Asymmetric multifractal spectrum distribution based on detrending moving average cross-correlation analysis

This paper proposes the asymmetric multifractal spectrum distribution based on detrending moving average cross-correlation analysis (A-DMCA-MFSD) algorithm to calculate time-varying multifractal spectrum under different market trends. Numerical results of this algorithm applied to analyzing artificially generated data show superior performance in terms of accuracy and robustness. The algorithm is further applied to investigate auto-correlations of Bitcoin and Gold return series. Asymmetric behaviors of Bitcoin and Gold are obviously observed in small-scale fluctuations. In addition, Bitcoin series shows greater singularity strength than Gold in most of the time. Cross-correlations between Bitcoin and Gold are also studied utilizing A-DMCA-MFSD. Greater cross-correlation is observed during upward trends of Bitcoin (downward trends of Gold) than during downward trends (upward trends, respectively).