Fractal Analysis Research Of China Stock Market Based On The Wavelet De-noising

Based on fractal market theory and wavelet de-noising theory, select-ing Shanghai Composite Index as a representative of Chinese stockmarket, we divide2000-2013years stage into four stages according majorevent in stock market, before and after the share reform, during and afterfinancial crisis stage. So we analyse the noise and fractal measurementsin stock market for different periods, furthermore, we de-noise theearnings yield by wavelet and analyse changes before and afterde-noising, and then use the de-noised stock price series to predict price.We find out the following conclusions:1. This paper argues that irrational behavior and security market events,the asymmetry of information cause stock market noise. By use of thevariance ratio test, Hurst index and asymmetry model, we find the levelof noise and fractal measurements are significantly different in differentperiods, during the financial crisis is higher, before share reform andcrisis later are in middle, after share reform is lower.2. We use db2and coif wavelet function to de-noise the earnings yieldwith2-4layers, and we confirm4layers of db2wavelet decomposition isbest; Comparing de-noised yield’s noise and fractal measurement withunde-noisied yield’s, we find Hurst are larger and more significant by R/Sand ARFIMA model, which makes fractal sequence long memoryenhanced and better predictability. 3. Using2010-2013Index closed price de-noised by db2-4, we makeup EGARCH (2,2) model to predict prices in40days and find that themodel can fit the price trend better, It is good for short-term prediction.