Underlying Trend Extraction via Joint Ensemble Intrinsic Timescale Decomposition Algorithm and Matching Pursuit Approach

Time series usually consist of an underlying trend and the irregularities. Therefore, the underlying trend extraction plays an important role in the analysis of the time series. This paper proposes a method which combines the ensemble intrinsic timescale decomposition (EITD) algorithm and the matchi...

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Bibliographic Details
Published in:Circuits, systems, and signal processing Vol. 38; no. 10; pp. 4621 - 4639
Main Authors: Wang, Xiaoling, Ling, Bingo Wing-Kuen
Format: Journal Article
Language:English
Published: New York Springer US 01.10.2019
Springer Nature B.V
Subjects:
Algorithms
Circuits and Systems
Decomposition
Electrical Engineering
Electronics and Microelectronics
Empirical analysis
Engineering
Instrumentation
Matching
Noise reduction
Optimization
Signal,Image and Speech Processing
Time series
Underlying trend extraction
Ensemble intrinsic timescale decomposition
Matching pursuit
ISSN:0278-081X, 1531-5878
Online Access:Get full text
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Summary:Time series usually consist of an underlying trend and the irregularities. Therefore, the underlying trend extraction plays an important role in the analysis of the time series. This paper proposes a method which combines the ensemble intrinsic timescale decomposition (EITD) algorithm and the matching pursuit (MP) approach for performing the underlying trend extraction. In order to extract the underlying trend, the EITD algorithm is applied to obtain a set of components. Then, the first component which contains most of the noise is removed. Next, some appropriate components are selected by the MP approach. In particular, the total number of components that composites of the underlying trend is minimized. To guarantee that the underlying trend tracks the signal, it is required to impose a constraint on the maximum absolute error between the underlying trend and the denoised signal. As the selection of the EITD components is binary, this component selection problem is formulated as an L 0 -norm binary programming problem subject to the specification on the maximum absolute error between the denoised signal and the underlying trend. This optimization problem is further solved by the MP approach. Finally, the underlying trend is constructed. Compared with the conventional empirical mode decomposition algorithm and the ensemble empirical mode decomposition algorithm, our proposed approach could extract a better underlying trend for some random time series.
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ISSN:0278-081X
1531-5878
DOI:10.1007/s00034-019-01069-2