Evolution and Dynamics of the Currency Network
We study the statistical and spectral properties of the foreign exchange of 21 different currencies from January 4, 1999 to March 30, 2018. The correlation matrix is calculated for different periods with a rolling window method and the properties are studied for each window. The basic statistics on the correlation matrix shows that the currencies are more and more correlated with times. The distribution of the correlation matrix was very asymmetric with non zero skewness which shows a fat tail behavior for the initial years but approach Gaussian distribution for the later time. The spectral properties of the correlation matrices for each window when compare with the properties of the correlation matrix formed for the complete period and with analytical results for Wishart matrices shows that the distribution is different for the windows comprising the calm and the crisis period. The study of the number of eigenvalues which are outside the random matrix bounds for each window on both sides of spectrum reveals that for the crisis period, the number of eigenvalues outside the lower bound increases as compared to the calm period. This increase in the number of eigenvalues on the lower side of the spectrum for a window also implies a crisis in the near future. The lower end of the spectra contains more information than the higher side as revealed by the entropic measures on the eigenvalues. This entropic measure shows that the eigenvectors on the lower side are more informative and localized. In this work, the analysis of individual eigenvector captures the evolution of interaction among different currencies with time. The analysis shows that the set of most interacting currencies that are active during the calm period and the crisis period are different. The currencies which was dominating in the calm period suddenly lose all weight and new set of currencies become active at the onset and during the crisis. The largest eigenvector of the correlation matrix can separate currencies based on their geographical location.
We acknowledge the Department of Science and Technology (DST), India, (SERB-DST No- EMR/2016/006536) for financial support.
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