Intro; Acknowledgements; Contents; 1 Introduction; 1.1 A Historical Evolution of Fractal Methods; 1.2 Application Areas; References; 2 Long Memory Methods and Comparative Analysis; 2.1 Methodology; 2.1.1 R/S and Modified R/S; 2.1.2 DFA Method; 2.2 Data; 2.3 Estimation and the Descriptive Statistics of the Time-Varying Hurst Exponent; 2.3.1 Estimation; 2.3.2 Descriptive Statistics; 2.4 Relationship Between the Two Time-Varying Hurst Exponent Series; 2.4.1 Unit Root Test; 2.4.2 Cointegration Test; 2.4.3 Granger Causality Test; 2.5 Conclusions; References

3 Multifractal Detrended Fluctuation Analysis (MF-DFA)3.1 Methodology; 3.1.1 MF-DFA; 3.1.2 Partition Function; 3.2 Empirical Analysis on Developed-Emerging Agricultural Futures Markets; 3.2.1 Data; 3.2.2 Multifractal Spectrum Analysis; 3.2.3 Sources of Multifractality; 3.2.4 Comparative Analysis; 3.2.5 Conclusions; 3.3 Empirical Analysis on Crude Oil Markets; 3.3.1 Data; 3.3.2 Multifractality and Its Dynamical Formation Mechanisms; 3.3.3 Multifractal Detrended Fluctuation Analysis; 3.3.4 Sources of Multifractality; 3.3.5 Multifractal Analysis of Price Fluctuations at Different Scales

3.3.6 ConclusionsReferences; 4 Multifractal Detrended Cross-Correlation Analysis (MF-DCCA); 4.1 Methodology; 4.2 Empirical Analysis on Chinese Stock-Exchange Market; 4.2.1 Data; 4.2.2 Cross-Correlation Test; 4.2.3 Multifractal Detrended Cross-Correlation Analysis; 4.2.4 Scaling Consistency Analysis; 4.2.5 Dynamics of Cross-Correlations Over Time; 4.2.6 Discussion; 4.2.6.1 Rolling Windows; 4.2.6.2 Relationship Between Bivariate Cross-Correlation Exponents and the Generalized Hurst Exponents; 4.2.6.3 Implications; 4.2.7 Conclusions

4.3 Empirical Analysis on Price-Volume Relationships in Agricultural Commodity Futures Markets4.3.1 Data; 4.3.2 Cross-Correlation Test; 4.3.3 Results and Discussions; 4.3.4 Conclusions; References; 5 Asymmetric Multifractal Detrended Fluctuation Analysis (A-MFDFA); 5.1 Methodology; 5.1.1 A-MFDFA Method; 5.1.2 Asymmetric GARCH Model; 5.2 Empirical Analysis on Shanghai-Shenzhen Stock Market; 5.2.1 Data; 5.2.2 Empirical Results; 5.2.3 Discussion; 5.2.3.1 Origin of Multifractality with Different Trends; 5.2.3.2 Source of the Asymmetry; 5.2.3.3 Time-Varying Feature of Asymmetry; 5.2.4 Conclusions

5.3 Empirical Analysis on International Gold Markets5.3.1 Descriptive Statistics Analysis of Gold Price; 5.3.2 Analysis of Asymmetric Scaling Behavior; 5.3.2.1 Asymmetry of the Fluctuation Function; 5.3.2.2 Estimating the Generalized Hurst Exponent H(q); 5.3.2.3 Analyzing the Multifractal Singularity Spectrum; 5.3.2.4 Time-Varying Analysis of Multifractal Asymmetry; 5.3.3 Discussion; 5.3.3.1 Statistical Tests; 5.3.3.2 Origin of Multifractality with Different Trends; 5.3.3.3 Source of the Asymmetry; 5.3.4 Asymmetric Influences of Good and Bad News on Gold Price Fluctuation; 5.3.5 Conclusions