The Risk And Cross-correlation Of Gold And Silver Markets Based On Multifractal Analysis

In recent years,the precious metals market is developing pretty rapidly.Especially with the aggravation of the global economic crisis,inflation and Brexit,as the star products of the precious metals,gold and silver are the best hedging tools against the inflation.Therefore,analyzing the changing rule of the gold and silver markets is particularly important to avoid investment risk and make correct market operation mechanism.This article exploits the fractal theory and fractal tools to detect the features of the spot gold market and spot silver market.Finally,we find the multifractality of these two markets and the relationship between their risks.And these conclusions could lay a theoretical foundation for the investors to make decisions.Firstly,this article reviews the development of fractal theory,and introduces the application and research results of fractal theory in the economic field.Secondly,we use the R/S analysis method,and find that both of the Hurst exponent of spot gold market and spot silver market are larger than 0.5,which indicates the long-term memory.Then,based on the multifractal detrended fluctuation analysis method?MF-DFA method?,we modify this method and obtain the Binary Overlapped Sliding Window-Based MF-DFA?Bi-OSW-MF-DFA?which possesses stronger robustness.Daily return of spot gold and spot silver?from February,2004 to June,2016?are used as our samples.From the theoretical analysis and the experimental data,we have proved the superiority of the Bi-OSW-MF-DFA method.Combined with the multifractal scaling exponent??q?and multifractal spectrum f???,we compare the multifractality,factors of multifractal structure and risk between these two markets.In addition,we use theQ_CC?m?statistic to qualitatively test cross correlation between spot gold market and spot silver market.Then we use the improved MF-DXA method to quantitatively detect and analyze the cross correlation between spot gold market and spot silver market.It was found that the crossover of these two markets occurred at s^*=81days,and in the short term,the cross correlations of the two markets'returns were more persistent.