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

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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.