Applications Of Multifractal Analysis Methods In Financial Markets

Since the 1990 s,the rapid developments of nonlinear dynamics,fractal theory,chaos theory and other nonlinear scientific theories have provided new theoretical tools for exploring the characteristics of financial markets.The empirical studies have also shown that the financial market is a nonlinear complex dynamic system with fractal and chaotic structure.Therefore,the theories and methods of nonlinear analysis,including fractal analysis,are used to study the related issues of financial markets.It can not only describe finely the complex structural characteristics in the financial market and discuss deeply the cross-correlations between different markets,but also clearly show the risk within the market and the risk spillover between the markets,which can provide valuable reference for the policy making,risk supervision and investment decision of financial market.Firstly,this thesis studies the inherent fluctuation characteristics of China's carbon emission allowance market,energy stock market and crude oil market by using multifractal detrended fluctuation analysis(MF-DFA)method.Meanwhile the multiscale multifractal detrended cross-correlation analysis(MM-DCCA)method is used to construct the Hurst surface in the three-dimensional space and visualize quantitatively the cross-correlations between the three markets,thereby describing the dynamic behaviors of cross-correlations between the markets.The empirical result shows that the volatility of the three markets has significant multifractal characteristics,and the risk of carbon emission allowance market is greater than those of energy stock market and crude oil market.In addition,the correlation between the energy stock market and the crude oil market is strongest,while the correlations between the carbon market and the other two markets are weaker.Then,based on the existing fractal analysis methods,two new multifractal analysis methods are developed to study the cross-correlation and coupling cross-correlation between two multivariate time series systems.We select the five kinds of futures varieties in the CBOT and their corresponding spot varieties as the representative of the agricultural commodity futures and spot markets,and regard their return series as two multivariate systems.The multiple multifractal analysis methods,including the two methods mentioned in this thesis,are adopted to investigate the autocorrelations,cross-correlations and coupling cross-correlations of the two systems and their components as well as the risk spillover effect.The empirical results show that the autocorrelations and cross-correlations of the two systems show different multifractal characteristics at different time scales.In the short term,the risk of the futures market is smaller than that of the spot market;while in the long term,the co-movement between the two markets is not strong and the risk spillover effect is not obvious.In addition,there exist the coupling cross-correlations among the corresponding components of the two systems,and the coupling cross-correlation strengths of their corresponding components are distinct due to the different influence of long-range correlations and fat-tailed distribution.Finally,we give a summary of the thesis and further research prospects.