Analysis of the efficiency and multifractality of gold markets based on multifractal detrended fluctuation analysis

In this paper, we investigate the efficiency and multifractality of a gold market based on multifractal detrended fluctuation analysis. Our evidence shows that the gold return series are multifractal both for time scales smaller than a month and for time scales larger than a month. For time scales smaller than a month, the main contribution of multifractality is fat-tail distribution. For time scales larger than a month, both long-range correlations and fat-tail distribution play important roles in the contribution of multifractality. Using the method of rolling windows, we find that the gold market became more and more efficient over time, especially after 2001. The abnormal points of scaling exponents can also be related to some occasional events. By defining a new inefficiency measure related to the multifractality, we find that the gold market is more efficient during the upward periods than during the downward periods.