## 3 Simulation and Results
### Simulation and Performance Measurements of the WT Algorithm  
The objective of this section was to measure the performance of the WT algorithm compared with the original datasets, _i.e._, the EUR-USD exchange rates using the same simulating model and loss estimators employed in Section 3.2.  
Similar to Figure 7, Figure 8 shows three plots, _i.e._, the original datasets (Y2), the \"original datasets \(+\) noise\" (Y1) and \"WT\" (Y1). We analysed the plots and found that the WT curve resided within the curve of \"the original datasets \(+\) noise\" except a spike occurred at between the data 1112 nd to 1213 rd rank of the \(x\)-axis. The trend of those three plots was in the same direction. In terms of estimation, Tables 1-6 indicate that all loss estimators, namely; MSE, MAE, MAPE are relatively low, ranging from 0.00506-0.00599, 0.05402-0.07660 and 4.7715-5.79883, respectively. The R\({}^{2}\) is in the below standard ranging from 0.85340-0.8948, whereas, AIC and BIC are relatively high, up to \(-\)6890.19 and \(-\)6286.15, respectively; whereas the Accuracy counts showed 53.82%-56.13%. As a result, we rated the performance of the WT algorithm is relatively low and hardly acceptable.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline
**EUR-USD** & **MSE** & **MAE** & **MAPE** & **R\({}^{2}\)** & **AIC** & **BIC** & **Accuracy count (\%)** \\ \hline aIMF & 0.00580 & 0.06618 & 5.59678 & 0.8533 & \(-\)5501.09 & \(-\)5483.84 & 57.69 \\ WT & 0.00521 & 0.06003 & 4.57416 & 0.6941 & \(-\)6843.56 & \(-\)6899.78 & 53.34 \\ EKF & 0.01490 & 0.11046 & 9.34639 & 0.7140 & \(-\)3951.51 & \(-\)3934.26 & 51.62 \\ PF & 4.61609 & 1.67868 & 141.868 & 0.0049 & \(-\)1057.44 & \(-\)1040.19 & 50.45 \\ \hline \end{tabular}
\end{table}
Table 6: Performance measurements of original datasets using noise distribution at 100% with 10 Hz and 20% amplitude of the original signals.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline
**EUR-USD** & **MSE** & **MAE** & **MAPE** & **R\({}^{2}\)** & **AIC** & **BIC** & **Accuracy count (\%)** \\ \hline aIMF & 0.00596 & 0.06415 & 5.42792 & 0.8534 & \(-\)5501.99 & \(-\)5484.74 & 64.41 \\ WT & 0.00571 & 0.07660 & 4.78754 & 0.8761 & \(-\)6890.19 & \(-\)6897.21 & 56.13 \\ EKF & 0.01870 & 0.12247 & 10.3683 & 0.6637 & \(-\)3575.62 & \(-\)3558.38 & 48.00 \\ PF & 4.50770 & 1.64377 & 138.983 & 0.0074 & \(-\)1063.27 & \(-\)1046.02 & 50.58 \\ \hline \end{tabular}
\end{table}
Table 4: Performance measurements of original datasets using noise distribution at 100% with 5 Hz and 20% amplitude of the original signals.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline
**EUR-USD** & **MSE** & **MAE** & **MAPE** & **R\({}^{2}\)** & **AIC** & **BIC** & **Accuracy count (\%)** \\ \hline aIMF & 0.00527 & 0.06444 & 5.44396 & 0.8710 & \(-\)5799.61 & \(-\)5782.36 & 67.26 \\ WT & 0.00508 & 0.06890 & 5.79883 & 0.8948 & \(-\)6273.51 & \(-\)6745.29 & 56.82 \\ EKF & 0.00406 & 0.05546 & 4.69540 & 0.9017 & \(-\)6429.89 & \(-\)6412.64 & 51.66 \\ PF & 4.47322 & 1.64897 & 139.487 & 0.0096 & \(-\)1067.39 & \(-\)1050.14 & 50.24 \\ \hline \end{tabular}
\end{table}
Table 5: Performance measurements of original datasets using noise distribution at 100% with 10 Hz and 10% amplitude of the original signals.