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

Abstract

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.