Imagine you’re a detective trying to solve a mysterious case. You have multiple methods at your disposal, like following the money trail or analyzing fingerprints. In the world of academic studies, causality inference is like solving a puzzle to understand how different events are connected. Researchers have developed various methods, such as Granger causality and Convergent Cross Mapping (CCM), to tackle this challenge. Now, they have released an open-source Matlab code called Noise-Assisted Multivariate Empirical Mode Decomposition (NA-MEMD) that helps you unlock the secrets of causality in bivariate time series. This code, developed on Matlab2020, consists of three subfunctions: na_memd, Plseries, and cd_na_memd. Together, they generate matrices of Intrinsic Mode Functions (IMFs) and perform causal decomposition to reveal the main Intrinsic Causal Component (ICC). By removing this component from the original time series, the code unveils the result of NA-MEMD Causal Decomposition. The code’s performance has been evaluated in terms of executing time, robustness, and validity. It shows promising results with linear execution time and high robustness in handling larger datasets. Furthermore, its validity is demonstrated by aligning with results from a real-world predator-prey dataset. So, if you’re curious about unraveling the hidden causal relationships in your data, dive into the fascinating realm of NA-MEMD Causal Decomposition using this Matlab open-source code!

Causality inference has arrested much attention in academic studies. Currently, multiple methods such as Granger causality, Convergent Cross Mapping (CCM), and Noise-assisted Multivariate Empirical Mode Decomposition (NA-MEMD) are introduced to solve the problem. Motivated by the researchers who uploaded the open-source code for causality inference, we hereby present the Matlab code of NA-MEMD Causal Decomposition to help users implement the algorithm in multiple scenarios. The code is developed on Matlab2020 and is mainly divided into three subfunctions: na_memd, Plseries, and cd_na_memd. na_memd is called in the main function to generate the matrix of Intrinsic Mode Functions (IMFs) and Plseries can display the average frequency and phase difference of IMFs of the same order in a matrix which can be used for the selection of the main Intrinsic Causal Component (ICC) and ICCs set. cd_na_memd is called to perform causal redecomposition after removing the main ICC from the original time series and output the result of NA-MEMD Causal Decomposition. The performance of the code is evaluated from the perspective of executing time, robustness, and validity. With the data amount enlarging, the executing time increases linearly with it and the value of causal strength oscillates in an ideally small interval which represents the relatively high robustness of the code. The validity is verified based on the open-access predator-prey data (wolf-moose bivariate time series from Isle Royale National Park in Michigan, USA) and our result is aligned with that of Causal Decomposition.

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