## 4 Results and Discussion
### IMF's Statistics
Similarly, the sum of the variances of other components, in contrast to the dominant modes that include IMF1, IMF2, IMF3, and IMF4, accounts for only 0.2224% of the total variation (82.638%) as well as having nearly zero correlation with the actual stock prices, and therefore, has no serious impact on bringing changes in the KSE-100 index closing price. To summarize, the results presented in Tables 3-6 indicate that the low correlated components with the actual KSE-100 index closing price are considered as noise in the signal and kept aside before building our proposed hybrid Akima-LSTM model. The remaining components that have moderate to high correlation with the actual data are used to build our proposed hybrid model, and the tuning parameters of each correlated sub-components to build the LSTM network are outlined in the following sub-section. \begin{table}
\begin{tabular}{c c c c c} \hline  & \begin{tabular}{c} **Pearson** \\ **Correlation** \\ \end{tabular} & **Variance** & \
\begin{tabular}{c} **Variance as \%** \\ **of the Actual** \\ \end{tabular} &
\begin{tabular}{c} **Variance as \%** \\ **(_IMFs+Residue_)** \\ \end{tabular} \\ \hline Actual & - & 28,577,484 & - & - \\ \hline IMF1 & 0.049 & 31,847.84 & 0.111 & 0.153 \\ \hline IMF2 & 0.072 & 33,497.54 & 0.117 & 0.161 \\ \hline IMF3 & 0.103 & 67,152.56 & 0.234 & 0.324 \\ \hline IMF4 & 0.139 & 219,347.2 & 0.767 & 1.058 \\ \hline IMF5 & 0.374 & 467,575.5 & 1.636 & 2.256 \\ \hline IMF6 & 0.763 & 2,118,902 & 7.414 & 10.226 \\ \hline IMF7 & 0.749 & 3,713,021 & 12.992 & 17.921 \\ \hline IMF8 & 0.639 & 9,935,052 & 34.765 & 47.952 \\ \hline IMP9 & \(-\)0.267 & 445.702 & 0.0015 & 0.00215 \\ \hline Residue & 0.0977 & 4,131,881 & 14.458 & 19.942 \\ \hline Total & & 20,718,722 & 72.4955 & 99.995 \\ \hline \end{tabular}
\end{table} 
Table 4: Statistical measures of IMFs and residue extracted by implementing EEMD. \begin{table}
\begin{tabular}{c c c c c} \hline  & \begin{tabular}{c} **Pearson** \\ **Correlation** \\ \end{tabular} & **Variance** & \
\begin{tabular}{c} **Variance as \%** \\ **of the Actual** \\ \end{tabular} &
\begin{tabular}{c} **Variance as \%** \\ **(_\(\sum\)IMFs+Residue_)** \\ \end{tabular} \\ \hline Actual & - & 25,829,097 & - & - \\ \hline IMF1 & 0.0720 & 67,535.05 & 0.261 & 0.255 \\ \hline IMF2 & 0.090 & 90,198.41 & 0.349 & 0.349 \\ \hline IMF3 & 0.082 & 146,130.4 & 0.565 & 0.553 \\ \hline IMF4 & 0.0733 & 746,324.3 & 2.88 & 2.825 \\ \hline IMF5 & 0.397 & 3,162,753 & 12.244 & 11.973 \\ \hline IMF6 & 0.227 & 1,907,672 & 7.385 & 7.22 \\ \hline IMF7 & 0.859 & 18,470,085 & 71.508 & 69.921 \\ \hline Residue & 0.360 & 1,824,661 & 7.064 & 6.907 \\ \hline Total & & 26,415,359 & 102.26 & 100.003 \\ \hline \end{tabular}
\end{table} 
Table 5: Statistical measures of IMFs and residue extracted by implementing SEMD. The tuning phase of the hyper-parameters of the LSTM network is of extreme importance, and any wrong selection may distort the prediction accuracy. The number of epochs and batch size that play a significant role in the training of our model varies from high to low-frequency IMFs and residue. It can be seen from the results presented in the above Tables that from high to low-frequency IMFs and single monotone residue components, the number of epochs and batch size reduced systematically as it is easy to train the model for such non-complex subcomponents that have a smooth trend in an upward direction. The low-frequency IMFs and residue component shows the long-term oscillation in the data, and modeling such components with the help of a hybrid LSTM model is not a difficult task with a lower number of epochs and batch size. The reason is that the network learns very easily from the pattern of these components that are not chaotic.