Hierarchical structures of correlations networks among Turkey’s exports and imports by currencies

We have examined the hierarchical structures of correlations networks among Turkey’s exports and imports by currencies for the 1996–2010 periods, using the concept of a minimal spanning tree (MST) and hierarchical tree (HT) which depend on the concept of ultrametricity. These trees are useful tools for understanding and detecting the global structure, taxonomy and hierarchy in financial markets. We derived a hierarchical organization and build the MSTs and HTs during the 1996–2001 and 2002–2010 periods. The reason for studying two different sub-periods, namely 1996–2001 and 2002–2010, is that the Euro (EUR) came into use in 2001, and some countries have made their exports and imports with Turkey via the EUR since 2002, and in order to test various time-windows and observe temporal evolution. We have carried out bootstrap analysis to associate a value of the statistical reliability to the links of the MSTs and HTs. We have also used the average linkage cluster analysis (ALCA) to observe the cluster structure more clearly. Moreover, we have obtained the bidimensional minimal spanning tree (BMST) due to economic trade being a bidimensional problem. From the structural topologies of these trees, we have identified different clusters of currencies according to their proximity and economic ties. Our results show that some currencies are more important within the network, due to a tighter connection with other currencies. We have also found that the obtained currencies play a key role for Turkey’s exports and imports and have important implications for the design of portfolio and investment strategies.     

Hierarchical structure of Turkey’s foreign trade

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.     

Topology of the correlation networks among major currencies using hierarchical structure methods

We studied the topology of correlation networks among 34 major currencies using the concept of a minimal spanning tree and hierarchical tree for the full years of 2007-2008 when major economic turbulence occurred. We used the USD (US Dollar) and the TL (Turkish Lira) as numeraires in which the USD was the major currency and the TL was the minor currency. We derived a hierarchical organization and constructed minimal spanning trees (MSTs) and hierarchical trees (HTs) for the full years of 2007, 2008 and for the 2007-2008 period. We performed a technique to associate a value of reliability to the links of MSTs and HTs by using bootstrap replicas of data. We also used the average linkage cluster analysis for obtaining the hierarchical trees in the case of the TL as the numeraire. These trees are useful tools for understanding and detecting the global structure, taxonomy and hierarchy in financial data. We illustrated how the minimal spanning trees and their related hierarchical trees developed over a period of time. From these trees we identified different clusters of currencies according to their proximity and economic ties. The clustered structure of the currencies and the key currency in each cluster were obtained and we found that the clusters matched nicely with the geographical regions of corresponding countries in the world such as Asia or Europe. As expected the key currencies were generally those showing major economic activity.     

Investigation of major international and Turkish companies via hierarchical methods and bootstrap approach

We present a study, within the scope of econophysics, of the hierarchical structure of 98 among the largest international companies including 18 among the largest Turkish companies, namely Banks, Automobile, Software-hardware, Telecommunication Services, Energy and the Oil-Gas sectors, viewed as a network of interacting companies. We analyze the daily time series data of the Boerse-Frankfurt and Istanbul Stock Exchange. We examine the topological properties among the companies over the period 2006–2010 by using the concept of hierarchical structure methods (the minimal spanning tree (MST) and the hierarchical tree (HT)). The period is divided into three subperiods, namely 2006–2007, 2008 which was the year of global economic crisis, and 2009–2010, in order to test various time-windows and observe temporal evolution. We carry out bootstrap analyses to associate the value of statistical reliability to the links of the MSTs and HTs. We also use average linkage clustering analysis (ALCA) in order to better observe the cluster structure. From these studies, we find that the interactions among the Banks/Energy sectors and the other sectors were reduced after the global economic crisis; hence the effects of the Banks and Energy sectors on the correlations of all companies were decreased. Telecommunication Services were also greatly affected by the crisis. We also observed that the Automobile and Banks sectors, including Turkish companies as well as some companies from the USA, Japan and Germany were strongly correlated with each other in all periods.     

Analysis of the effects of the global financial crisis on the Turkish economy, using hierarchical methods

We have analyzed the topology of 50 important Turkish companies for the period 2006-2010 using the concept of hierarchical methods (the minimal spanning tree (MST) and hierarchical tree (HT)). We investigated the statistical reliability of links between companies in the MST by using the bootstrap technique. We also used the average linkage cluster analysis (ALCA) technique to observe the cluster structures much better. The MST and HT are known as useful tools to perceive and detect global structure, taxonomy, and hierarchy in financial data. We obtained four clusters of companies according to their proximity. We also observed that the Banks and Holdings cluster always forms in the centre of the MSTs for the periods 2006-2007, 2008, and 2009-2010. The clusters match nicely with their common production activities or their strong interrelationship. The effects of the Automobile sector increased after the global financial crisis due to the temporary incentives provided by the Turkish government. We find that Turkish companies were not very affected by the global financial crisis.     

Hierarchical structure of countries based on carbon dioxide emission over the periods of 1971–2012; the relationships economic growth and energy consumption

This study uses hierarchical structure methods (minimal spanning tree, (MST) and hierarchical tree, (HT)) to examine the hierarchical structures of the carbon dioxide emission from the 84 countries by three main sectors, namely electricity/heat, manufacturing/construction and transportation sectors. We obtain the topological properties among the countries based on carbon dioxide emission over the periods of 1971–2012. We also perform the bootstrap techniques to investigate a value of the statistical reliability to the links of the MSTs. The results of the topologies structural of these trees are as follows: (i) We identified different groups of countries according to their economic growth and geographical location. (ii) Our results show that the high income and low energy consuming country groups are more important within the network.     

Will the US economy recover in 2010? A minimal spanning tree study

We calculated the cross correlations between the half-hourly times series of the ten Dow Jones US economic sectors over the period February 2000 to August 2008, the two-year intervals 2002-2003, 2004-2005, 2008-2009, and also over 11 segments within the present financial crisis, to construct minimal spanning trees (MSTs) of the US economy at the sector level. In all MSTs, a core-fringe structure is found, with consumer goods, consumer services, and the industrials consistently making up the core, and basic materials, oil & gas, healthcare, telecommunications, and utilities residing predominantly on the fringe. More importantly, we find that the MSTs can be classified into two distinct, statistically robust, topologies: (i) star-like, with the industrials at the center, associated with low-volatility economic growth; and (ii) chain-like, associated with high-volatility economic crisis. Finally, we present statistical evidence, based on the emergence of a star-like MST in Sep 2009, and the MST staying robustly star-like throughout the Greek Debt Crisis, that the US economy is on track to a recovery.     

The relationships between electricity consumption and GDP in Asian countries,using hierarchical structure methods

This study uses hierarchical structure methods (minimal spanning tree (MST) and hierarchical tree (HT)) to examine the relationship between energy consumption and economic growth in a sample of 30 Asian countries covering the period 1971–2008. These countries are categorized into four panels based on the World Bank income classification, namely high, upper middle, lower middle, and low income. In particular, we use the data of electricity consumption and real gross domestic product (GDP) per capita to detect the topological properties of the countries. We show a relationship between electricity consumption and economic growth by using the MST and HT. We also use the bootstrap technique to investigate a value of the statistical reliability to the links of the MST. Finally, we use a clustering linkage procedure in order to observe the cluster structure. The results of the structural topologies of these trees are as follows: (i) we identified different clusters of countries according to their geographical location and economic growth, (ii) we found a strong relationship between energy consumption and economic growth for all income groups considered in this study and (iii) the results are in good agreement with the causal relationship between electricity consumption and economic growth.     

Multifractal detrended fluctuation analysis for clustering structures of electricity price periods

A new model is proposed to investigate the structure of electricity price in different time periods. A popular method — the multifractal detrended fluctuation analysis (MF-DFA) method is employed to analyze the features achieved from three types of electricity price data after filtering some trends by Fourier detrended fluctuation function. Twelve multifractal parameters are calculated and selected as the characteristic indicators for comparison. Moreover, the minimum number of indicators is determined so that the discriminant accuracy reaches maximum based on Fisher’s linear discriminant algorithm (Fisher’s LDA) for each time period. These indicators form a multi-dimensional space, in which each point represents a price time series. This allows us to cluster the three price time periods, namely, the low price time periods, the average price time periods and the peak price time periods. Fisher’s LDA is employed to evaluate the discriminant accuracy on these three kinds of time periods. Our analysis is then applied to the data in California1999–2000 and PJM2001–2002 electricity markets to demonstrate the applicability of our methods.     

Correlation based networks of equity returns sampled at different time horizons

We investigate the planar maximally filtered graphs of the portfolio of the 300 most capitalized stocks traded at the New York Stock Exchange during the time period 2001–2003. Topological properties such as the average length of shortest paths, the betweenness and the degree are computed on different planar maximally filtered graphs generated by sampling the returns at different time horizons ranging from 5 min up to one trading day. This analysis confirms that the selected stocks compose a hierarchical system progressively structuring as the sampling time horizon increases. Finally, a cluster formation, associated to economic sectors, is quantitatively investigated.     

Similarity measure and topology evolution of foreign exchange markets using dynamic time warping method: Evidence from minimal spanning tree

In this study, we employ a dynamic time warping method to study the topology of similarity networks among 35 major currencies in international foreign exchange (FX) markets, measured by the minimal spanning tree (MST) approach, which is expected to overcome the synchronous restriction of the Pearson correlation coefficient. In the empirical process, firstly, we subdivide the analysis period from June 2005 to May 2011 into three sub-periods: before, during, and after the US sub-prime crisis. Secondly, we choose NZD (New Zealand dollar) as the numeraire and then, analyze the topology evolution of FX markets in terms of the structure changes of MSTs during the above periods. We also present the hierarchical tree associated with the MST to study the currency clusters in each sub-period. Our results confirm that USD and EUR are the predominant world currencies. But USD gradually loses the most central position while EUR acts as a stable center in the MST passing through the crisis. Furthermore, an interesting finding is that, after the crisis, SGD (Singapore dollar) becomes a new center currency for the network.     

Structural and topological phase transitions on the German Stock Exchange

We find numerical and empirical evidence for dynamical, structural and topological phase transitions on the (German) Frankfurt Stock Exchange (FSE) in the temporal vicinity of the worldwide financial crash. Using the Minimal Spanning Tree (MST) technique, a particularly useful canonical tool of the graph theory, two transitions of the topology of a complex network representing the FSE were found. The first transition is from a hierarchical scale-free MST representing the stock market before the recent worldwide financial crash, to a superstar-like MST decorated by a scale-free hierarchy of trees representing the market’s state for the period containing the crash. Subsequently, a transition is observed from this transient, (meta)stable state of the crash to a hierarchical scale-free MST decorated by several star-like trees after the worldwide financial crash. The phase transitions observed are analogous to the ones we obtained earlier for the Warsaw Stock Exchange and more pronounced than those found by Onnela–Chakraborti–Kaski–Kertész for the S&P 500 index in the vicinity of Black Monday (October 19, 1987) and also in the vicinity of January 1, 1998. Our results provide an empirical foundation for the future theory of dynamical, structural and topological phase transitions on financial markets.     

Hierarchical cluster-tendency analysis of the group structure in the foreign exchange market

A hierarchical cluster-tendency (HCT) method in analyzing the group structure of networks of the global foreign exchange (FX) market is proposed by combining the advantages of both the minimal spanning tree (MST) and the hierarchical tree (HT). Fifty currencies of the top 50 World GDP in 2010 according to World Bank’s database are chosen as the underlying system. By using the HCT method, all nodes in the FX market network can be “colored” and distinguished. We reveal that the FX networks can be divided into two groups, i.e., the Asia-Pacific group and the Pan-European group. The results given by the hierarchical cluster-tendency method agree well with the formerly observed geographical aggregation behavior in the FX market. Moreover, an oil-resource aggregation phenomenon is discovered by using our method. We find that gold could be a better numeraire for the weekly-frequency FX data.     

The use of dynamical networks to detect the hierarchical organization of financial market sectors

Two kinds of filtered networks: minimum spanning trees (MSTs) and planar maximally filtered graphs (PMFGs) are constructed from dynamical correlations computed over a moving window. We study the evolution over time of both hierarchical and topological properties of these graphs in relation to market fluctuations. We verify that the dynamical PMFG preserves the same hierarchical structure as the dynamical MST, providing in addition a more significant and richer structure, a stronger robustness and dynamical stability. Central and peripheral stocks are differentiated by using a combination of different topological measures. We find stocks well connected and central; stocks well connected but peripheral; stocks poorly connected but central; stocks poorly connected and peripheral. It results that the Financial sector plays a central role in the entire system. The robustness, stability and persistence of these findings are verified by changing the time window and by performing the computations on different time periods. We discuss these results and the economic meaning of this hierarchical positioning.     

Is the wealth of the world’s billionaires Paretian?

This paper investigates the issue of whether or not the top world wealth distribution is Paretian in nature. To this end, Forbes’ data on the net worth of the world’s billionaires for each of the ten years from 2000 to 2009 is used. The results of the Kolmogorov–Smirnov (KS), Anderson–Darling (AD) and chi-squared tests for Pareto power law conducted do not reveal any evidence of Paretian behavior at the conventional 5% level of significance.     

Penrose tiling fractality in coordination Cayley’s tree graphs representation

We offer the mathematical apparatus for mapping lattice and cellular systems into the generalized coordination Cayley’s tree graphs. These Cayley’s trees have a random branchiness property and an intralayer interbush local intersection. Classical Bethe-Cayley tree graphs don’t have these properties. Bush type simplicial decomposition on Cayley’s tree graphs is introduced, on which the enumerating polynomials or enumerating distributions are built. Within the entropy methodology three types of fractal characteristics are introduced, which characterize quasi-crystalline pentagonal Penrose tiling. The quantitative estimate for the frontal-radial fractal percolation on a Cayley’s tree graph of a Penrose tiling leading to the overdimensioned effect is calculated.     

Does pop music exist? Hierarchical structure in phonographic markets

I find a topological arrangement of assets traded in phonographic markets which has associated a meaningful economic taxonomy. I continue using the Minimal Spanning Tree and the correlations between assets, but now outside the stock markets. This is the first attempt to use these methods on phonographic markets where we have artists instead of stocks. The value of an artist is defined by record sales. The graph is obtained starting from the matrix of correlation coefficients computed between the world’s most popular 30 artists by considering the synchronous time evolution of the difference of the logarithm of weekly record sales. This method provides the hierarchical structure of the phonographic market and information on which music genre is meaningful according to customers. Statistical properties (including the Hurst exponent) of weekly record sales in the phonographic market are also discussed.     

Research on the relationships of the domestic mutual investment of China based on the cross-shareholding networks of the listed companies

Enterprises are the core power and the carriers to promote the country’s economy developing sustainably and rapidly; the listed enterprises are the outstanding companies which can represent the economic level at the places where the enterprises are located, so we establish the cross-shareholding networks of the listed companies between 2002 and 2009, and then analyze the mutual investment at company-level, province-level and region-level. We have researched the overall trend of economic development and the overall tendency of capital flow of China in the recent 8 years based on the cross-shareholding networks, the influence of a global economic crisis on the stock markets and the overall economics of China in 2008 and the recovery of the economy after the economic crisis. Moreover, we analyze the variations of the cross-shareholding networks and the influence of the state-owned large and medium enterprises listing frequently on Chinese stock markets. We divide the provinces of China into 3 main categories according to their industrial situations. Though the analysis, we find that the wealth gap between the different areas is not significantly reduced even though the government has carried out strategies such as the Development of the West Regions and the Rejuvenation of Old Industrial Bases in Northeastern China. We analyze the cumulative distribution function of the degree of the vertices and use large amounts of data to do empirical analysis. The methods used include the hierarchical cluster analysis, regression analysis, etc.     

Sovereign debt crisis in the European Union: A minimum spanning tree approach

In the wake of the financial crisis, sovereign debt crisis has emerged and is severely affecting some countries in the European Union, threatening the viability of the euro and even the EU itself. This paper applies recent developments in econophysics, in particular the minimum spanning tree approach and the associate hierarchical tree, to analyze the asynchronization between the four most affected countries and other resilient countries in the euro area. For this purpose, daily government bond yield rates are used, covering the period from April 2007 to October 2010, thus including yield rates before, during and after the financial crises. The results show an increasing separation of the two groups of euro countries with the deepening of the government bond crisis.