Multifractal detrended cross-correlation analysis of carbon emission allowance and stock returns

The nonlinear relationship between carbon emission allowance and stock markets has attracted special attention from economists around the world. This paper uses the technique of multifractal detrended cross-correlation analysis (MF-DCCA) to investigate the cross-correlations between carbon emission allowance and stock series as well as their dynamics for European and Chinese markets, respectively. The results show that the cross-correlations between carbon and stock series are significantly multifractal in European and Chinese markets. The cross-correlations of small fluctuations are persistent while those of large fluctuations are anti-persistent. Moreover, the degree and width of multifractality is found to be stronger in China than in Europe. We confirm that the multifractality of cross-correlations could be attributed to both the persistence of fluctuations of carbon emission allowance and stock markets and fat-tail distributions of the time series. By employing rolling estimate of MF-DCCA, we find that the scaling exponent varies over time and across fluctuations in European and Chinese markets. In particular, the Hurst exponent fluctuates around 0.5 in recent years.