The Multifractal Analysis For Some Time Series

Based on the multifractal theory and analysis method, we analyzed the multifractal property of the fixational eye movements.This paper contained the following aspects:First, by using a qth-order moment structure partition function we analyzed the multifractals for the horizontal and vertical fixational movements of both eyes. The results shew that there were different multifractal scaling behavior between the horizontal and vertical movements. When microsaccades were removed , the scaling behavior of horizontal and vertical components became similar. It suggested that microsaccades might be one of the cause of difference behavior between horizontal and vertical fixaional movements, and also might be the cause of multifractal property.Second, by using multifractal detrended fluctuation analysis we investigated the multifractal property of the horizontal and vertical movements of both eyes, and got similar results as in the qth-order moment structure partition function analysis. After shuffling the horizontal and vertical movements respectively, all the series had weaker multifractal property .Those results can be due to long-range correlations and a broad probability density function.The consistent results obtained by using above two methods illuminated the feasibility of the two methods , and the veracity of results were ensured.