中文摘要：

运用改进的多重分形消除趋势波动分析法，对大宗商品期货市场中大豆及铝两种期货合约的对数收益率序列进行多重分形分析，并结合多重分形谱方法，对它们的多重分形强度进行比较。实证研究表明，这两种合约的对数收益率序列均具有明显的多重分形特征，且大豆期货序列的多重分形强度更大。证实了大宗商品市场的多重分形性是由序列的波动相关性及厚尾概率分布两个因素共同引起的。对于大豆和铝的对数收益率序列，序列的波动相关性是形成多重分形性的主要原因。此外，研究还发现，虽然买入大豆期货合约的风险较铝的风险更大，但获利的机会也更大。

英文摘要：

Using the improved method of the multifractal detrended fluctuation analysis, we investigate the muhifractal na- tures of the series of logarithmic returns for two futures contracts, soybean and aluminum futures contracts, in the commodities futures market. Combined with the muhifractal spectrum method, we make a comparison between their strengths of muhifractal- ity. The empirical results show that they all have muhifractal natures, and the strength of multifractality for the series of soy- bean is greater than that of aluminum. Further study points out that the multifractal natures of the commodity market are deter- mined by two factors, and the fluctuation correlation is the main factor that forms a muhifractal nature. Besides, the study also finds that the risk of buying soybean futures contract is greater than that of aluminum, but at the same time its profit opportunity is bigger.