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.     

Correlations,hierarchies and networks of the world’s automotive companies

We investigate, within the scope of econophysics, the correlations, hierarchies and networks of the world’s automotive companies over the 2003–2010 period by using the concept of a minimal spanning tree (MST) and hierarchical tree (HT). We derive a hierarchical organization and construct the MSTs and HTs for the 2003–2010 period and illustrate how the MSTs and their associated HTs developed over time. These periods are divided into two subperiods, such as 2003–2006 and 2007–2010, in order to test various time-windows and understand the temporal evolution of the correlation structure over time. We perform the bootstrap techniques to investigate a value of the statistical reliability to the links of the MSTs. We also use average linkage cluster analysis (ALCA) to observe the cluster structure more clearly in HTs. From the structural topologies of these trees, we identify different clusters of companies according to their geographical proximity and economic ties. Our results show that some companies are more important within the network, due to a tighter connection with other companies. We also find that these important companies play a predominant role in the world’s automotive industry.     

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.     

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.     

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.     

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.     

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.     

An ever-closer union? Examining the evolution of linkages of European equity markets via minimum spanning trees

The concept of a minimum spanning tree (MST) is used to study the process of comovements for 21 European Union stock market indices. We show how the minimum spanning tree and its related hierarchical tree evolve over time and describe the dynamics. Over the period studied, 1999-2006, the French equity market provides the main linkages in the system. The 2004 Accession states are more loosely connected to the other markets; they form two groupings, with the Czech Republic, Hungary, and Poland having tighter links to the main markets than the remaining Accession markets. Shorter distances between markets indicate a potential reduction of the benefits of international portfolio diversification in European markets, with the possible exception of those markets at the outer limits of the MST.     

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.     

Comovements in government bond markets: A minimum spanning tree analysis

The concept of a minimum spanning tree (MST) is used to study patterns of comovements for a set of twenty government bond market indices for developed North American, European, and Asian countries. We show how the MST and its related hierarchical tree evolve over time and describe the dynamic development of market linkages. Over the sample period, 1993-2008, linkages between markets have decreased somewhat. However, a subset of European Union (EU) bond markets does show increasing levels of comovements. The evolution of distinct groups within the Eurozone is also examined. The implications of our findings for portfolio diversification benefits are outlined.     

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.     

Sector analysis for a FTSE portfolio of stocks

Using a portfolio of stocks from the London Stock Exchange FTSE100 index (FTSE), we study both the time dependence of their correlations and the normalized tree length of the associated minimal spanning tree (MST). The first four moments of the distribution of correlations and lengths of the tree are examined in detail and differences in behavior noted. For different economic groups and industries, clustering is evident. However, comparing the classification used prior to 2006 with that introduced in January 2006 it is clear that the new classification, apart from one or two notable exceptions, is much more compatible with the clustering obtained by the MST analysis. We finally compare the MST for real data with that obtained for a synthetic random market. The latter tree would seem more like the structure found by Coronnello et al. for trees based on high-frequency data.     

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.     

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.     

Analysis of cross-correlations between financial markets after the 2008 crisis

We analyze the cross-correlation matrix C of the index returns of the main financial markets after the 2008 crisis using methods of random matrix theory. We test the eigenvalues of C for universal properties of random matrices and find that the majority of the cross-correlation coefficients arise from randomness. We show that the eigenvector of the largest deviating eigenvalue of C represents a global market itself. We reveal that high volatility of financial markets is observed at the same times with high correlations between them which lowers the risk diversification potential even if one constructs a widely internationally diversified portfolio of stocks. We identify and compare the connection and cluster structure of markets before and after the crisis using minimal spanning and ultrametric hierarchical trees. We find that after the crisis, the co-movement degree of the markets increases. We also highlight the key financial markets of pre and post crisis using main centrality measures and analyze the changes. We repeat the study using rank correlation and compare the differences. Further implications are discussed.     

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.     

Multidimensional minimal spanning tree: The Dow Jones case

This paper introduces a new methodology in order to construct Minimal Spanning Trees (MST) and Hierarchical Trees (HT) using the information provided by more than one variable. In fact, the Symbolic Time Series Analysis (STSA) approach is applied to the Dow Jones companies using information not only from asset returns but also for trading volume. The US stock market structure is obtained, showing eight clusters of companies and General Electric as a central node in the tree. We use different partitions showing that the results do not depend on the particular partition. In addition, we apply Monte Carlo simulations suggesting that the tree is not the result of random connections.     

Minimal spanning tree problem in stock networks analysis: An efficient algorithm

Since the last decade, minimal spanning trees (MSTs) have become one of the main streams in econophysics to filter the important information contained, for example, in stock networks. The standard practice to find an MST is by using Kruskal’s algorithm. However, it becomes slower and slower when the number of stocks gets larger and larger. In this paper we propose an algorithm to find an MST which has considerably promising performance. It is significantly faster than Kruskal’s algorithm and far faster if there is only one unique MST in the network. Our approach is based on the combination of fuzzy relation theory and graph theoretical properties of the forest of all MSTs. A comparison study based on real data from four stock markets and four types of simulated data will be presented to illustrate the significant advantages of the proposed algorithm.     

Network structure of cross-correlations among the world market indices

We report the results of an investigation of the properties of the networks formed by the cross-correlations of the daily and weekly index changes of 143 stock market indices from 59 different countries. Analysis of the asset graphs, minimum spanning trees (MST) and planar maximally filtered graphs (PMFG) of the afermentioned networks confirms that globalization has been increasing in recent years. North American and European markets are observed to be much more strongly connected among themselves compared to the integration with the other geographical regions. Surprisingly, the integration of East Asian markets among themselves as well as to the Western markets is found to be rather weak. MST and PMFG of both daily and weekly return correlations indicates that the clustering of the indices is mostly geographical. The French fsbf250 index is found to be most important node of the MST and PMFG based on several graph centrality measures.     

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.