Application Of Fractal In Economics

Fractal theory is an important branch of nonlinear science and has been used in many fields of science, such as meteorology, biology, geography, economics and so on. In our paper, we mainly study how to analysis economic time series using fractal methods. First, this paper applies DFA method to study the absolute returns time series, and there is evidence of long-range correlations for stock absolute returns series. The capabilities of different orders DFA in eliminating exponential trends are discussed. In the process of research, the superposition rule of uncorrelated time series is found and proved. After that, we try to improve the traditional DFA method, changing the polynomial fit to B-spline fit, so a new DFA method is given, which we call it B-spline DFA. Then this paper studies the capabilities of this new method in eliminating different exponential trends. We find that the effects of B-spline DFA in eliminating exponential trends are much better than the traditional DFA. Furthermore, the tradition DFA fail in effectively eliminating the periodic trends, but the B-spline DFA could eliminate the periodic trends effectively in most cases. At last, the Gini coefficient of china is calculated using fractal method, supporting a new nonlinear method to the calculation of Gini coefficient.