Abstract: Using the multifractal detrended fluctuation analysis and multifractal detrended cross-correlation analysis, to research the Baltic Dry Index（BDI） and China coastal Bulk Freight Index（CBFI）, auto-correlative multifractality and the cross-correlation of multifractal characteristics between the two series are studied. The time series is from January 1, 2004 to September 15, 2008（before the crisis） and from September 16, 2008 to 2013 on December 31（after the crisis）. Firstly, the MF-DFA is applied to discover the auto-correlative multifractal characteristics of the BDI and CBFI index return series respectively. The results show that the post-crisis multifractal strength is greater than pre-crisis. Secondly, the MF-DCCA is applied to reveal the cross-correlation of the BDI and CBFI index return series. The results show that the cross-correlation of two time series exists a strong multifractal character and the long range correlation, and the multifractal intensity is stronger after the crisis. It is also proved that the multiplicity is due to the persistence of time series fluctuation and the distribution of fat tail.

Key words: before and after financial crisis, Baltic Dry Index（BDI）, China coastal Bulk Freight Index（CBFI）, multifractal analysis

摘要： 针对BDI指数和CBFI指数收益时间序列的相关性特征，运用多重分形去趋势波动分析法（MF-DFA）和多重分形去趋势交叉相关分析法（MF-DCCA），对2004-01-01到2008-09-15（危机前）和2008-09-16到2013-12-31（危机后）BDI指数和CBFI指数自相关的多重分形性以及二者交互相关的多重分形特征进行分析。首先，基于MF-DFA方法分析BDI和CBFI指数收益序列的自相关性，发现金融危机前后，BDI指数和CBFI指数收益序列演变呈现出非平稳性、自相关的多重分形特征，危机后自相关性的多重分形强度大于危机前。其次，基于MF-DCCA方法分析BDI和CBFI指数收益序列的交叉相关性，结果表明两者交叉相关关系具有很强的多重分形特征，呈现出时间序列的长程相关性，危机后互相关的多重分形强度大于危机前。同时也证实多重性归因于时间序列波动的持续性和胖尾分布。

关键词: 金融危机前后, 波罗的海干货指数（BDI）, 中国沿海散货运价指数（CBFI）, 多重分形