By discussing the connections between mono-fractal model and multi-fractal model as represented by wavelet leader, intrinsic weaknesses of wavelet leader method are analyzed to make an improvement, and Monte Carlo simulation is used to compare the effect between traditional wavelet leader method and improved wavelet leader method. Within the framework of improved wavelet leader method. Bayesian estimation based on Approximation technique is used to compute the multifractal spectrum and the related parameters of the return rate series of the Shanghai Composite Index.Our theoretical analysis indicates that in the conventional wavelet leader method, the setting-wavelet sum of energy equals one-leads to inconsistence with both canonical R/S analysis method and the actual situation of the real stock market. Thus, conventional wavelet leader method can cause a significant underestimation of scaling index and other adverse outcomes. Under the improved wavelet leader method, based on approximation technology, Bayesian estimation method can not only reduce the parameters that need to be estimated, but also identify the significant turning point of China's stock market, and the result is also very robust.
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