Correlation analysis of carbon price and coal price based on wavelet coherence

The correlation of carbon price and coal price is a hot issue in the domestic and international academic communities. By performing cross-wavelet analysis on the two time series, extracting the energy spectrum, condensed spectrum and phase spectrum and displaying the relevant details of the two signals in the time-frequency domain at multiple scales, the mutual influence of the two signals can be accurately distinguished at multiple periods and scales. The experimental results show that: (1) the two signals have a statistically significant correlation; (2) the carbon price is positively correlated with the coal price in the low-frequency domain, with the coal price leading the carbon price; and (3) the carbon price is negatively correlated with the coal price in the high-frequency domain for a given period, with the carbon price leading the domestic coal price and lagging the imported coal price. The experimental results support the results of our theoretical analysis both quantitatively and qualitatively.