تجزیه و تحلیل نمودار قابلیت دید در سری سه ماهه اقتصاد کلان چین بر ​​اساس تئوری شبکه های پیچیده

The visibility graph approach and complex network theory provide a new insight into time series analysis. The inheritance of the visibility graph from the original time series was further explored in the paper. We found that degree distributions of visibility graphs extracted from Pseudo Brownian Motion series obtained by the Frequency Domain algorithm exhibit exponential behaviors, in which the exponential exponent is a binomial function of the Hurst index inherited in the time series. Our simulations presented that the quantitative relations between the Hurst indexes and the exponents of degree distribution function are different for different series and the visibility graph inherits some important features of the original time series. Further, we convert some quarterly macroeconomic series including the growth rates of value-added of three industry series and the growth rates of Gross Domestic Product series of China to graphs by the visibility algorithm and explore the topological properties of graphs associated from the four macroeconomic series, namely, the degree distribution and correlations, the clustering coefficient, the average path length, and community structure. Based on complex network analysis we find degree distributions of associated networks from the growth rates of value-added of three industry series are almost exponential and the degree distributions of associated networks from the growth rates of GDP series are scale free. We also discussed the assortativity and disassortativity of the four associated networks as they are related to the evolutionary process of the original macroeconomic series. All the constructed networks have “small-world” features. The community structures of associated networks suggest dynamic changes of the original macroeconomic series. We also detected the relationship among government policy changes, community structures of associated networks and macroeconomic dynamics. We find great influences of government policies in China on the changes of dynamics of GDP and the three industries adjustment. The work in our paper provides a new way to understand the dynamics of economic development.

In recent years, complex network theory has flourished in many fields. A complex network is helpful to understand the impacts of topological structures on dynamics and functions of a system. It is interesting that some research results have made a bridge between time series and networks or graphs [1], [2], [3], [4], [5] and [6]. Networks from corresponding time series can be generated with different methods. The studies of the first type deal with many time series to form a complex network with each node standing for a time series and the weight of a link between two nodes characterized by the correlation coefficient of the two time series [7] or by the distance between the two time series [8]. Lacasa et al. [5], [6] and [9] proposed a new tool for time series which is called the visibility algorithm and attracted wide attention. Lacasa et al. have shown that time series structure is inherited in the associated graph, such that periodic, random, and fractal series map into a random exponential and scale-free network. The visibility graph allows us to apply methods of complex network theory for characterizing time series simply. However, most discussions at present mainly focus on stationary time series generated with theoretical models. The applications to analyze real world data are limited. So far the visibility algorithm to analyze real time series is mainly presented in fields of stock market indices, occurrence of hurricanes in the United States, foreign exchange rates and energy dissipation rates in three-dimensional fully developed turbulence [10], [11], [12], [13] and [14]. In this work, we will investigate some important actual macroeconomic time series by the visibility graph approach which include the quarterly growth rate of value-added of the primary industry series, quarterly growth rate of value-added of the secondary industry series, quarterly growth rate of value-added of the tertiary industry series and growth rate of the Gross Domestic Product series of China from the first quarter of 1992 to the third quarter of 2010. The methods and research thinking in our paper are also suitable for macroeconomic data of other countries. After transferring these time series to networks, we will investigate the statistic characteristics of constructed networks and the dynamic process of macroeconomic series using complex network theory. Finally, we obtain some meaningful conclusions.

The visibility graph is used in the present paper to find the characteristics and dynamics embedded in quarterly macroeconomic series from Jan-1992 to Sep-2010 of China. The growth rates of value-added of three industry series approximately convert into exponential networks and the growth rates of GDP series approximately convert into scale-free networks. Local vertices with relatively extreme degree in the constructed network usually reflect turning points in business activity. The associated networks from the growth rate of the Gross Domestic Product series, growth rate of value-added of the secondary industry series and growth rate of value-added of the tertiary industry series have assortative architectures, and the associated network from the growth rate of value-added of the primary industry series has disassortative architectures. All the constructed networks have higher clustering coefficient yet smaller characteristic path lengths, which indicate that the constructed networks from four macroeconomic series of China are all “small-world” networks. The community structures of all constructed networks are detected. Belonging to the same community means that there are the same dynamic properties in the economic development process of a country in these periods. Especially, we find government policies in China have great influences on the changes of dynamics of GDP and three industry series. The work in our paper provides a new way to understand the dynamic process of economic development. The methods can be applied to the data of other countries.