The Multifractal Cross-correlation Analysis Based On Singular Value Decomposition

Detrended cross-correlation analysis (DCCA) is proposed by Podobnik et al based on detrended fluctuation analysis (DFA), it makes the correlation can be quantitative analysis between two time serier.The method is similar to the DFA, first remove the trend of each time point, then take the logarithm and calculated DCCA index, which reflects the size of the correlation. Once the method was proposed it applied in so many fields,such as DNA sequences, cardiac dynamics, geology, ethnology, solid-state physics, economics and so on. This paper mainly discusses Multifractal cross-correlation analysis based on the singular value decomposition and its application on the Dow Jones and NASDAQ. Firstly, we study three methods of the dection of multifractal cross-correlation:the multifractal detrended cross-correlation analysis (MF-DXA), multifractal moving average cross-correlation analysis (MF-DMA), Multifractal height cross-correlation analysis (MF-HXA); then use singular value decomposition to improve these methods to minimize the effects of external trends on long-range scaling behavior,besides, we draw the figures of logarithmic return and volatility of stock markets; Finally, we discuss and summarize the improved methods.