Multifractal behavior in return and volatility series of Bitcoin and gold in comparison

In this study, we investigate multifractal nature of return and volatility (proxied by absolute and squared returns) series of Bitcoin and gold throughout full sample periods and sub-sample periods which are decided accordingly the results of the structural breaks in the full sample periods. Applying the Multifractal Detrended Fluctuation Analysis (MFDFA), it is found that Bitcoin return series have distinctly different multifractal properties than of gold. Our evidence shows that all return and volatility series of Bitcoin have a persistent behavior, and have higher degree of multifractality than of gold. Using rolling windows approach, we confirm the persistence and the higher degree of multifractality of Bitcoin time series. Return series of gold have uncorrelated behavior while volatility series of gold have persistent behavior. Moreover, applying structural break test for the series of complexity parameters retrieved from the multifractal analysis of the return and volatility series of gold and Bitcoin, our results indicate that time series of gold have different regimes with different characteristics of multifractality. Furthermore, impact of temporal correlations and fat-tails is also examined and both are found to be the source of multifractality in the return series of Bitcoin and gold. In volatility series of Bitcoin, multifractality arises mostly due to long-range correlations and fat-tails. However, presence of long-range correlations and fat-tails in the original volatility series of gold mostly yields to less degree of multifractality.