## Appendix C  
The system of equations in structural form:  
\[\left\{ \begin{array}{l}Y_{1}^{1}\ =\ c_{5}^{2}*Y_{1}^{5}+c_{4}^{1}*X_{t}^{4}+c_{6}^{1}*X_{ t}^{6}+a_{1}^{1}*Y_{1-1}^{1}\\ Y_{1}^{2}\ =\ d_{4}^{2}*X_{t}^{4}+d_{6}^{2}*X_{t}^{6}+c_{1}^{1}*Y_{1-1}^{1}\\ Y_{t}^{3}\ =\ d_{5}^{3}*X_{t}^{2}+d_{5}^{5}*X_{t}^{6}+a_{6}^{2}*Y_{1}^{5}+b_{3}^{3}*Y_{1 -1}^{3}\\ Y_{t}^{4}\ =\ b_{4}^{4}*Y_{t}^{5}+d_{6}^{3}*X_{t}^{5}+b_{3}^{4}*Y_{t-1}^{4}\\ Y_{t}^{5}\ =\ c_{3}^{5}*Y_{t}^{3}+d_{6}^{5}*X_{t}^{6}\\ Y_{t}^{6}\ =\ d_{4}^{6}*X_{t}^{5}\end{array} \right. \tag{1}\]  
\(a_{j}^{i}\), \(b_{j}^{i}\), \(c_{j}^{i}\), \(d_{j}^{i}\) (\(i=\overline{1.6}\), \(j=\overline{1.6}\)) are the structural form coefficients. The transition from the structural form to the reduced form has been made. A transition means several iterations, as a result of which \(\mathbf{Y}_{t}^{i}\) will not remain on the right side of the equations. The system of equations in the reduced form. \[\left\{\begin{array}{l}Y_{1}^{1}\ =\ j_{1}^{1}*X_{t}^{6}+j_{1}^{2}*Y_{1-1}^{5}+c_{ 6}^{1}*X_{t}^{6}+c_{2}^{2}*Y_{t-1}^{1}\\ Y_{2}^{2}\ =\ d_{4}^{2}*X_{t}^{4}+d_{6}^{2}*X_{t}^{6}+c_{2}^{2}*Y_{t-1}^{2}\\ Y_{t}^{3}\ =\ d_{5}^{3}*X_{t}^{5}+k_{1}^{3}*X_{t}^{5}+k_{1}^{3}*Y_{t-1}^{5}+b_{3}^{3}*Y_{ t-1}^{3}\\ Y_{t}^{4}\ =\ b_{4}^{4}*Y_{t}^{3}+d_{6}^{3}*X_{t}^{6}+b_{3}^{4}*Y_{t-1}^{4}\\ Y_{t}^{5}\ =\ l_{1}^{5}*X_{t}^ \begin{table}
\begin{tabular}{c c c c c c c} \hline  & **Estimate** & **Standard Error** & **t-Value df = 13** & \(p\)**-Level** & **Lo. Conf Limit** & **Up. Conf Limit** \\ \hline \(x_{t}^{2}\) & \(0.354256\) & \(0.160375\) & \(2.20893\) & \(0.045741\) & \(0.00779\) & \(0.700725\) \\ \(x_{t}^{3}\) & \(0.891334\) & \(0.397307\) & \(2.24344\) & \(0.042924\) & \(0.03301\) & \(1.749663\) \\ \(y_{t-1}^{3}\) & \(-0.300417\) & \(0.516319\) & \(-0.58184\) & \(0.570625\) & \(-1.41586\) & \(0.815024\) \\ \(x_{t}^{6}\) & \(-0.139665\) & \(0.127365\) & \(-1.09658\) & \(0.292725\) & \(-0.41482\) & \(0.135489\) \\ \hline \multicolumn{5}{c}{\(\chi_{t}^{5}=0.354256*X_{t}^{2}+0.891334*X_{t}^{3}+(-0.300417)*Y_{t-1}^{3}+( -0.139665)*X_{t}^{6}\).} \\ \end{tabular}
\end{table} 
Table 14: Coefficients of the third equation of the structural form of the model. \begin{table}
\begin{tabular}{c c c c c c} \hline  & **Estimate** & **Standard Error** & **t-Value df = 13** & \(p\)**-Level** & **Lo. Conf Limit** & **Up. Conf Limit** \\ \hline \(y_{t}^{3}\) & \(0.975343\) & \(0.0\) & \(21.05930\) & \(0.00000\) & \(1\) & \(1.1\) \\ \(x_{t}^{6}\) & \(-0.028588\) & \(0.0\) & \(-0.62667\) & \(0.541724\) & \(-0\) & \(0.1\) \\ \(y_{t-1}^{4}\) & \(-0.001165\) & \(19688.8\) & \(-0.00000\) & \(1.000000\) & \(-42535\) & \(42535.1\) \\ \hline \multicolumn{5}{c}{\(\chi_{t}^{4}=0.975343*Y_{t}^{3}+(-0.028588)*X_{t}^{6}+(-0.001165)*Y_{t-1}^{ 4}\).} \\ \end{tabular}
\end{table} 
Table 15: Assessing the reliability of the third equation of the structural form of the model. \begin{table}
\begin{tabular}{c c c c c c c} \hline  & **Estimate** & **Standard Error** & **t-Value df = 13** & \(p\)**-Level** & **Lo. Conf Limit** & **Up. Conf Limit** \\ \hline \(x_{t}^{5}\) & \(-0.185153\) & \(0.070376\) & \(-2.63091\) & \(0.020751\) & \(-0.337192\) & \(-0.033115\) \\ \(x_{t}^{6}\) & \(-0.002232\) & \(0.02727\) & \(-0.08180\) & \(0.936048\) & \(-0.061165\) & \(0.056701\) \\ \(y_{t-1}^{5}\) & \(0.504226\) & \(0.078349\) & \(6.43562\) & \(0.000022\) & \(0.334962\) & \(0.673489\) \\ \(y_{t-1}^{4}\) & \(0.686448\) & \(0.058185\) & \(11.79759\) & \(0.000000\) & \(0.560746\) & \(0.812150\) \\ \hline \multicolumn{5}{c}{\(Y_{t}^{3}=(-0.185153)*X_{t}^{5}+(-0.002232)*X_{t}^{6}+0.504226*Y_{t-1}^{5}+ 0.686448*Y_{t-1}^{4}\).} \\ \end{tabular}
\end{table} 
Table 14: Coefficients of the third equation of the structural form of the model.