Green cryptocurrencies versus sustainable investments dynamics: Exploration of multifractal multiscale analysis, multifractal detrended cross-correlations and nonlinear Granger causality

Within this study, we analyse green cryptocurrencies versus sustainable investments dynamics by calculating a multifractal multiscale analysis (MMA) with Hurst surfaces paired with powerlaw distributional coherence tests for each series. Next, we determine multifractal cross-correlations by applying a maximal overlap discrete wavelet transform (MODWT) based trend-filtered variation of a multifractal detrended cross-correlation analysis (MF-DCCA). Finally, to determine the strength and directionality of potential causations, we determine the results of a nonlinear Granger causality test. The results for the MMA state $q$-dependent unstable multifractality for each series. The coherence tests indicate that the series follow powerlaws or exponentially nested powerlaws and yield fat-tails in some cases. Moreover, we find strong scaling and multifractal cross-correlations between the cryptocurrencies and the sustainability series. Finally, the nonlinear Granger causality tests across four lags indicate a complex interplay between some of the selected cryptocurrencies and various indices. These results suggest the existence of potential predictive powers of these cryptocurrencies on the market indices.