Statistical properties of the yuan exchange rate index

► The statistical properties of the yuan exchange rate index were studied by MFDMA. ► The long-range correlations and multifractal nature in the two periods are unveiled. ► Fat-tail plays a critical role in the origins of multifractality in the first period. ► Long memory is the major cause of multifractality in the second period. ► Exchange rate reform in July 2008 has effect on the effective exchange rate of RMB.