Before revision:  Furthermore, asymmetric reactions in the volatility process to price fluctuations between uptrend (bull) and downtrend (bear) regimes are discussed from the viewpoint of cross-correlations quantified by the asymmetric DCCA coefficient , which is a different approach from the conventional GARCH-class models .
After revision:  Furthermore, asymmetric reactions in the volatility process to price fluctuations between uptrend (bull) and downtrend (bear) regimes are discussed from the viewpoint of cross-correlations quantified by the asymmetric DCCA coefficient . The approaches take into account the nonlinearity and asymmetric multifractal scaling properties, providing new insights in investigating the relationships in a dynamical way .