Noise Reduction for Nonlinear Nonstationary Time Series Data using Averaging Intrinsic Mode Function

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.

Keywords

• empirical mode decomposition
• Intrinsic Mode Function
• Wavelet Transform
• noise reduction
• exchanges rates