## 5 Results
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \(A_{4}\) & \(D_{1}\) & \(D_{2}\) & \(D_{3}\) & \(D_{4}\) \\ \hline
3.5860 & 0.0040 & 0.0065 & \(-\)0.0023 & 0.0700 \\
3.5754 & \(-\)0.0054 & 0.0013 & 0.0038 & 0.0589 \\
3.5577 & 0.0023 & \(-\)0.0063 & 0.0101 & 0.0436 \\
3.5407 & \(-\)0.0007 & \(-\)0.0086 & 0.0162 & 0.0246 \\
3.5288 & 0.0012 & \(-\)0.0017 & 0.0209 & 0.0035 \\
3.5121 & \(-\)0.0021 & 0.0039 & 0.0207 & \(-\)0.0158 \\
3.4874 & 0.0026 & 0.0038 & 0.0141 & \(-\)0.0307 \\
3.4623 & \(-\)0.0023 & 0.0031 & 0.0026 & \(-\)0.0406 \\
3.4390 & 0.0010 & 0.0017 & \(-\)0.0113 & \(-\)0.0452 \\
3.4203 & \(-\)0.0003 & \(-\)0.0006 & \(-\)0.0224 & \(-\)0.0473 \\
3.4102 & \(-\)0.0002 & \(-\)0.0016 & \(-\)0.0267 & \(-\)0.0485 \\
3.4078 & 0.0022 & \(-\)0.0031 & \(-\)0.0253 & \(-\)0.0474 \\
3.4128 & \(-\)0.0028 & \(-\)0.0049 & \(-\)0.0191 & \(-\)0.0435 \\
3.4281 & 0.0019 & \(-\)0.0027 & \(-\)0.0095 & \(-\)0.0372 \\
3.4513 & \(-\)0.0013 & 0.0032 & 0.0012 & \(-\)0.0282 \\
3.4756 & \(-\)0.0056 & 0.0071 & 0.0131 & \(-\)0.0179 \\
3.4955 & 0.0145 & 0.0061 & 0.0241 & \(-\)0.0068 \\
3.5077 & \(-\)0.0077 & 0.0012 & 0.0284 & 0.0066 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Four-level wavelet decomposition of \(V_{6}\). \begin{table}
\begin{tabular}{c c c c c} \hline \hline \(A_{4}\) & \(D_{1}\) & \(D_{2}\) & \(D_{3}\) & \(D_{4}\) \\ \hline
0.5827 & \(-\)0.0027 & \(-\)0.0051 & 0.0128 & \(-\)0.0564 \\
0.5908 & 0.0032 & 0.0004 & 0.0064 & \(-\)0.0523 \\
0.6045 & \(-\)0.0005 & 0.0056 & 0.0004 & \(-\)0.0450 \\
0.6199 & \(-\)0.0009 & 0.0086 & \(-\)0.0068 & \(-\)0.0343 \\
0.6336 & 0.0004 & 0.0066 & \(-\)0.0144 & \(-\)0.0216 \\
0.6481 & 0.0009 & 0.0006 & \(-\)0.0174 & \(-\)0.0100 \\
0.6658 & \(-\)0.0018 & \(-\)0.0066 & \(-\)0.0138 & \(-\)0.0014 \\
0.6895 & 0.0015 & \(-\)0.0101 & \(-\)0.0049 & 0.0035 \\
0.7196 & \(-\)0.0006 & \(-\)0.0072 & 0.0071 & 0.0051 \\
0.7472 & \(-\)0.0002 & \(-\)0.0027 & 0.0154 & 0.0058 \\
0.7682 & 0.0018 & 0.0021 & 0.0155 & 0.0073 \\
0.7888 & \(-\)0.0018 & 0.0120 & 0.0105 & 0.0086 \\
0.8050 & \(-\)0.0030 & 0.0211 & 0.0031 & 0.0093 \\
0.8002 & 0.0028 & 0.0092 & \(-\)0.0032 & 0.0098 \\
0.7798 & 0.0042 & \(-\)0.0209 & \(-\)0.0048 & 0.0097 \\
0.7826 & 0.0064 & \(-\)0.0286 & \(-\)0.0046 & 0.0100 \\
0.8167 & \(-\)0.0277 & \(-\)0.0039 & \(-\)0.0044 & 0.0108 \\
0.8391 & 0.0149 & 0.0119 & \(-\)0.0039 & 0.0103 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Four-level wavelet decomposition of \(V_{7}\). Figure 3: The wavelet decomposition of the variable \(V_{3}\) at the level 4. Figure 2: The wavelet decomposition of the variable \(V_{2}\) at the level 4. Figure 4: The wavelet decomposition of the variable \(V_{4}\) at the level 4. Figure 5: The wavelet decomposition of the variable \(V_{5}\) at the level 4. Figure 6: The wavelet decomposition of the variable \(V_{6}\) at the level 4. Figure 7: The wavelet decomposition of the variable \(V_{7}\) at the level 4. Next, as the components of our sample are completed and the sample has now no missing values, we provide the resulting quality of life index HDI issued from the model (5). The values are provided in Table 10 below. Figure 9 illustrates graphically the behavior of the quality of life index HDI and provides thus a graphical comparison between the real values and the one due to our wavelet multiscale model (5). \begin{table}
\begin{tabular}{c c c c c} \hline \hline \(\mathbf{HD_{0}}\) & \(\mathbf{HD_{1}}\) & \(\mathbf{HD_{2}}\) & \(\mathbf{HD_{3}}\) & \(\mathbf{HD_{4}}\) \\ \hline  
0.0008\) & \(0.0013\) & \(-0.0071\) & \(0.0034\) \\ \hline \hline \end{tabular}
\end{table} 
Table 10: The \(HDI\) index, real and time-scale model (5). Figure 8: The wavelet decomposition of the variable \(V_{8}\) at the level 4.