ساختار سلسله مراتبی از تجارت خارجی ترکیه

We examine the hierarchical structures of Turkey’s foreign trade by using real prices of their commodity export and import move together over time. We obtain the topological properties among the countries based on Turkey’s foreign trade during the 1996–2010 period by using the concept of hierarchical structure methods (minimal spanning tree, (MST) and hierarchical tree, (HT)). These periods are divided into two subperiods, such as 1996–2002 and 2003–2010, in order to test various time-window and observe the temporal evolution. We perform the bootstrap techniques to investigate a value of the statistical reliability to the links of the MSTs and HTs. We also use a clustering linkage procedure in order to observe the cluster structure much better. From the structural topologies of these trees, we identify different clusters of countries according to their geographical location and economic ties. Our results show that the DE (Germany), UK (United Kingdom), FR (France), IT (Italy) and RU (Russia) are more important within the network, due to a tighter connection with other countries. We have also found that these countries play a significant role for Turkey’s foreign trade and have important implications for the design of portfolio and investment strategies.

Complex networks provide a very general framework, based on the concepts of statistical physics, for studying systems with large numbers of interacting assets. These networks have been able to successfully describe the topological properties and characteristics of many real-life systems such as multilocus sequence typing for analyses of clonality [1], scientific collaboration in the European framework programmes [2], international hotel industry in Spain [3], taxonomy of correlations of wind velocity [4], Brazilian term structure interest rates [5] and legislative election results [6]. We present, within the best of our knowledge, the first study using the MST on the basis of foreign trade data. Moreover, the most recent literature has studied networks generated by correlations of stock prices [7], [8], [9], [10], [11], [12], [13], [14], [15] and [16]. In this paper, we focus on foreign trade and the main objective is to characterize the topology and taxonomy of the country’s network. Foreign trade is recognized as one of the most significant determinants of economic development of country, all over the world. The foreign trade of a country consists of the inward and the outward movement of goods and services, which results into outflow and inflow of foreign exchange. The primary objective of foreign trade is to increase production and raise the standard of living of its people. If a country is deficient in some of the resources, it has also to import consumer goods to satisfy the rising expectations of the people with the improvement in their economic conditions. These imports have to be paid for foreign exchange. Besides foreign trade, many papers have reported a negative association between country wealth and corruption level, where on average richer countries are less corrupt [17] and [18]. In addition to these, some papers reported that financial and economics time series of developed markets exhibit different scaling behavior than the series of undeveloped and developing markets [19]. Moreover, similar differences between developed markets and developing markets are reported also in financial series during large market crashes [20]. Turkey’s foreign trade has been rising since 1980s and maintaining the same development in 2000s. Turkey’s export was 23 224 million dollars in 1996, increased to 27 775 Million Dollars in 2000, amounted to 73 476 Million Dollars in 2005, and 102 143 Million Dollars in 2009, respectively. Between 1990 and 2009, the yearly average increase in exports was over 12.2%. In the same period, there has also been a higher rate increasing in imports. In 1996, imports was 43 627, increased to 54 503 Million Dollars in 2000, amounted to 116 774 Million Dollars in 2005 and 140 928 Million Dollar s in 2009. The yearly average increase in imports was 14.1% during the 1990–2009 periods. Moreover, Turkey became a member of World Trade Organization in 1995 and Customs Union with the European Union (EU) was established. Increasing of Turkey’s export and import were very small during the 1980–1995 period, but after 1996 the export and import have been risen much more up to 2009 [21]. We should also mention that Podobnik et al., studied annual logarithmic growth rates, R, of various economic variables such as exports and imports, and find that the distributions of R can be approximated by double exponential Laplace distributions in the central parts and power-law distributions in the tails [22]. Moreover, the foreign trades ultimately diminished the differences between developed and developing countries; hence we suggested to state that some experts believe that convergence across all countries exists because of globalization [23], [24] and [25]. Therefore, the aim of the present paper is to examine relationships among countries based on Turkey’s foreign trade by using the concept of minimal spanning tree (MST) and hierarchical tree (HT) over the period of 1996–2010. From these trees, both geometrical (through the MST) and taxonomic (through the HT) information about the correlation between the elements of the set can be obtained. Note that the MST and then the HT are constructed using the Pearson correlation coefficient as a measure of the distance between the time series. Moreover, we performed bootstrap technique to associate a value of reliability to the links of MSTs and HTs. We also used the average linkage cluster analysis for obtaining the HT. These methods give a useful guide to determining the underlying economic or regional causal connections for individual countries. The MST and HT introduced by Mantegna [7], and Mantegna and Stanley [8], have been applied to analyze currency markets [15], [16], [26], [27] and [28], especially to find clustered structure of currencies and the key currency in each cluster [16], [26], [29] and [30] and to resolve contagion in a currency crisis [27] and [28]. These trees are also used to study the clustering behavior of individual stocks within a single country [31], [32], [33], [34], [35], [36], [37], [38] and [39]. The concept of the MST and the HT is also used to examine the extent and evolution of interdependence between world equity markets [10] and [40], European equity markets [41] and commodity markets [42] and [43]. Finally, we should also mention that a variety of dynamic MST analysis has also been developed and applied to the time-varying behavior of stocks in Refs. [11], [12], [44], [45], [46] and [47]. In correlation based hierarchical investigations, the statistical reliability of hierarchical trees and networks is depending on the statistical reliability of the sample correlation matrix. Laloux et al. [48] and Plerou et al. [49] have been applied Random Matrix Theory methods to obtain the quantitative estimation of the statistical uncertainty of the correlation matrix. However, theoretical results providing the statistical reliability of hierarchical trees and correlation based networks are still not available and, therefore, a bootstrap approach has been used to quantify the statistical reliability of hierarchical trees and correlation based networks Tumminello et al. [50], [51] and [52]. The correlation matrix of the time series of a multivariate complex system can be used to extract information about aspects of hierarchical organization of such a system. Correlation based clustering has been used to infer the hierarchical structure of a portfolio of stocks from its correlation coefficient matrix [7], [9] and [53]. The correlation based clustering procedure also allows to associate a correlation based network with the correlation matrix. For example, it is natural to select the MST as the correlation based network associated with the single linkage cluster analysis. Different correlation based on networks can be associated with the same hierarchical tree putting emphasis on different aspects of the sample correlation matrix. Useful examples of correlation based networks different from the minimum spanning tree are the planar maximally filtered graph [54] and the average linkage minimum spanning tree [52]. The remainder of the paper is structured as follows. Next section introduces the methodology and the sampling procedures while Section 3 shows the data and Section 4 presents empirical results. Finally, Section 5 provides some final considerations.

We presented the hierarchical structures of countries based on Turkey’s foreign trade by using the concept of the MST and the HT, including the bootstrap values, for the 1996–2010 periods. We also divided this period into two subperiods in order to test various time-window and observe the temporal evolution. We obtained the clustered structures of the trees and identified different clusters of countries according to their geographical proximity and economic ties. From the topological structure of these trees, we found that the DE, UK, FR, IT and RU are the center of the network and the bootstrap values show that they are closely connected each other. We also found that these countries play an important role for Turkey’s foreign trade and have a significance implication for the design of portfolio and investment strategies. We performed the bootstrap technique to associate a value of statistical reliability to the links of MSTs and HTs for getting the information about statistical reliability of each link of trees. From the results of the bootstrap technique, we can see that in general, the bootstrap values in MSTs and HTs are highly consistent with each other. We also used the average linkage cluster analysis for obtaining cluster structure much better of the hierarchical trees. We also introduce the level of Turkey’s exports and imports which generally used in economics when analyzing trading in order to investigate the total trading of Turkey. The results show that Turkey’s import is more dominant than Turkey’s export in Turkey’s foreign trade. Finally, we expect that the present paper helps for a better understanding of overall structure of Turkey’s foreign trade, and also provide a valuable platform for the theoretical modeling and further analysis. The same analysis will also successfully apply to the developed markets; hence in a future study, we aim to perform the analysis to investigate the developed markets.