Interactive Wavelet Analysis and Coherence Analysis

Interactive Wavelet Analysis and Coherence Analysis are methodologies designed to study the mutual relationships and consistency between two correlated time series. In Interactive Wavelet Analysis, we can observe the correlations and interactions between the two time series datasets through wavelet transform computations. Coherence Analysis helps determine whether these correlations remain stable over time and can be utilized for predicting and interpreting the relationship between the two series. These techniques are widely applied across various fields including economics, finance, and ecology. Implementation typically involves using wavelet transform functions (e.g., continuous wavelet transform) to decompose time series into time-frequency domains, followed by coherence calculations using cross-wavelet spectra and phase differences. These methods not only enhance our understanding and interpretation of data but also provide more accurate predictions and decision-making support through algorithmic analysis of temporal patterns.