The Relationship Structure of Global Exchange Rate Based on Network Analysis

The optimal threshold strategy is put forward for establishing a suitable network for analyzing the correlation among the different exchange rates. The 33 currencies of the world’s major countries and regions are analyzed by the method of network analysis, and the multilateral exchange rate correlation network is established based on the optimal threshold. Combining with geographical features and the exchange rate regime, it is found that the international currency has obvious community structure, which is composed of three levels: the core currency area, the arbitrage currency area and the shadow currency area. The conclusion reveals the structural characteristics of the Jamaica international monetary system.


Introduction
33 currencies of the world's major countries and regions are analyzed by the method of network analysis, and the multilateral exchange rate correlation network is established based on the optimal threshold. Our research found that due to the economic and trade characteristics and international political status of countries as well as the choice of exchange rate regimes in countries, 3 major levels are finally displayed in the overall network of exchange rates. One of these levels is USD-centered USD core area that is composed of Renminbi and oil currency, and its periphery is composed of the consumption-based currencies in the Eurozone and upstream resource-based currencies, such as Indonesian rupiah and Australian dollar; the second level is the arbitrage currency that is represented by Japanese Yen and Australian Dollar; and the third level is Korean won and U.K. pound as shadow currency. Correlation structure for the currency exchange rate H. D. Cao et al. of various countries shows a regional feature and has obvious geographical characteristics. Our research showed that the choice of exchange rate regimes in countries is the result of differences in economic development and economic system and the characteristics of international trade as well as the result for location choice of country's currency in international monetary system. The research section in this paper reveals the structural characteristics of international monetary system under the Jamaica system with USD as the core 1 .

Literature Review
Analysis of bilateral relations based on exchange rate has gradually formed the purchasing power parity theory that reflects equilibrium of commodity markets, the interest rate parity theory that reflects equilibrium of asset markets, and the asset market theory that is determined by exchange rate under the floating exchange rate regime in the general equilibrium analysis determined by integrating these two preconditions into exchange rate. These theories don't give a final solution to the so-called "mysteries of exchange rate" such as "deviation of exchange rate from fundamentals", "excessive exchange rate fluctuations", and The method of network analysis adheres to Aristotle's holistic theory at the philosophical level and has an obvious methodological "structure-function" characteristic. In the research, the network analysis establishes a network model with the studied individuals as nodes and connection between individuals as the side. At mathematics, it belongs to the "graph theory" network model. For network analysis, there are two research paradigms: social networks and complex networks (Jackson, 2008), and Yang Jianmei (2010) thinks that there is a tendency that the two coexistent research paradigms narrow differences and converge [1] [2]. Social network analysis began with the study of social metrology and group dynamics in the 1930s. By 1969, the anthropologist Mitchell (1969) proposed a systematic framework for social network analysis [3], and then it was matured through the mathematic deepening by White in Harvard to form a con- 1 In January 1976, the "Interim Committee on the International Monetary System" of the Board of Governors of the International Monetary Fund (IMF) held a meeting in Kingston, the capital of Jamaica, to discuss the terms of the IMF Agreement and sign the "Jamaica Agreement". In April of same year, the Board of Governors of IMF adopted the Second Amendment to the IMF Agreement, confirmed the legalization of the floating exchange rate regime, and formed a new international monetary system. temporary social network analysis (Scott, 2000) [4]. Social networks generally focus on studying social relationships and name them after these research objects, such as Granovetter's (1973) study of weak link information superiority theory [5].
In macroeconomic governance and financial market micro analysis, social network is a research method and a research object. For example, Cohen, Frazzini, and Malooy (2008) used educational background as a proxy variable for social relations to study the effect of social networks on asset prices [6]. Zhang Min, Tong Lijing and Xu Haoran (2015) studied the role of social networks in corporate risk sharing with their employment experience as proxy variables [7]. This type of research focuses on social relations and "metaphorizes" it as the network connection, but it is subjective to certain extent in setting of relational proxy variables.
Complex network research starts with statistical physics and complexity science, and is marked by two groundbreaking research efforts: small-world network theory (Watts & Strogatz, 1998) [8] and scale-free network theory (Barabasi & Albert, 1999) [9]. The geometrical nature of complex network analysis makes it has the advantages of natural visualization; at the same time, adjusting the network structure according to the "connection" strength, enables the complex network analysis to effectively carry out the dimensionality reduction analysis for data, which also becomes a kind of method for data mining. For complex network paradigm, there are 3 ways in the network construction: the way based on the existing real relationship, the way of building based on theory, and the way based on data. Complex network itself is the complex representation for temporal and spatial evolution of nature and human society, which also exists in economic and financial systems. For example, Glasserman and Young (2015) studied the European interbank lending network and found that the expected loss caused by network effect is very small when there is no significant difference in bank sizes that are highly dependent on interbank market financing [10]. Based on shareholding relationship, Yan et al. (2015) analyzed the shareholdings of U.S. corporations in the "Fortune Global 500" through complex network models [11]. With difficulty of acquiring relational data in reality, it is an important direction to analyze the network structure, characteristics and effect based on theory-based network building. Nier et al. (2007) refined 4 typical risk transmission mechanisms in financial networks through theoretical modeling [12]. Li Ying, Cao Hongduo and Xing Haoke (2012) used the agent-based computational experiments to analyze the roles and different market effects of learning mechanism, learning structure and duration strategy in the game for 3 networks: stochastic, small-world and scale-free networks [13].
Data-based network analysis is getting more and more attentions because of Lu Feifei (2014) constructed a network based on fluctuation correlation of the stock market to study correlation of stock indexes [15]. Big data weakens the causal relationship and pays more attention to mining the correlation between different factors. At present, there are mainly two methods for network construction that are based on data dependency. Mantegna (1999) established a minimum spanning tree (MST) based on the stock network. MST network is concise and intuitive, and provides a new perspective for the networked research of financial market [16]. Johnson and McDonald (2005) used MST method to study the dynamic causes of exchange rate network, scrutinize the dominant currency and dependent currency, and find that the exchange rate network is very geographical [17]. Naylor (2007) used MST and hierarchy tree method to study the foreign exchange market from 1995 to 2001 and found a clear and steady scale-free network, and studied the crisis transmission path during the Asian financial crisis to find that the crisis transmission influences other countries mainly via USD rather than having a direct impact [18]. Keskin (2011) MST studied the network and hierarchy structures of 34 major currencies using MST with USD and Turkish lira as the base currencies respectively, and verified the view that the major currencies come from countries participating in the world's major economic events [19]. Despite MST network is simply, it filters out a great deal of important information during building network. Boginski (2005) applied threshold method for building network to the financial market for the first time: by building correlation coefficient matrix C_(i, j) for the daily returns of each stock in the U.S. stock market, the adjacency matrix D was built. Studies found that stock market network complies with power-law distribution and shows the scale-free property [20]. Kwapień, Gworek and Drożdż (2009) used threshold method to study the foreign exchange market that includes 63 currencies including precious metals, and screen the closely connected currencies [21]. The key to build network via the threshold method is to choose a suitable threshold θ so that network structure reflects characteristics of the market. If the threshold chosen is too small, the effective structure can't be highlighted; the network filters a large amount of information if it's too small. Therefore, choosing an appropriate threshold is very important for building network. This paper presents an optimal method for setting threshold, and accordingly conducts network analysis on the opposite side exchange rate structure.

Data and Network Modeling
Data are sourced from the statistical database of the International Monetary Fund (IMF) and include daily exchange rate data from 33 countries. By considering the international recognition of currency, [19] established two MST networks with USD and Turkish lira as the benchmark currencies, while others chose precious metal as the benchmark. The benchmark used in this paper is the Special Drawing Rights (SDR). We selected the data from June 2003 to May 2013. Table  1 shows the currencies and abbreviations of 33 countries and regions. The method adopted in this paper was to establish a network with threshold method. The basic idea was to select an appropriate threshold θ based on the correlation coefficient matrix that is formed by N return rate series. If the correlation coefficients of two nodes ( ) were considered as being connected with each other, which are represented as a connection in the network diagram and represent an element 1 ij A = in the adjacency matrix A; if ij C θ < , the two nodes ( ) , i j were not considered to be connected, which are represented as a non-connection in network diagram and represent an element 0 ij A = in the adjacency matrix A. If i P was the daily return rate of the i th currency, 1, ,55 i =  . We could establish the daily corresponding logarithmic return rate series: And establish a correlation coefficient matrix C with the correlation coeffi- The research in this paper focuses on the correlation of exchange rates. Therefore, the absolute-valued correlation coefficient matrix was used as the basis for network building via the threshold method: abs C C = . A total of 120 correlation coefficient matrices were monthly created for data of all trading days in a total of 120 months from June 2003 to May 2013, and each correlation coeffi-DOI: 10.4236/jmf.2020.101006 cient matrix had 528 (33 × 32/2) valid correlation coefficients. A statistical description of all the correlation coefficients is shown in Figure 1. Average of correlation coefficient was 0.107040 that reflects positive correlation of world exchange rate network as a whole. There are mainly two reasons for this: firstly, the economic globalization is more manifested in that the complementarity of economy and trade among cooperative countries is greater than the competition; secondly, it is the benchmark currency's coupling of SDR. Overall coupling effect among currencies is enhanced and network links are more closely.
From disorder to order, the power-law phenomenon exists generally. Barabasi (2002) pointed out that the power law is a sign for the self-organization of complex systems [22]. Power law can be used as the inherent geometric invariance of economic system complexity. Cao Hongduo et al. (2013) put forward the optimal method for determining threshold based on empirical analysis [23]. It was found that increase of the threshold θ can enhance the power-law fitting and help highlight the inherent invariance. Meanwhile, with increase of threshold, the connection between some nodes was removed, which reduces the overall information. To balance the integrity and validity of network information, the optimal threshold index W is as follows after two indexes N and R 2 were normalized in this paper: R θ are the number of nodes and goodness of fit, which are functions of θ ,

Analysis on Geographical Characteristics and Exchange Rate System Arrangements of Multilateral Exchange Rate Network
The topological structure of the network established under time window from June 1, 2003 to May 31, 2013 was analyzed. As shown in Figure 5, the currencies of the two Middle East countries-Iran and Israel-were completely isolated, but all other nodes maintained certain connection. 3 South American countries-Colombia, Chile and Brazil, were interconnected but separated from other nodes, the remaining nodes constituted a component with higher connectivity and more complicated connection. This paper analyzed the topology of full-time exchange rate network in combination with geographical characteristics and impact of exchange rate regime. ( ) N is the number of nodes in the i th area. In particular, there was only one node in Africa, so there was no connection in this area.
For the connections between area i and area j, namely A_Dis ij , the following method was used for standardization:

A_Dis A_Dis_Std
A_Dis_Std is defined as the inter-area fluctuation correlation matrix, A_Dis_Std ij is the relative fluctuation correlation between area i and area j.
A_Dis_Std is shown in Table 2. The areas of 33 countries were grouped according to Table 3. The network structures after considering the geographical factors are shown in Figure 5.
Coupled with geopolitical consideration, the network structure was clearer.  Oceania had a highest fluctuation correlation (1.00) in terms of connection strength because it had only two nodes that are connected with each other. But, Oceania had very weak connection with other areas, and had only weak connections with Europe and Asia (except West Asia). Although Asia (except West Asia) had a highest number of nodes among all areas, it had the fluctuation correlation strength up to 0.50, which shows that the fluctuation correlation effect among currencies of Asia (except West Asia) is relatively strong, and Asian currencies are also more strongly associated with the fluctuations in countries beyond South America and Africa, and the correlation strength (0.5) with West Asia is even higher than that within West Asia (0.4). The fluctuation correlation strength within South America was same to that in Asia. Three of the four nodes were fully connected. But South America was relatively independent and had only a weak connection with North America. The intra-European correlation strength was higher (0.47), and there was a stronger correlation with North America, Africa and West Asia, of which the Europe's correlation strength with West Asia exceeded that within Europe; the internal connection strength in West Asia, and the internal connection strength with Europe, North America and Asia (except West Asia) were stronger, which shows that the entire West Asia region has a strong connectivity in the network and plays a bridging role, but there is no connection between this area and Oceania, South America or Africa. There were H. D. Cao et al. only two countries in North America-the United States and Canada and they had a poor inter-area connectivity and stronger connections with West Asia, Asia (except West Asia) and Europe (0.33, 0.39 and 0.44). All connections in this area came from USD, and CAD only connected with Mexico peso, reflecting USD's core position in the network. As the most marginal part of the network, Africa was only connected with Europe. It was noteworthy that South African currency ZAR was connected with 4 European currencies but not connected with euro and USD.
Overall, except for Africa and North America, currencies in other areas had a higher internal fluctuation correlation strength, which reflects the geography of currencies. For Africa, it couldn't reflect the internal connection of currencies within Africa because only one node was selected, so there may be more comprehensive conclusions if we thought about other currencies in Africa. For external connections, there were stronger external correlation strengths among Europe, Asia (except West Asia), West Asia, and North America. The geographical characteristics of exchange rate network reflect the economic and trade ties among areas, and the political, economic and historical factors behind them deserve further consideration.
2) Analysis on impact of exchange rate regime The tripartite paradox proposed by Paul Krugman (1999) on the basis of Mundell-Fleming Model states that one country can only choose two among the exchange rate stability, free flow of capital and independence of monetary policy [24]. Therefore, one country also determines its capital mobility and monetary policy independence when choosing the exchange rate regime. According to the de facto exchange rate regime classification of IMF annual reports (Classification of Exchange Rate Arrangements and Monetary Policy, IMF Annual Report, 2004Report, , 2006Report, , 2008Report, , 2010Report, , 2012 [25] and the three-kind division standards of exchange rate regime conducted by Von Hagen and Zhou (2007) on basis of the IMF de facto exchange rate regime [26], the exchange rate arrangements of currencies are shown in Table 4.
In the exchange rate policy arrangements under 3 major categories, the currencies of the selected 33 countries and regions didn't use the pegged exchange rate policy, about 25 nodes used the floating exchange rate regime, and the rest used the intermediate exchange rate regime. After the financial crisis of 2008, the currencies with change from the intermediate exchange rate regime to the floating exchange rate regime increased. In particular, PKR, RUB and IRR switched from the intermediate exchange rate regime to the floating exchange rate regime, and chose the floating exchange rate regime again after 2008. Overall, the network de facto exchange rate regime that is adopted in relatively central nodes in the network remained unchanged from 2004 to 2012. Changes in the exchange rate policy in each year are shown in Table 5.
3) Comprehensive analysis of geopolitical nature and exchange rate regime a) Currencies of South America DOI: 10.4236/jmf.2020.101006

c) Currencies of Europe
As a whole, the degree centrality of each node in Europe is shown in Table 6.  Middle East oil countries and the United States, but it didn't have any direct connection with European countries. The degree centralities of several other European countries were high, and they had at least 10 connections. From the perspective of internal connection of European currencies, Russian ruble and U.K. pound were not connected with other European currencies; the Swiss franc CHF was connected only with DKK and EUR; the other 6 currencies were interconnected, indicating a higher correlation between the major European currencies. The internal connections of European currencies are shown in Figure 6.
From an external connection perspective, European currencies were connected with USD, AED, SAR, and QAR, and were also more connected with KWD; among all currency connections with Asia (except West Asia), and they were all connected with CNY. Currencies connected with THB and PKR were EUR, CZK, DKK, and CHF, and those connected with JPY were HUF and PLN, but had no connection with other currencies in Asia. They had no connection with South American currencies; those connected with ZAR were NOK, PLN and HUF. It is worth noting that although JPY, THB and PKR have connections with European currencies, the connections with former and the latter two are completely different, and JPY didn't have any connection with other Asian currencies.
As one of the most developed economies in economy and trade in the world, Europe has stronger economic ties that are reflected in the highly connected exchange rate network. It is very closely connected with US and Middle East and relatively connected with some currencies in Asia (except West Asia). However, the connections are much weaker than that with US and Middle East. d) Currencies of Asia (except West Asia) From the internal connection perspective, the currencies in this area were more closely connected. JPY was in an isolated position, and IDR was connected with SGD only. The nodes that were located at more central were CNY, THB, PKR and MYR, as shown in Figure 7. For exchange rate regime, the RMB de  facto exchange rate regime belonged to other traditional fixed-peg system that is pegged to USD prior to July 21, 2005

Conclusions and Suggestions
In transferring time series into network by the threshold method, the threshold reflects the trade-off between the retaining of the overall system information and presentation of those more important related information. The larger the threshold is, the more the subordinate information is deleted, and the more obvious the key related information is in the network. In the event of reasonably preserving the integrity of the system information and simultaneously considering the power law of the network degree distribution, the optimal threshold will be obtained. Under the optimal threshold, transferring the numerous related time series into a network, the real related structure features will emerge. Based on the optimal threshold, analyzing the exchange rate network of major currencies, it is found that the major international currencies show an obvious community structure. Around USD, the RMB-denominated capacity currency and the West Asia oil currency have formed a core area; peripheries are the demand-based currencies of mid-low end manufacturing products in Europe and the resource currencies represented by Indonesian rupiah and Australian dollar. Korean won and pound are in shadow currency position in the entire network structure. Meanwhile, the Australian dollar and Japanese yen have similar structures if New Zealand dollar isn't considered. As arbitrage behavior has weakened the connection between the two major currencies and other major currencies, it can be considered that the two currencies have the arbitrage function. The difference is that the Australian dollar arbitrage is dominated by the resource and core area currencies, while the Japanese yen arbitrage is dominated by the core area currency and demand-type currency, which should be given enough attention. The choice of exchange rate regime in countries is the result of the differences in economic development, economic systems and the characteristics of international trade, as well as the result of this country currency's location choice in the international monetary system. USD had always occupied the core status of network, but its core status had declined to some extent after the financial crisis occurred. With the gradual recovery of the U.S. economy from impact of financial crisis, its core status has rebounded to some extent. As China is facing the transformation of social and economic structures, the internal pressure becomes increasingly prominent, and the relatively stable exchange rate of RMB is very important. From the external perspective, stability of the RMB exchange rate that is one of the core associated nodes also helps maintain the sound development of international economy and trade. Therefore, implementation of a managed floating exchange rate regime is necessary, as well as an expression of international responsibility of a great power. At same time, the long-term one-way changes of RMB, an associated core node, has a significant impact on the order of international monetary market. Under the current economic and trade patterns, maintaining stability of exchange rate structure is the unanimous demand of all countries in the world. Therefore, RMB doesn't have the conditions of long-term devaluation under the premise of smooth operation of the domestic politics and economy.