Cross-correlations between Renminbi and four major currencies in the Renminbi currency basket

We investigate the cross-correlations between Renminbi (CNY) and four major currencies (USD, EUR, JPY, and KRW) in the Renminbi currency basket, i.e., the cross-correlations of CNY–USD, CNY–EUR, CNY–JPY, and CNY–KRW. Qualitatively, using a statistical test in analogy to the Ljung-Box test, we find that cross-correlations significantly exist in CNY–USD, CNY–EUR, CNY–JPY, and CNY–KRW. Quantitatively, employing the detrended cross-correlation analysis (DCCA) method, we find that the cross-correlations of CNY–USD, CNY–EUR, CNY–JPY, and CNY–KRW are weakly persistent. We use the DCCA cross-correlation coefficient ρ DCCA to quantify the level of cross-correlations and find the currency weight in the Renminbi currency basket is arranged in the order of USD>EUR>JPY >KRW. Using the method of rolling windows, which can capture the time-varying cross-correlation scaling exponents, we find that: (i) CNY and USD are positively cross-correlated over time, but the cross-correlations of CNY–USD are anti-persistent during the US sub-prime crisis and the European debt crisis. (ii) The cross-correlation scaling exponents of CNY-EUR have the cyclical fluctuation with a nearly two-year cycle. (iii) CNY–JPY has long-term negative cross-correlations, during the European debt crisis, but CNY and KRW are positively cross-correlated.