\) \\ \([IPAC].\beta 1\) & \(0.974251\) & \(0.007748\) & \(1.2574\times 10^{+2}\) & \(0.000000\) \\ \([IPAC].\gamma 1\) & \(0.262762\) & \(0.082990\) & \(3.1662\) & \(0.001545\) \\ \([DX-\gamma.NYB].\omega\) & \(-0.059457\) & \(0.027381\) & \(-2.1714\) & \(0.029897\) \\ \([DX-\gamma.NYB].\omega 1\) & \(-0.041247\) & \(0.024270\) & \(-1.6995\) & \(0.089231\) \\ \([DX-\gamma.NYB].\beta 1\) & \(0.994205\) & \(0.002453\) & \(4.0529\times 10^{+2}\) & \(0.000000\) \\ \([DX-\gamma.NYB].\gamma 1\) & \(0.177653\) & \(0.034066\) & \(5.2149\) & \(0.000000\) \\ \([GC=F].\omega\) & \(-1.470428\) & \(0.828544\) & \(-1.7747\) & \(0.075945\) \\ \([GC=F].\alpha 1\) & \(0.104286\) & \(0.088503\) & \(1.1783\) & \(0.238664\) \\ \([GC=F].\beta 1\) & \(0.824632\) & \(0.097232\) & \(8.4811\) & \(0.000000\) \\ \([GC=F].\gamma 1\) & \(0.525887\) & \(0.192437\) & \(2.7328\) & \(0.006280\) \\ \hline \end{tabular}
\end{table} 
Table 9: Optimal parameters. To confirm that the chosen DCC-eGARCH(1,1) model accurately captured the interactions among the indexes, the Weighted Ljung-Box test on standardized residuals and on standardized squared residuals of the estimated univariate GARCH(1,1) models was executed. The tests' statistics confirm that the residuals and squared residuals are uncorrelated. All the p-values are greater than 0.05, so the null hypothesis of no serial correlation is never rejected (results are available upon request).