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分形理论是现代非线性科学中的重要分支之一,它的发展为经济学研究提供了一种全新的工具。该文通过分形理论着重考察了GDP规模与股票市场的统计分布特征,以及其分形维数,认为GDP规模和股指的统计也具有分形的性质,其经验分布为稳定的幂律分布。结果表明:GDP的拟合函数为Y=11.48X-1.30,沪市股指的拟合函数为Y=15.63X-1.28,两者均严格符合Zipf分布;通过回归分析,得到以沪市股指为因变量,GDP为自变量的方程:Y=113.825+0.11X。
Fractal theory is one of the important branches of modern nonlinear science. Its development provides a completely new tool for economics research. This paper focuses on the statistical distribution characteristics of GDP and stock market and its fractal dimension by means of fractal theory. It holds that the statistics of GDP scale and stock index also have fractal properties, and the empirical distribution is a stable power law distribution. The result shows that the fitting function of GDP is Y = 11.48X-1.30, the fitting function of Shanghai stock index is Y = 15.63X-1.28, both of which are in strict accordance with the Zipf distribution. Through the regression analysis, Variable, GDP is an independent variable equation: Y = 113.825 + 0.11X.