Abstract
A novel noise filtering algorithm based on averaging Intrinsic Mode Function (aIMF), which is a derivation of Empirical Mode Decomposition (EMD), is proposed to remove white-Gaussian noise of foreign currency exchange rates that are nonlinear nonstationary times series signals. Noise patterns with different amplitudes and frequencies were randomly mixed into the five exchange rates. A number of filters, namely; Extended Kalman Filter (EKF), Wavelet Transform (WT), Particle Filter (PF) and the averaging Intrinsic Mode Function (aIMF) algorithm were used to compare filtering and smoothing performance. The aIMF algorithm demonstrated high noise reduction among the performance of these filters.
Highlights
Kalmam Filter (KF) was conceptualised for use in a linear system
We applied a variety of loss estimations, i.e., Mean Square Error (MSE), Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE), R2, AIC, BIC and Accuracy count which is a sum of the upward and downward movements of all the underlying local signals after they had transited the reversion points
Based on the simulations of the algorithms namely; averaging Intrinsic Mode Function (aIMF), Wavelet Transform (WT), Extended Kalman Filter (EKF) and Particle Filter (PF), we have found that the aIMF performed the best, following in the order to WT, EKF and PF
Summary
Kalmam Filter (KF) was conceptualised for use in a linear system. In a nonlinear filter, ExtendedKF (EKF) requires Jacobian mappings, which can be computationally intensive if the vector measurement is high. An EKF can estimate a highly non-stationary data series, with a known state space model incorporated along with EKF [3]. The basic principle of PF is to use a set of weighted samples, known as particles, to approximate the posterior probability of a time-varying signal of interest, given related observations. PFs generalize traditional KFs and can be applied to nonlinear and non-Gaussian state-space models. Similar to EKF, the PF algorithm is a two-state approach, i.e., prediction and correction; and is a technique for implementing recursive Bayesian filters by Monte Carlo sampling. The advantages of PF over EKF are in the representation of nonlinear functions because optimal estimation uses nonlinear non-Gaussian state-space models [5,6,7]
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