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The Multifractal Analysis for Some Time Series

Author: DingLiJuan
Tutor: LiangJinRong
School: East China Normal University
Course: Basic mathematics
Keywords: Singular Spectrum Singularity strength Multifractal eliminate fluctuations trend analysis Long-range correlation q -order moments of the structure function segmentation method
CLC: O189
Type: Master's thesis
Year: 2007
Downloads: 249
Quote: 3
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Abstract


Based on multi- fractal theory and analysis methods , and empirical analysis , analysis of multi-fractal nature of real determination like eye movement data . The article includes the following aspects : First, the q -order moment structure partition function of binocular fixation eye movements , horizontal and vertical movement of the branches do multifractal analysis . The results showed that the the eyes horizontal displacement time series sequence of multiple fractal strong vertical displacement . The horizontal displacement of the left and right eye are basically the same , the vertical displacement of the left and right eye also showed substantially similar properties . Also remove microsaccades eyes horizontal and vertical movement branch multifractal analysis . Found that , after the removal of microsaccades four showed a similar weak multifractal nature , suggesting that microsaccades may be one of the reasons caused by and branch multiple fractal differences in the horizontal and vertical movement , it may be caused by multiple points form one of the reasons . Secondly, the multifractal detrended fluctuation analysis (MF-DFA) the multifractal analysis branch sequence of horizontal and vertical movement of the eye movement fixation on the eyes , draw and q order moments structure partition function analysis similar conclusions . By randomly disrupted eyes fixed like the level of eye movement and vertical movement branch sequence , its multifractal analysis , given the results of the various branches sequence comparison like eye movement and disrupted before the fixing eye movement sequences multifractal are two reasons for joint action by the sequence of the long-range correlation and fat tail distribution from results . The conclusion is consistent with the two methods used to analyze the resulting analysis multifractal nature of the feasibility and accuracy of the conclusions .

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CLC: > Mathematical sciences and chemical > Mathematics > Geometry, topology > Topology ( the situation in geometry )
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