## 5 Results and Discussion  
The method proposed enables us to estimate the alpha values, which can be shown here as indicators of volatility. The higher these parameters are, the higher the volatility is. As explained above, once the value for alpha is obtained, it is easy to run simulations and obtain the full distribution of the number of flights per hour and per country analysed. In \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{6}{c}{**Dependent Variable: Number of Flights**} \\ \hline  & **Beta** & **Coefficient** &
\begin{tabular}{c} **Standard** \\ **Deviation** \\ \end{tabular} & **z Value** & \(p\) Value** & **Significance** \\ \hline \(\beta_{1}\) & Constant & 5.563280 & 0.003409 & 1632 & \(<\)0.0001 & *** \\ \(\beta_{2}\) & Trend & 0.030876 & 0.000680 & 45.43 & \(<\)0.0001 & *** \\ \(\beta_{3}\) & Yearly cycle & \(-\)0.0628108 & 0.001338 & \(-\)46.93 & \(<\)0.0001 & *** \\ \(\beta_{4}\) & Yearly cycle & \(-\)0.185169 & 0.001478 & \(-\)125.3 & \(<\)0.0001 & *** \\ \(\beta_{5}\) & Yearly cycle & 0.040903 & 0.001338 & 3.664 & 0.0002 & *** \\ \(\beta_{6}\) & Yearly cycle & \(-\)0.0252754 & 0.001390 & \(-\)18.18 & \(<\)0.0001 & *** \\ \(\beta_{7}\) & Yearly cycle & 0.021829 & 0.001334 & 16.36 & \(<\)0.0001 & *** \\ \(\beta_{8}\) & Yearly cycle & \(-\)0.00780915 & 0.001389 & \(-\)5.621 & \(<\)0.0001 & *** \\ \(\beta_{10}\) & Yearly cycle & 0.011339 & 0.001382 & 8.206 & \(<\)0.0001 & *** \\ \(\beta_{11}\) & Yearly cycle & \(-\)0.0123824 & 0.001351 & \(-\)9.167 & \(<\)0.0001 & *** \\ \(\beta_{12}\) & Yearly cycle & \(-\)0.00649979 & 0.001367 & \(-\)4.754 & \(<\)0.0001 & *** \\ \(\beta_{13}\) & Weekly cycle & 0.066178 & 0.003786 & 17.48 & \(<\)0.0001 & *** \\ \(\beta_{14}\) & Weekly cycle & 0.060554 & 0.003828 & 15.82 & \(<\)0.0001 & *** \\ \(\beta_{15}\) & Weekly cycle & 0.093100 & 0.003728 & 24.97 & \(<\)0.0001 & *** \\ \(\beta_{16}\) & Weekly cycle & 0.099576 & 0.003777 & 26.36 & \(<\)0.0001 & *** \\ \(\beta_{17}\) & Weekly cycle & 0.122761 & 0.003790 & 32.39 & \(<\)0.0001 & *** \\ \(\beta_{18}\) & Weekly cycle & \(-\)0.0478952 & 0.003816 & \(-\)12.55 & \(<\)0.0001 & *** \\ \(\beta_{19}\) & Daily cycle & \(-\)0.366208 & 0.001467 & \(-\)249.7 & \(<\)0.0001 & *** \\ \(\beta_{20}\) & Daily cycle & \(-\)0.979481 & 0.001491 & \(-\)656.9 & \(<\)0.0001 & *** \\ \(\beta_{21}\) & Daily cycle & \(-\)0.436885 & 0.001492 & \(-\)292.8 & \(<\)0.0001 & *** \\ \(\beta_{22}\) & Daily cycle & \(-\)0.429011 & 0.001464 & \(-\)293.1 & \(<\)0.0001 & *** \\ \(\beta_{23}\) & Daily cycle & \(-\)0.242307 & 0.001535 & \(-\)157.8 & \(<\)0.0001 & *** \\ \(\beta_{24}\) & Daily cycle & \(-\)0.111641 & 0.001407 & \(-\)79.33 & \(<\)0.0001 & *** \\ \(\beta_{25}\) & Daily cycle & \(-\)0.0974446 & 0.001428 & \(-\)68.23 & \(<\)0.0001 & *** \\ \(\beta_{26}\) & Daily cycle & \(-\)0.00667475 & 0.001485 & \(-\)4.494 & \(<\)0.0001 & *** \\ \(\beta_{27}\) & Daily cycle & 0.009193 & 0.001274 & 7.218 & \(<\)0.0001 & *** \\ \(\beta_{28}\) & Daily cycle & 0.003709 & 0.001525 & 2.432 & 0.015 & ** \\ alpha & 0.038011 & 0.000587 & 64.7 & \(<\)0.0001 & *** \\ \hline \hline \end{tabular} Note: Asterisks denote significance at the following levels: *** 0.1%; ** 1% standard deviations QML.  
\end{table} 
Table 4: Negative binomial parameters for Germany. addition, correlations can be estimated between the numbers of flights in different countries in an effort to better understand the interrelationship of airspaces at given times. For the following calculations, Equation (6) is used. This is a reduced version of Equation (1), where the weekly cycle is erased and calculations are performed per hour. This enables an alpha value to be calculated for each hour and country. However, note that the method proposed can be used with a higher level of disaggregation for each country, hour and day of the week and even for other time periods such as months. \[E(Y|X)=\exp(\beta_{1}+\beta_{2}t+AC(t)+DC(t))=\mu \tag{6}\]  
Table 5 presents the values for Belgium as an illustration. The values for the other countries are shown in Appendix A.