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The Application of Wavelets in the Fractal Singularity Spectrum Estimation and Their Numerical Comparison

Author: ZhangWei
Tutor: YuHaiYuan
School: Xiangtan University
Course: Computational Mathematics
Keywords: Wavelet Analysis Multifractal Analysis Singular Spectrum Shaped multifractal detrended fluctuation analysis Detrended fluctuation analysis method based on wavelet Wavelet transform modulus maxima
CLC: O241.5
Type: Master's thesis
Year: 2008
Downloads: 108
Quote: 0
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Abstract


For various types of fractal signals , including fractional Brownian motion , based on the the multifractal wavelet Log-poisson and Log-normal signal generation model generation , the effects of several commonly used numerical methods estimated multifractal spectrum , including multiple fractal detrended fluctuation analysis ( MFDFA ) wavelet - based detrended fluctuation analysis (WB-DFA) and the wavelet transform modulus maxima (WTMM), in different circumstances , and the three detailed comprehensive analysis and comparison . Which MFDFA no involved in wavelets, wavelet applications related to the latter two . We focus on examining their parameters determine the stability and accuracy , the purpose is understood wavelet multifractal analysis applications and get selected basis in dealing with the practical problems of the various methods . From the results of the comparison , the stability and accuracy of the MFDFA is satisfactory , WTMM as a mature method has its unique advantages , but the data requirements are relatively high . WB-DFA as a new method , the data is high, its stability and accuracy is not good enough , the applicability remains to be further discussion . In addition, in order to examine the differences in the practical application of these methods , we select a stock market daily income data , some multifractal nature with MFDFA their visits , found that immature stock markets of developed countries mature stock markets and developing countries significant difference exists between ; using the WTMM local H ( ? ) lder index can be used to predict a greater risk in the stock market .

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CLC: > Mathematical sciences and chemical > Mathematics > Computational Mathematics > Numerical Analysis > Numerical approximation
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