Decomposing the persistence structure of Islamic and green crypto-currencies with nonlinear stepwise filtering

The multi-fractal chaotic dynamics of Islamic and Green crypto-currency series are investigated for the first time in econophysics literature. Specifically, we decompose and analyse the temporal signals of prices, returns, volume and volatility of Islamic and Green cryptos vis-à-vis conventional ones in a com parative manner. We introduce a multi-step resolution approach based on detrended fluctuation analysis, Generalized Hurst and Lyapunov exponents as well as fractionally integrated conditional heteroskedastic ity. Moreover, various tests are employed to investigate the statistical significance of any (dis)similarities of long memory patterns, multi-fractality measures and chaotic dynamics observed among Islamic, Green and conventional crypto-currency markets. Our findings suggest that while the returns of Islamic and green crypto-currencies exhibit anti-persistent dynamics, their price, volatility and volume series embed high persistence compared to the conventional crypto-currencies. Further statistical testing indicates that the distributions of the chaotic parameter estimates are significantly different versus common crypto currencies, a fact that reveals heterogeneity in multi-fractality and long memory patterns. As the Islamic and Green cryptos exhibit a distinct and more profound chaotic behaviour compared to conventional ones, their short-term predictability could further induce financial agents.