Multifractal Detrended Cross-Correlation Analysis of the Return-Volume Relationship of Bitcoin Market

We investigate the cross-correlations of return-volume relationship of the Bitcoin market. In particular, we select eight exchange rates whose trading volume accounts for more than 98% market shares to synthesize Bitcoin indexes. The empirical results based on multifractal detrended cross-correlation analysis (MF-DCCA) reveal that (1) the nonlinear dependencies and power-law cross-correlations in return-volume relationship are found; (2) all cross-correlations are multifractal, and there are antipersistent behaviors of cross-correlation for q=2; (3) the price of small fluctuations is more persistent than that of the volume, while the volume of larger fluctuations is more antipersistent; and (4) the rolling window method shows that the cross-correlations of return-volume are antipersistent in the entire sample period