## 4 Conclusion  
Noise reduction for a nonlinear nonstationary time series is challenging since the models require a large amount of computational power and more complicated logic than conventional filters. This paper proposed a new filter, the aIMF algorithm, which demonstrated its accuracy and robustness, compared with the WT, EKF and PF algorithms. In this study, we discovered that PF is not suitable for this kind of work. Additionally, the EKF and WT algorithms should be optimised. It may be because the number  
\begin{table}
\begin{tabular}{c c c c c c c} \hline
**EUR-JPY** & **MSE** & **MAE** & **MAPE** & **R\({}^{2}\)** & **AIC** & **BIC** & **Accuracy count (\%)** \\ \hline aIMF & 0.00424 & 0.057854 & 8.29746 & 0.5219 & \(-\)6782.23 & \(-\)6764.98 & 63.85 \\ WT & 0.00626 & 0.05676 & 8.67169 & 0.5514 & \(-\)6839.68 & \(-\)682.42 & 53.46 \\ EKF & 0.00516 & 0.063797 & 9.15559 & 0.4046 & \(-\)6272.94 & \(-\)6255.69 & 49.50 \\ PF & 3.37133 & 1.42611 & 204.696 & 0.0020 & \(-\)5074.33 & \(-\)5057.08 & 50.19 \\ \hline \end{tabular}
\end{table}
Table 7: Performance measurements of original dataset, EUR-JPY, using noise distribution at 10% with 10 Hz and 20% amplitude of the original signals’.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline
**EUR-CHF** & **MSE** & **MAE** & **MAPE** & **R\({}^{2}\)** & **AIC** & **BIC** & **Accuracy count (\%)** \\ \hline aIMF & 0.03772 & 0.145457 & 0.420782 & 0.9983 & \(-\)1086.41 & \(-\)1069.16 & 88.96 \\ WT & 0.08124 & 0.1745481 & 0.53478 & 0.5905 & \(-\)6852.24 & \(-\)6699.54 & 53.20 \\ EKF & 0.37038 & 0.176222 & 0.519026 & 0.5588 & \(-\)11843.6 & \(-\)11860.9 & 45.71 \\ PF & 1218.50 & 34.52886 & 101.8893 & 0.4421 & \(-\)12388.2 & \(-\)12405.5 & 50.84 \\ \hline \end{tabular}
\end{table}
Table 8: Performance measurements of original dataset, EUR-CHF, using noise distribution at 10% with 10 Hz and 20% amplitude of the original signals’.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline
**EUR-CHF** & **MSE** & **MAE** & **MAPE** & **R\({}^{2}\)** & **AIC** & **BIC** & **Accuracy count (\%)** \\ \hline aIMF & 0.00424 & 0.057854 & 8.306478 & 0.5191 & \(-\)6802.20 & \(-\)6784.98 & 64.92 \\ WT & 0.00826 & 0.065946 & 9.319482 & 0.6435 & \(-\)6699.65 & \(-\)6382.98 & 51.08 \\ EKF & 0.00517 & 0.063851 & 9.171988 & 0.4055 & \(-\)6309.97 & \(-\)6292.68 & 49.20 \\ PF & 3.33789 & 1.435658 & 206.7395 & 0.0006 & \(-\)5104.53 & \(-\)5087.27 & 48.68 \\ \hline \end{tabular}
\end{table}
Table 9: Performance measurements of original dataset, EUR-GBP, using noise distribution at 10% with 10 Hz and 20% amplitude the original signals’.  
of particles for sampling and weights were not enough albeit the number of data-points used were more than 2000. Future work to enhance the efficiency of the aIMF algorithm are in the area of (i) optimising the cubic spline algorithm to be more suitable to the input which sometimes persisted to its mean, and (ii) investigating the possibility of designing a DSP chip for the aIMF algorithm.  
This work is fully inspired by the collaborations of the Department of Electrical and Electronic Engineering and Centre of Bio-Inspired Technology, Imperial College London. Additionally, we are thankful to [PERSON] and [PERSON] for their editing.