Applications Of Multifractal Analysis In Time Series

Resource allocation and environmental protection are the two most concerned problems in the process of sustainable development of national economy.Since reform and opening up more than 40 years ago,China's economic level has been greatly improved under the promotion of rapid urbanization,heavy industrialization and global trade opening.However,Because the theory and technology of early industrial production are not mature enough,not only the waste of basic metal resources is serious,but also the atmospheric environment is seriously polluted by a large number of exhaust gases from industrial production,it has aroused the close attention of the public as well as experts and scholars.In recent years,In order to strengthen the regulation of air pollutants,China's environmental protection departments have set up monitoring points in many parts of the country to detect and publish data on the air pollutant concentration index.These data are not only helpful to understand the daily air pollution situation,but also provide the basic information for experts and scholars to carry out relevant research.In the process of economic development,futures market plays an important role in realizing the optimal allocation of commodity resources,avoiding market risks,improving market structure and so on.It is of great theoretical and practical significance to reveal the operational efficiency of futures market for the rational allocation of market resources.With the deepening of global economic integration,the relationship between the domestic futures market and the international futures market is becoming closer and closer.Hence,it is also very important to explore the international relevance of the futures markets.In this thesis,the multifractal structure characteristics and cross-correlations of air pollutant concentration index time series,basic metal futures and spot price time series in China are studied from the perspective of system theory.First,the nonlinear fluctuation characteristics and dynamic complexity of three-dimensional air pollutant?PM2.5,PM10,NO₂?concentration index systems in Beijing and Shanghai are studied by using multivariate multifractal detrending fluctuation analysis?MV-MFDFA?,and the main reasons for multifractality are discussed.Secondly,in order to study the multivariate interaction between the two systems,we extend the univariate multifractal detrending cross-correlation analysis?MF-DCCA?to multivariate cases,a multivariate multifractal detrending cross-correlation analysis?MV-MFDCCA?is proposed.Using the multifractal analysis methods including MV-MFDCCA,we empirically study the multivariate correlation between the futures and spot daily rate of return series of copper,aluminum and zinc in China.Finally,we use multivariate multifractal analysis method to study the statistical characteristics and interaction mechanism of two major metal futures markets in China and the United Kingdom.