| In this dissertation, we study multifractal properties and cross-correlation properties of traffic time series and financial time series. Firstly, fractal interpolation filter is proposed to transform Guangshen highway volume series, we investigate effects of fractal interpolation filter on multifractal analysis. Secondly, we improve multifractal detrended fluctuation analysis(MFDFA) and use fractal fitting to replace polynomial fitting in detrend process. The result shows that fractal fitting can get a better detrend effect than polynomial fitting. And we use this method to research the long-range correlation characteristics and multifractal property of Guangshen highway volume series. Finally, due to the development of economic globalization is rapid and violent, the economic connections between countries are more closely while the interaction between countries is more apparent. We study mixed multifractal properties of stock index series both in China and US by mixed multifractal analysis and exploit the inner relationship between them.In Chapter 1, We elaborated the concept, properties and background of fractals and multifractals. We explain the significance of multifractal analysis of time series.In Chapter 2, fractal interpolation filter is proposed to transform original signals.We compare the multifractal scaling properties of signals before and after transforms and investigate effects of fractal interpolation filter on multifractal analysis.In Chapter 3, we improve multifractal detrended fluctuation analysis and get a new method called multifractal detrended fluctuation analysis based on fractal fitting(MFDFA-FF). And we use this method to research the long-range correlation characteristics and multifractal property of Guangshen highway volume series.In Chapter 4, we study mixed multifractal properties of stock index series both in China i.e., SSEC, SZSE and US i,e., DJIA, NASDAQ by mixed multifractal analysis and exploit the inner relationship between them. |
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