Matlab Open Source Code: Noise-Assisted Multivariate Empirical Mode Decomposition Based Causal Decomposition for...

Area of Science:

• Complex Systems Analysis
• Time Series Analysis
• Computational Science

Background:

• Causality inference is a critical area in academic research, with existing methods including Granger causality, Convergent Cross Mapping (CCM), and Noise-assisted Multivariate Empirical Mode Decomposition (NA-MEMD).
• The availability of open-source code facilitates the adoption and implementation of advanced analytical techniques by researchers.

Purpose of the Study:

• To present user-friendly Matlab code for implementing the NA-MEMD Causal Decomposition algorithm.
• To enable researchers to apply this causality inference method in diverse scientific scenarios.

Main Methods:

• Development of a Matlab code package comprising three core subfunctions: `na_memd`, `Plseries`, and `cd_na_memd`.
• `na_memd` generates Intrinsic Mode Functions (IMFs); `Plseries` aids in selecting Intrinsic Causal Components (ICCs) by analyzing IMF frequency and phase.
• `cd_na_memd` performs causal redecomposition after ICC removal, yielding the final NA-MEMD Causal Decomposition results.

Main Results:

• The code demonstrates a linear increase in execution time with data size, indicating efficient scaling.
• High robustness is observed, characterized by causal strength values oscillating within a small, stable interval.
• Validity is confirmed using predator-prey time series data, with results aligning with established Causal Decomposition methods.

Conclusions:

• The developed Matlab code provides a practical and reliable tool for NA-MEMD Causal Decomposition.
• The code's performance in terms of execution time, robustness, and validity makes it suitable for various causality inference tasks.