The Multifractal Extension Of Detrended Cross Correlation Analysis With Its Application In Financial Market

Fractal Market Theory is not only the powerful challenge to the Efficient Market Theory, but also the creative extension. The understanding of Fractal Market Theory on the financial market is complex and in accordance with the real features of market. Detrended cross correlation analysis is a powerful tool to catch the nonlinear cross correlation of financial market based on the Fractal Market Theory. In recent years, large quantities of literature try to extend the detrended cross correlation analysis to multifractal situation, in order to comprehensively figure out the nonlinear correlation. Multifractal cross correlation analysis (MFCCA) raised by Oswiecimka is a sensitive tool to identify the multifractal character and the natural extension of detrended cross correlation analysis. We demonstrate that multifractal cross correlation analysis is an effective algorithm from the general two-component ARFIMA processes model. To discover the multifractal behavior of Chinese stock market, multifractal detrended fluctuation analysis (MF-DFA) and multifractal cross correlation analysis are applied in the price return, volume change and price-volume of CSI300index. We draw the conclusion that the multifactality exists in both the price return and volume change, however, the multifractality cross correlation only exists among the large fluctuations.This thesis is concerned of5chapters and its detailed content is exhibited as follows:Chapter1, Prolegomenon. We briefly introduce the background and significance of this research, concluding that the Fractal Market Theory is the realistic extension of Efficient Market Theory. By reviewing the journals of this field, we introduce the MFCCA algorithm, which was raised by Oswiecimka firstly. Then we give the main research content and the creative points of this thesis.Chapter2, Fractal theories and algorithms. We elaborate the sources and definitions of fractality and multifractality. The detailed procedures of multifractal detrended fluctuation analysis and detrended cross correlation analysis are given.Chapter3, focusing on the multifractal cross correlation analysis (MFCCA), we compare it with multifractal detrended cross correlation analysis (MF-DXA)by virtue of simulating the general two component ARFIMA processes. MFCCA algorithm is a more effective tool than MF-DXA.Chapter4, the empirical part. By utilizing the MF-DFA algorithm, we discuss the multifractality of price return and volume change of CSI300index. The multifractal cross correlation is discussed by applying MFCCA algorithm. Furthermore, we decompose the two series into the special forms, which is a creative breakthough of analyzing the multifractality of the stock market.Chapter5, the conlusion and prospect. We summary the main research results and look ahead to the future work in this field.