Time Series Decomposition Using CEEMD: Algorithm Implementation and Application

CEEMD (Complementary Ensemble Empirical Mode Decomposition) represents an enhanced time series signal decomposition methodology that builds upon traditional EMD (Empirical Mode Decomposition). By incorporating noise-assisted analysis concepts, CEEMD effectively addresses mode mixing issues, enabling more accurate extraction of signal components across different temporal scales. In practical implementation, this involves adding positive and negative white noise pairs to the original signal before performing multiple EMD decompositions.

In time series analysis, CEEMD's core algorithm operates through iterative noise injection to simulate various perturbed states of the signal. The process typically involves: 1) Generating multiple noise-realized versions of the input signal, 2) Performing EMD decomposition on each noisy version, and 3) Ensemble-averaging the resulting IMFs to obtain stable intrinsic mode functions. These IMF components, arranged from high-frequency to low-frequency characteristics, represent distinct oscillatory modes within the original signal, facilitating advanced analysis or predictive modeling. Key implementation functions include noise generation routines, sifting process algorithms, and ensemble averaging operations.

CEEMD's superiority lies in its dual capability of effectively separating noise from underlying trends while reducing decomposition uncertainties inherent in single realizations. The method demonstrates particular robustness through its complementary noise cancellation mechanism, where positive and negative noise additions collectively neutralize residual noise in the final ensemble. This technique finds extensive applications in financial data analysis, meteorological forecasting, and mechanical fault diagnosis, providing a reliable analytical framework for complex time series interpretation. Code implementation typically requires parameters such as ensemble size, noise amplitude, and stopping criteria for the sifting process.