中文摘要：

BDI指数是国际航运市场的风向标，摸清BDI指数波动幂律分布特性，对于进一步掌握运费规律、预测BDI趋势、协助航运决策等方面具有重要意义．基于此，本文对已运行30年BDI指数的波动幂律分布特性进行了详细研究，主要特色有：一是借助Pareto、Exponential以及Fokker—Planck函数首次深入探讨了BDI指数波动幂律分布特性．二是在跳跃识别的基础上，构建了基于跳跃时间和跳跃幅度两标度的BDI指数波动幂律分布特性分析模型，并转化成最小二乘法的线性回归测算模型．三是对BDI指数日、周和月增长率的跳跃时间和跳跃幅度幂律分布特性进行了实证分析．结果表明：BDI指数具有尖峰薄尾的增长率分布和波动聚集性；Fokker—Planck函数拟合BDI指数增长率跳跃时间更合适；Exponential函数拟合BDI指数增长率跳跃幅度更合适；BDI指数增长率跳跃时间和跳跃幅度都具有薄尾幂律特性，且向上、向下幂律呈现对称性．

英文摘要：

The baltic dry index （BDI） index is the international shipping market barometer. BDI index fluctuation power law distribution features are important for further mastering shipping freight character- istics, BDI trends forecasting, shipping decision-making and so on. This paper has a detailed research on 30 years BDI index fluctuation power law distribution features. The main characteristics includes： Firstly, the BDI index power law distribution features are discussed with Pareto, Exponential and Fokker-Planck function for the first time. Secondly, on the basis of jump identify, the jump time and jump range scales BDI index fluctuation power law distribution models are set up, which are transformed into a least square method of linear regression models. Thirdly, empirical analysis on BDI index daily, weekly and monthly growth rates jump time and jump range power law distribution features, results showed that BDI index growth rate distribution has pointed peak, thin tail and fluctuation gathered. Fokker-Planck function fit- ting BDI index growth rate jump time is more appropriate, Exponential function fitting BDI index growth rate jump range is more appropriate. BDI index growth rate jump time and jump range are has thin tail power law feature, and jump upon and jump down power law features are symmetry.