The Application Of Multifractal In The Stock Market

The stock market is a vital and essential component of the financial industry, and it is widely concerned by the investors, so the study of the stock price fluctuation law is a very important issue for many scholars. Fractal theory is a new branch of nonlinear scientific research. It studies the smooth and irregular geometric form of nonlinear system. It has been used in the other fields of science more and more widely.This paper uses fractal theory's methods and many of statistical methods to study the stock price fluctuation law of the stock market. Firstly, we use single-fractal, such as classical R/S, DFA methods to study a long memory of the series about stock prices by.Secondly analysis of multifractal characteristics of the stock market returns was made by using multifractal.Based on the multifractal analysis of the Shanghai and Shenzhen 300 index and stocks related industries, we found financial sector, transportation, electrical industry have smaller stock index volatility, steel industry, coal industry and real estate have larger stock index volatility, civil construction, pharmaceutical industry in the middle of stock index volatility. By analyzing the parameter Cq and the three-dimensional images constituted by Cq we can see that the relationship between the whole market index and steel industry, coal industry, real estate sectors are more closely.The last we employ multifractal theory to study the volatility of stock market, concluding that the fluctuations of stock market have the feather of asymmetry. The fluctuations of Shanghai stock market has the feather of a negative "leverage effect ",the fluctuations of Dow, Nasdaq, the London index have the "leverage effect".