تجزیه و تحلیل سلسله مراتب نمادی در بازار ارز:کاربرد سرایت در بحران ارز

In this paper we introduce a new method to describe dynamical patterns of the real exchange rate co-movements time series and to analyze contagion in currency crisis. The method combines the tools of symbolic time series analysis with the nearest neighbor single linkage clustering algorithm. Data symbolization allows us obtaining a metric distance between two different time series that is used to construct an ultrametric distance. By analyzing the data of various countries, we derive a hierarchical organization, constructing minimal-spanning and hierarchical trees. From these trees we detect different clusters of countries according to their proximity. We show that this methodology permits us to construct a structural and dynamic topology that is useful to study interdependence and contagion effects among financial time series.

There is no doubt that currency markets are extremely important. As highlighted by McDonald, Suleman, Williams, Howison, and Johnson (2005) they represent the largest market in the world, having daily transactions totaling trillions of dollars, exceeding the yearly GDP of most countries. This global integration of capital markets has accelerated since the early 1990s, as illustrated, for example, by the rapid simultaneous increase in foreign assets and liabilities. The trend toward larger external assets and liabilities has been particularly relevant for industrial countries, where, relative to output, both average external assets and liabilities about tripled between 1990 and 2003. In emerging markets global trend has been similar, unless much smaller than in industrial countries (IMF, 2005). During the 90s there has been a great amount of important turbulences, labeled currency crisis, in the world exchange markets. The European Monetary System (EMS) speculative attacks in 1992; the “Tequila crisis” originated in Mexico in December 1994; the collapse of southern Asian currencies from mid 1997 to first months 1998; the Brazilian currency devaluation on January 1999 and the Argentine currency board collapse and external debt default on January 2002 are the most relevant episodes of currency crisis in the 1990s generating interest in both academic and policy circles in the potential causes on symptoms of currency crisis and contagion. Precisely the objective of this work is to understand the structure and dynamics of cross-country exchange rate liaisons to inquiry on the contagion phenomenon in currency markets. Ortega and Matesanz (2006) use Minimal Spanning Tree (MST) methodology in order to detect clusters of countries which could be affected when a crisis occurs.3 Constructing a cross-country hierarchical structure they detect three groups of countries which are clearly divided in regional dimension (EU, Asian countries, and Latin-American). In this paper we will study the same problem, but applying a different methodology and including cross-country analysis of the structures and linkages when countries are swimming into more volatile periods and currency crises events. We will combine the Symbolic Time Series tools with the nearest neighbor single linkage clustering algorithm in order to construct different MST that can be used to represent the evolution of the phenomena. The theoretical setup of Symbolic Time Series Analysis is based on Daw et al., 2003 and Brida and Punzo, 2003. In the first stage we introduce a partition of the space of states. Using this partition, all the values of the time series data are transformed into a finite string of symbols. This converts the original signal into a symbolic sequence, from where symbolic sequence statistics can be computed. In particular we apply concepts from information theory and symbolic dynamics to process the symbolic sequence. The paper is organized as follows. In the next section we briefly review the theoretical literature in currency crisis and contagion and we state some possible causes of contagion during currency crisis. In Section 3 we introduce the minimal spanning tree, the ultrametric distance and the hierarchical tree, constructed from the Pearson correlation coefficient. Section 4 describes the data, introduces a criteria for data symbolization and the Symbolic Time Series tools. Next, by analyzing the data of various countries, we derive a hierarchical organization, constructing minimal-spanning and hierarchical trees constructed from different distances. From these trees we detect different clusters of countries according to their proximity. In the last section we draw our conclusions and present some future lines of studying.

In the last years interest in studying currency crises, and in particular the effects of contagion has grown due to the important crises during the nineties. Events such as occurred with the EMS in 1992, the Tequila crisis originated in Mexico and the Southern Asian crisis had a high impact in the international financial markets. A strand on the empirical literature has been interested in the debate of the existence, or not, of contagion effects among currencies. A great amount of work has been done on the issue but conclusive results have not been obtained (Dungey et al., 2005). In this sense the present article introduce a methodology based on the symbolic time series analysis with the nearest neighbor single linkage clustering algorithm. The aim of this methodology is to study interdependence among financial time series in different volatility situations. Using this method was possible to construct the MST and the associated HT. These trees seem to be useful as a theoretical description of the currency markets showing the most narrowly connected countries and those who seem to be more distant. Therefore, countries with strong links among them are subject to spread rapidly. From our results we obtain three regions or clusters of countries. They are related with their geographical and commercial closeness: Europe, Asia and Latin America. As expected, the European countries are the most connected in our group of countries. In this group, Denmark is the most linked country. In second place appears a group of Asiatic countries where the most connected country is Thailand, which was precisely the country where the Asian crisis started in 1998. Finally there is a group of Latin American countries which are the less connected in our study. We have shown that this regional hierarchical structure prevails in tranquil times and in more volatile and crises periods which we analyze by moving up our threshold. In this sense, this new methodology help to inquiry on the contagion-interdependence debate around currency and financial crises, supporting no evidence of contagion during currency crises in the nineties, but stable interdependence among exchange rate dynamics. Besides, we have observed some countries which could be generators of currency crises contagion in their regions because they became centre of all the regional links in crises periods (Thailand and Brazil are clear examples).