Researches On Fractal Properties Of Time Series

Fractal theory is an active researching branch of nonlinear science that has been used in many fields of science.Fractal properties of time series are our mainly studied in this paper.First,we discuss how various linear and nonlinear filters affect the multifractal properties of time series.It is shown that linear filters do not change the multifractal properties,but nonlinear filters do and the effects depend on the order of the polynomial filter.After that,we study the correlations between extreme events using return interval,and compare the multifractal properties of the three types of time series. We found that multifractal properties of return interval of different time series are similar.At last,we research the application of H(o|¨)lder exponent in traffic time series. Furthermore,we study the changing law of singularity(H(o|¨)lder exponent) in traffic time series by extending one dimension H(o|¨)lder exponent algorithm to high dimension that establish some theory basis for prediction of urban traffic congestion.There are twenty-three pictures,twenty tables,and thirty-eight references...