Applications Of Fractal Analysis Methods In Financial Markets

With the deepening trend of trade globalization and capital internationalization,the volatility transmission and risk spillover effect among the financial markets are affected by exogenous shocks such as the COVID-19 pandemic and Russia-Ukraine conflict.Market price fluctuations are more unstable and unpredictable,and the relevant fluctuation data are typical non-stationary time series.Early scholars mainly adopted traditional econometric methods to analyze the fluctuation and complexity of financial markets based on the framework of efficient market hypothesis.With more in-depth research,at present,many scholars have confirmed through nonlinear models that financial markets are nonlinear dynamic complex systems with fractal structures such as scaling,heterogeneity,long memory of fluctuations,and fluctuation clustering,among which the multifractal analysis methods can effectively describe the cross-correlations between various markets.Energy and agricultural markets are important components of financial markets.With the accelerating process of market globalization and trade liberalization,the price fluctuation of energy and agricultural products is extremely complicated.As an international strategic resource,energy is very important to the national security and economic development of all countries in the world,and the fluctuation of international agricultural prices is related to the stability of food supply and demand of all countries in the world.The sudden outbreak of the Russia-Ukraine conflict on February 24,2022,immediately triggered a spike in international commodity prices,including energy and agricultural products.The intensifying conflict between Russia and Ukraine has brought new external shocks to the global financial markets,which not only stimulates the doubling of international energy prices,but also poses a severe challenge to global food security,and exerts a significant impact on the global financial markets,which is gradually emerging from the shadow of the COVID-19 pandemic.Energy security and food security are of great significance to maintaining the long-term,stable and healthy development of all countries.Ensuring the security of energy and food supply is an important goal in the development strategies of all countries.In the context of Russia-Ukraine conflict and global carbon neutrality,the world’s major economies have taken a lot of actions in developing green finance and mitigating climate change.Green development is an important issue of sustainable economic development of countries around the world at present.The sustainable development of the green finance markets provides an important support for the green recovery plan in the post-COVID-19 era.The enhanced correlations between the green finance markets imply deeper institutional changes.The research on the correlations between the international carbon market,green bond market and stock market is of far-reaching significance.Firstly,this thesis selects the natural gas futures,WTI crude oil futures of New York Mercantile Exchange(NYMEX),Brent crude oil futures of London’s Inter Continental Exchange(ICE)and wheat futures,corn futures and soybean futures of Chicago Board of Trade(CBOT)as the research objects.The multifractal analysis methods are used to study the fluctuation characteristics,market risks and the cross-correlations between the international energy markets and the agricultural markets since the outbreak of the Russia-Ukraine conflict,and explores the reasons for the multifractality of correlations between the interactive markets.The empirical results show that both the autocorrelations and the cross-correlations between the international energy markets and the agricultural markets have obvious multifractal features,and the fat-tailed distribution of fluctuations is the main reason for the multifractality of the cross-correlations.After the outbreak of the Russia-Ukraine conflict,the multifractal strength and market risks of the NYMEX natural gas,WTI crude oil and ICE Brent crude oil markets weakened,while the CBOT wheat,corn and soybean markets enhanced.In addition,the Russia-Ukraine conflict has intensified the multifractal strength and the complexity of the fluctuations between the NYMEX natural gas,WTI crude oil markets and the CBOT wheat,corn and soybean markets.Secondly,NYMEX natural gas,WTI crude oil and Brent crude oil represent the energy market,and CBOT wheat,corn and soybean represent the agricultural market.multivariate multifractal detrended fluctuation analysis(MV-MFDFA)and multiscale multivariate multifractal detrended fluctuation analysis(MMV-MFDFA)methods are used to explore the autocorrelations between the two whole markets.Multivariate multifractal detrended cross-correlation analysis(MV-MFDCCA)and multiscale multivariate multifractal detrended cross-correlation analysis(MMV-MFDCCA)methods are used to analyze the cross-correlation between the two whole markets.The empirical results show that the international energy market and agricultural market have significant multifractal autocorrelations and cross-correlation,and the Russia-Ukraine conflict has strengthened the autocorrelations of the two overall markets and the multifractality and complexity of the cross-correlation between the markets.Then,based on multifractal detrended fluctuation analysis(MF-DFA),multifractal detrended cross-correlation analysis(MF-DCCA)and multiscale multifractal detrended coss-correlation analysis(MM-DCCA)methods,This thesis takes the EU carbon emission permit(EUA)futures price,S&P green bond index and NASDAQ Clean Energy index as research objects to explore the fractal structures of the international carbon emission permit market,green bond market and clean energy stock market as well as the multifractal cross-correlations between these markets.The empirical results show that the autocorrelations of the international carbon emission permit market,green bond market and clean energy stock market all have significant multifractal features,and the multifractal strength of the carbon emission permit market is greater than that of the green bond market and the clean energy stock market.In addition,there is a significant multifractal cross-correlation between the three markets,among which the multifractal cross-correlation between the carbon emission permit market and the green bond market is stronger,while the multifractal cross-correlation between the green bond market and the clean energy stock market is weaker.Finally,we give the summary and suggestions.