Statistical Properties of the Foreign Exchange Network at Different Time Scales: Evidence from Detrended Cross-Correlation Coefficient and Minimum Spanning Tree

Gang-Jin Wang,Yi-Jun Chen,Shou Chen,Chi Xie

doi:10.3390/e15051643

Abstract

We investigate the statistical properties of the foreign exchange (FX) network at different time scales by two approaches, namely the methods of detrended cross-correlation coefficient (DCCA coefficient) and minimum spanning tree (MST). The daily FX rates of 44 major currencies in the period of 2007–2012 are chosen as the empirical data. Based on the analysis of statistical properties of cross-correlation coefficients, we find that the cross-correlation coefficients of the FX market are fat-tailed. By examining three MSTs at three special time scales (i.e., the minimum, medium, and maximum scales), we come to some conclusions: USD and EUR are confirmed as the predominant world currencies; the Middle East cluster is very stable while the Asian cluster and the Latin America cluster are not stable in the MSTs; the Commonwealth cluster is also found in the MSTs. By studying four evaluation criteria, we find that the MSTs of the FX market present diverse topological and statistical properties at different time scales. The scale-free behavior is observed in the FX network at most of time scales. We also find that most of links in the FX network survive from one time scale to the next.

Highlights

It has been a “stylized fact” that financial markets are deemed as complex systems with a mass of interacting entities [1,2]
Considering that there are too many minimum spanning tree (MST) to present for all the time scales s, for the foreign exchange (FX) market, we hereby only show and analyze three MSTs at three different time scales, but in the subsection we will present the statistical properties of the FX network at different time scales
To analyze the topological and statistical properties of the FX network, at different time scales s, we investigate the four evaluation criteria (i.e., LNTL, LAPL, kmax, and LMOL ) of MSTs and show the results in one can find that the two curves of LAPL and LMOL have a similar trend from Figure 6b,d

Summary

Introduction

It has been a “stylized fact” that financial markets are deemed as complex systems with a mass of interacting entities [1,2]. Since Mantegna [10] first introduced the topology network tool of MST for the portfolio of stocks in the U.S stock market, the correlation network-based methods have been widely used to quantify the cross-correlations and market properties in different financial markets [23], such as stock markets [13,14,24,25,26,27,28,29,30,31,32,33,34] and commodity markets [35]. To quantify the cross-correlations between two non-stationary time series i and j, a new detrended cross-correlation coefficient ρi j (s) was developed by Zenbende [48], which is expressed in terms of the detrended fluctuation analysis (DFA) [49] and the detrended cross-correlation analysis (DCCA) [20] , where s is the time scale. The DCCA coefficient was widely used to investigate the cross-correlations in different fields [50,51], such as the FX market [4,52] and stock markets [45,53,54]

Objectives

Methods

Results

Conclusion