- Mean Absolute Percentage Error
- Wavelet Transform
- instantaneous frequency
- particle filter
- Hilbert-Huang transform
- exchange rate
- noise reduction
- Extended Kalman Filter
- hidden Markov model
- sequential importance sampling
- empirical mode decomposition

This paper presents a new novel digital filter termed ―averaging Intrinsic Mode Function ‖ which is a derivative of Empirical Mode Decomposition

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- Kalmam Filter was conceptualised for use in a linear system
- A novel noise filtering algorithm based on averaging Intrinsic Mode Function, which is a derivation of Empirical Mode Decomposition, is proposed to remove white-Gaussian noise of foreign currency exchange rates that are nonlinear nonstationary times series signals
- Referring to Section 1, we propose theoretical considerations of existing algorithms using for filtering nonlinear nonstationary times series data; and those are, Wavelet Transform, Extended Kalman Filter, Particle Filter, and our proposed averaging Intrinsic Mode Function, which is a derivative of EMD
- 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
- Future work to enhance the efficiency of the aIMF algorithm are in the area of optimising the cubic spline algorithm to be more suitable to the input which sometimes persisted to its mean, and investigating the possibility of designing a DSP chip for the aIMF algorithm
- Future work to enhance the efficiency of the averaging Intrinsic Mode Function algorithm are in the area of optimising the cubic spline algorithm to be more suitable to the input which sometimes persisted to its mean, and investigating the possibility of designing a DSP chip for the aIMF algorithm

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