函数性数据的微分方程分析方法及经济应用

The Differential Equation Method and Its Economic Applications of Functional Data Analysis

讨论了函数性数据与微分方程的关系以及微分方程系数函数的估计方法。利用函数性数据的微分方程分析方法对中国及中美日三国GDP增长的波动特征、中国31个省份GDP增长速度的时段差异特征,以及投资率与经济增长速度之间的关系进行了分析。结果显示,微分方程分析方法不但能够很好地刻画经济变量的动态演变规律和波动特征,而且能够对多观察对象之间的差异以及多个经济变量之间的关系进行动态刻画和展示,易于对其进行经济解释。

This paper has discussed the relationship between functional data and differential equation, and the estimation methods which appropriate to coefficient functions in a given differential equation. Then the differential equation method has been used to analyze the characteristics of the growth variation of Chinese GDP, US GDP and Japanese GDP. The growth differences among different periods of China＇s 31 provinces, municipalities and autonomous regions have been analyzed also. Moreover the paper has analyzed the relationship between investment rate and economic growth rate. The results obtained indicate that the methods are not only appropriate to depict the dynamic evolutions and volatility characteristics of economic variables, but could describe the differences among more observing objects and display the relationships among economic variables, which is convenient to make economic interpretation.