شبکه همبستگی در میان ارزها

By analyzing the foreign exchange market data of various currencies, we derive a hierarchical taxonomy of currencies constructing minimal-spanning trees. Clustered structure of the currencies and the key currency in each cluster are found. The clusters match nicely with the geographical regions of corresponding countries in the world such as Asia or East Europe, the key currencies are generally given by major economic countries as expected.

A value of currency is expected to reflect the whole economic status of the country, and a foreign exchange rate is considered to be a measure of economic balance of the two countries. In the real world there are several economic blocks such as Asia, but it is not clarified whether such economic blocks affect the foreign exchange rate fluctuations or not. From the viewpoint of physics, the foreign exchange market is a typical open system having interactions with all information around the world including price changes of other markets. Also, the mean transaction intervals of foreign exchange markets are typically about 10 s, and it is not clear how the market correlates with the huge scale information of a whole country or the economic blocks. In order to empirically establish the relations between microscopic market fluctuations and macroscopic economic states, it is important to investigate the interaction of currency rates in the high precision data of foreign exchange markets. The correlations among market prices have been analyzed intensively for stock prices by using minimal-spanning trees or self-organizing maps [1], [2], [3], [4], [5] and [14]. The interaction among stocks is expected to be caused by information flow, and direction of the information flow has been investigated from a cross-correlation function with a time shift [6], [7] and [8]. Kullmann et al. and Kertesz et al. introduced a directed network among companies for the stocks [7] and [8]. We observe the interaction among foreign exchange markets using minimal-spanning tree. We construct a currency minimal-spanning tree by defining correlation among foreign exchange rates as the distance. The minimal-spanning tree is a kind of currency map and is helpful for constructing a stable portfolio of the foreign exchange rates. We use correlation coefficient of daily difference of the logarithm rate in order to detect the topological arrangement of the currencies. The correlation coefficient is computed between all the possible pairs of rates in a given time period. We classify the currencies on the minimal-spanning tree according to the correlation coefficients, and find key currencies in each cluster. We analyze 26 currencies and 3 metals from January ‘99 up to December ‘03 provided by Exchange Rate Service [9].