Multiresolution granger causality testing with variational mode decomposition: a python software

In this paper, we introduce a novel and advanced multiscale approach to Granger causality testing, achieved by integrating Variational Mode Decomposition (VMD) with traditional statistical causality methods. Our approach decomposes complex time series data into intrinsic mode functions (IMFs), each representing a distinct frequency scale, thus enabling a more precise and granular analysis of causal relationships across multiple scales. By applying Granger causality tests to the stationary IMFs, we uncover causal patterns that are often concealed in aggregated data, providing a more comprehensive understanding of the underlying system dynamics. This methodology is implemented in a Python-based software package, featuring an intuitive, user-friendly interface that enhances accessibility for both researchers and practitioners. The integration of VMD with Granger causality significantly enhances the flexibility and robustness of causal analysis, making it particularly effective in fields such as finance, engineering, and medicine, where data complexity is a significant challenge. Extensive empirical studies, including analyzes of cryptocurrency data, biomedical signals, and simulation experiments, validate the effectiveness of our approach. Our method demonstrates a superior ability to reveal hidden causal interactions, offering greater accuracy and precision than leading existing techniques.