## 4 Results and Discussion
### IMF's Statistics  
The variance and its proportion with each IMF have been calculated, as well as the Pearson coefficient of correlation between each IMF (residue) and the real stock prices. Tables 3-6 display the relevant details regarding this decomposition. The correlations between each IMF (residue) and the observed stock prices are simultaneously measured using the Pearson product-moment correlation coefficient. We utilized the percentage of variance to illustrate how much each IMF (residue) contributed to the overall movement of the observed stock price because these IMFs (residue) are independent of one another. The variance of these IMFs and residue, however, does not necessarily equal the overall variance due to various constraints, as can be seen, for instance, from Tables 3-6 that there is a 23.262% (123.258-99.996%), \(-\)27.75% (72.495-99.99%), 2.257% (102.260-100.003%), and \(-\)17.35(82.638-99.988) differences when the actual time series data are decomposed with EMD, EEMD, SEMD, and the new method. It can also be verified from Table 3 that when the decomposition is carried out with EMD, the dominant mode is the deterministic trend in terms of IMF8 with a Pearson coefficient of correlation of 0.758. We also found out that the variance of this deterministic trend accounted for 71.883% of the total variance. The sum of the variations for these significant components, namely IMF5, IMF6, IMF7, IMFs, IMF9, and trend, accounts for 97.8491% of the total variation. Contrarily, IMF1, IMF2, IMF3, and IMF4 have very low correlation coefficients with the original stock price and only contribute 2.147 of the total variance, indicating that they have little influence on stock price and are therefore not included in the development of the proposed Akima-EMD-LSTM model. Furthermore, it can be verified from the results presented in Table 4 that the dominant modes (based on the values of the Pearson correlation coefficient) when decomposition is carried out with the help of EEMD are IMF3, IMF4, IMF5, IMF6, IMF7, IMF8, and IMF9 with moderate to high Pearson coefficient of correlation with the actual data. Similarly, the sum of the variances of IMF1, IMF2, and residue accounts for only 14.686% of the total variation (72.4955%) as well as a very low correlation with the actual stock prices, which shows that these components have very little impact on the variation in the stock prices, and shows only noise in the actual time series data. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Description**} & **Pearson** & **Variance** & **Variance as \%** & **Variance as \%** \\  & **Correlation** & **of the Actual** & **(\(\sum\)_IMFs+Resolute_)** \\ \hline Actual & - & 285,774,84 & - & - \\ \hline IMF1 & 0.071 & 54,819.13 & 0.191 & 0.155 \\ \hline IMF2 & 0.053 & 69,825.12 & 0.244 & 0.198 \\ \hline IMF3 & 0.088 & 15,5121.3 & 0.542 & 0.440 \\ \hline IMF4 & 0.060 & 477,278.4 & 1.670 & 1.354 \\ \hline IMF5 & 0.122 & 537,974 & 1.882 & 1.527 \\ \hline IMF6 & 0.331 & 2,803,518 & 9.810 & 7.958 \\ \hline IMF7 & 0.102 & 5,288,340 & 18.505 & 15.012 \\ \hline IMF8 & 0.758 & 20,542,369 & 71.883 & 58.315 \\ \hline IMF9 & \(-\)0.111 & 389.3048 & 0.0013 & 0.0011 \\ \hline Residue & 0.399 & 5,296,823 & 18.53 & 15.036 \\ \hline Total & & 35,226,457 & 123.2583 & 99.9961 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Statistical measures of IMFs and residue extracted by implementing EMD. When the decomposition is conducted with the proposed new method, namely the Akima-EMD, we obtain the statistical measures as presented in Table 6. The dominant modes are now IMF5, IMF6, IMF7, IMF8, IMF9, and residue that contributes to 82.214% of the total variation with Pearson correlation coefficients of 0.139, 0.204, 0.495, 0.641, 0.688, and 0.523.