Identification Of Stock Market’s Significant Risk Based On Improved Wavelet Leader

As an important tool which can be used in analyzing multifractal character of financial market, wavelet leader has a broad application prospect in the fields of investment. During which we were doing the inductive analysis on algorithm and modeling ideas of monofractal models and multifractal models, this article found that there is a practical drawback of existing wavelet leader method, and we put forward an idea to improve wavelet leader method. After the analysis that comfirming the existence of abnormal phenomenons in daily returns data of Shanghai Stock Eschange(SSE) Composite index, we resorted to the improved wavelet leader method to locate significant inflection of China’s stock market. It is worth mentioning that by doing these, remarkable results has been achieved.To begin with, the inductive analysis of of monofractal models and multifractal models shows that there are some inconsistencies between the existed version of wavelet leader method and multifractal theory, fractal market hypothesis as well as the classical R/S method of monofractal model, which shows the wavelet leader’s flaws of in logic and it causes underestimation of singularity exponent. To calibrate this bias, the mother wavelet should be multiplied by scaling factor √2 in practical application.In addition, by analyzing the abnormal phenomenons of SSE Composite index, we found that there are typical characteristics of non-gaussian, nonlinearity and multifractal in past performance of daily returns of the SSE Composite index, which proves that it is reasonable to analyze the stock market with multifractal models.At last this paper used Legendre transform method and Bayesian method to for locating significant turning points of the SSE Composite index. Our research results found that, the stronger multifractal of stock market is, the higher risk investors are undertaking. From this view it, the improved wavelet leader has a very strong practicality.