Discovery of time-inconsecutive co-movement patterns of foreign currencies using an evolutionary biclustering method
Introduction
Over the past decades, foreign currency exchange rate determination based on international economics and finance has become increasing important since the collapse of the Bretton Woods regime in 1971 [1], [2], [3], [4]. Many researchers have worked on modeling and predicting the movement and future trend of floating exchange rates. It is known conventionally that macroeconomic fundamentals significantly influence the exchange rate behavior over the long-run [5], [6], [7]. Therefore, earlier models for analyzing the relationship between exchange rate and international macroeconomics consider the power purchasing parity (PPP) and some fundamental variables such as the interest rate and inflation as the core factors which force the exchange rates to reach a final equilibrium [3], [7]. However, those models are difficult to validate strictly because of the large variability of economic variables and financial conditions over a long period. Furthermore, an exchange rate often appears to be disconnected from its fundamentals [5], [6] due to deviations from PPP and the non-linear relationship between them [8]. The increased volatility in the short-run has thus made the modeling of floating exchange rates a difficult problem [6]. On the other hand, the nominal exchange rate regimes, as well as economic policies, can also affect the variability of macroeconomic quantities [9], resulting in huge macroeconomic changes. Though it is not easy to correctly model exchange rate economics, much attention has been paid to characterization of the natural relationship between exchange rate changes and domestic as well as international fundamentals in recent years [4], [5], [10].
Nowadays, more and more regional and international economic cooperation organizations are established to strengthen multi-literal trade and coordinate economic policies. A typical and successful example is the European Union (EU) in which 25 countries share a common market and 13 of the 25 countries share the common currency, the EURO. Improved financial and economic connections among the countries within an economic cooperation organization lead to more and more trades and capital flows, hence the closer links of nominal currency exchange rates among the member countries. Discovering the correlations of different currencies would be beneficial to studying the economic and financial connections between different member countries and provide economists and governments with verification evidences that are important for making financial policies. In addition, the correlations are potentially important for guiding investment in the market of foreign exchange rates.
Sopraseuth [9] demonstrated that the floating exchange rates of industrialized countries in a mutual business cycle were associated with high interdependence using a bootstrap test. The similar conclusions can also be drawn by using a conventional clustering technique. However, the economic or political events may often influence the nominal exchange rates in a specific short time period instead of a long time period. Because the specific period associated with a specific event is unknown, statistics based clustering analysis can only be performed with a long time period, hence ignoring important clues for relating short-term fluctuations to the specific economical or political events.
Some attentions have been paid to making use of biclustering methods to analyze the co-movement patterns of exchange rates [11], [12]. However, there are drawbacks in those previous studies. In [11], the biclustering method called plaid models detected a predefined small number of biclusters, hence often failing in detection of enough significant patterns. In [12], the authors used Hough transform (HT) to perform the search of biclusters. With a high dimensional data, HT is extremely computational expensive, making this technique impractical for real applications. Furthermore, in those analyses, the biclustering methods were actually regarded as alternatives of conventional clustering methods and took no advantage of their capability of clustering the instances and features simultaneously. As a result, the analysis of co-movement patterns that were not time-consecutive was ignored.
Accordingly, we propose a new biclustering algorithm using a genetic algorithm [13] to discover time-inconsecutive fluctuation patterns among different foreign exchange rates. The algorithm is developed with respect to a geometrical perspective and can find a typical bicluster by detecting a single hyperplane. Because enumerating the currencies is very time-consuming, we use a genetic algorithm to search for a subset of currencies for defining the dimensions of the hyperplane. In the preliminary experiments, the results demonstrate good performance of our algorithm in discovering biclusters from both of synthetic and real data sets with an acceptable computation time.
This paper is organized as follows. The next section provides a brief state-of-the-art discussion of biclustering algorithms. Our biclustering algorithm is detailed in Section 3. We illustrate the preliminary results and corresponding analysis in Section 4, and finally present conclusions in Section 5.
Section snippets
A brief state-of-the-art discussion on biclustering algorithms
In conventional clustering methods, a data matrix is partitioned in either the row or the column direction to classify the data into different groups. In biclustering, however, the data are portioned in both row and column directions to discover local subpatterns in the data matrix. The concept of biclustering goes back to the work of Hartigan [14], who called it direct clustering. The term biclustering was first proposed by Cheng and Church [15] in gene microarray data analysis. Because it can
Geometric interpretation of biclusters
In this study, we make use of a novel perspective for interpreting biclusters in a data matrix [22]. The biclusters with constant values in rows/columns, additive model, multiplicative model and linear model were addressed in their paper. As illustrated in Fig. 1, each column can be regarded as a variable denoting an axis in the 4-dimensional (4D) space [x, y, z, w] and each row is regarded as a point in the space. Without considering the coevolution biclusters, this geometric perspective can
Results and discussions
Table 1 demonstrates the averaged generations at which the embedded biclusters are found. It can be seen that the evolutionary strategy used in this study successfully detect the target bicluster. The average computation time is also acceptable in comparison with HT based method [22] by which the average computation time is more than 20 h. Therefore, the usefulness of the proposed algorithm can be proved for improving the computation time.
For the real exchange rate data series, an average of 289
Conclusions
In this study, we propose a new biclustering algorithm based on an evolutionary computation strategy. This algorithm can detect biclusters with general additive models. In comparison with previous work [11], [12], our algorithm is relatively more tolerant of noises and can discovery more useful patterns. The preliminary results demonstrate that the biclustering algorithm is able to extract biclusters from the synthetic and real foreign exchange rate data series. For the exchange rate data, each
Acknowledgments
This work is partially supported by the National Natural Science Foundation of China (Nos. 61001181 and 60902035), the Program for New Century Excellent Talents in University, Ministry of Education, China (No. NCET-10-0363), and the Specialized Research Funds for the Doctoral Program of Higher Education of China (No. 20100172120010).
References (24)
- et al.
Chaotic analysis of the foreign exchange rates
Appl. Math. Comput.
(2007) - et al.
The monetary approach to the exchange rate: long-run relationships and coefficient restrictions
Econ. Lett.
(1991) - et al.
Genetic algorithm-based clustering techniques
Pattern Recognit.
(2000) - et al.
Finding fuzzy classification rules using data mining techniques
Pattern Recognit. Lett.
(2003) Capital mobility and stabilization policy under fixed and flexible exchange rates
Can. J. Econ. Polit. Sci.
(1963)Domestic financial policies under fixed and floating exchange rates
IMF Staff Pap.
(1962)Expectations and exchange rate dynamics
J. Polit. Econ.
(1976)- et al.
Exchange rate dynamics redux
J. Polit. Econ.
(1995) - D. Backus, P. Kehoe, F. Kydland, International business cycles: theory versus evidence, in: T. Cooley (Ed.), Frontiers...
- et al.
Foundations of International Macroeconomics
(1996)
Exchange rate regimes and international business cycles
Rev. Econ. Dyn.
On fundamentals and exchange rates: a Casselian perspective
Rev. Econ. Stat.
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