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Based on a time-varying copula approach and the minimum spanning tree (MST) method, we propose a time-varying correlation network-based approach to investigate dynamics of foreign exchange (FX) networks. In piratical terms, we choose the daily FX rates of 42 major currencies in the international FX market during the period of 2005–2012 as the empirical data. The empirical results show that (i) the distributions of cross-correlation coefficients (distances) in the international FX market (network) are fat-tailed and negatively skewed; (ii) financial crises during the analyzed period have a great effect on the FX network’s topology structure and lead to the US dollar becoming more centered in the MST; (iii) the topological measures of the FX network show a large fluctuation and display long-range correlations; (iv) the FX network has a long-term memory effect and presents a scale-free behavior in the most of time; and (v) a great majority of links between currencies in the international FX market survive from one time to the next, and multistep survive rates of FX networks drop sharply as the time increases.

Financial markets are accounted as complex dynamical systems with large quantities of interacting unties [

The motivations that led us to combine the two aforementioned methods to investigate dynamics of FX networks can be summed up as follows. On the one hand, the MST and its improvements are usually used to identify the clustering behavior and dominant currencies in the FX network. To examine the dynamic behavior of the network, pervious works often employ a rolling window analysis, such as [

On the other hand, copula methods proposed by Sklar [

In consideration of the above-mentioned motives, based on a time-varying copula approach and the MST method, we aim to construct time-varying FX networks and analyze their topological dynamics and market properties. We choose 42 major currencies’ daily FX rate series in the international FX market during the years 2005–2012 as the empirical data. In empirical process, we first use a time-varying copula to calculate the dynamic cross-correlation coefficients

The remainder of the paper is organized as follows. Section

As for the empirical data set, we choose the daily FX rates of 42 major currencies in the international FX market from January 4, 2005, to December 31, 2012. Following Jang et al. [

In this section, we first introduce the time-varying copula model including the model for marginal distributions, the dynamic Student’s

Following Patton [

According to Diks et al. [

For all

As proposed in [

Following Wang et al. [

The marginal parameters are estimated by the maximum likelihood (ML) as

Given

After obtaining the time-varying cross-correlation coefficients between any two currencies by a time-varying copula approach, we can build

To investigate dynamics of FX networks, we introduce some topological measures as follows. We use a quantity of

The measure of

We introduce a concept of

The scale-free behavior is widely found in different networks [

Before studying dynamics of FX networks, we first analyze statistical properties of cross-correlation coefficients and distances of MST for 42 currencies in the international FX market. The cross-correlation coefficient series contains

The mean, standard deviation, skewness, and kurtosis of cross-correlation coefficients of 42 currencies in the international FX market as functions of time.

The mean, standard deviation, skewness, and kurtosis of distances of MST of 42 currencies in the international FX market as functions of time.

Considering that financial crises have a strong influence on the international FX market, we choose three days (i.e., January 5, 2005; January 2, 2008; and January 3, 2012) as representatives of three periods of before, during, and after financial crises. We present the three MSTs of 42 currencies in the international FX market in Figures

MST of 42 currencies in the international FX market on January 5, 2005, as a representative of the period of before financial crises.

MST of 42 currencies in the international FX market on January 2, 2008, as a representative of the period of during financial crises.

MST of 42 currencies in the international FX market on January 3, 2012, as a representative of the period of after financial crises.

From Figure

As illustrated in Figure

Compared with the MSTs in Figures

From Figures

In this subsection, we aim to investigate the dynamical evolution of time-varying FX networks’ topological features. To begin with it, we show the calculation results of the average path length (APL), mean occupation layer (MOL), and maximum degree

The average path length (APL), mean occupation layer (MOL), and maximum degree kmax of MST of 42 currencies in the international FX market as functions of time. In each panel, the red solid line stands for the corresponding statistical average value over the time investigated.

The estimated power-law exponent

Similar to Qiu et al. [

The DFA functions of the average path length (APL), mean occupation layer (MOL), and maximum degree

In order to study the robustness of links over time and the long-term evolution of FX networks, respectively, we use two measures, that is, the

In Figure

The single-step survival ratio (SSR) of MST of 42 currencies in the international FX market as a function of time. The red solid line stands for the corresponding statistical average value over the time investigated.

The DFA function of the single-step survival ratio (SSR) on a log-log plot. The red solid line stands for the associated linear fitting curve, and the estimated Hurst exponent

The multistep survival ratio (MSR) of MST of 42 currencies in the international FX market as a function of time for different initial time

In this paper, we investigate the daily FX rates of 42 major currencies in the international FX market during the period of 2005–2012 and construct time-varying FX networks by a time-varying copula approach and the MST method. In detail, we first use the AR(

Some basic finding for examining FX networks in this research can be summarized as follows. (i) By analyzing the descriptive statistics of cross-correlation coefficients and distances of MST, we find that distributions of cross-correlation coefficients (distances) in the international FX market (network) are fat-tailed and negatively skewed. (ii) On basis of MSTs for three different periods, we observe that some currencies gather together and form into several clusters, such as the international cluster with USD at its center, the Middle Eastern cluster, and the European cluster. The financial crises have a great influence on the FX network’s topology structure and lead to USD becoming more centered in the MST because lots of currencies from Asia, Latin America, Middle East, and Africa are directly or indirectly linked to USD. (iii) The topological measures of the FX network present a large fluctuation and have a long-term memory effect. By estimating the degree distribution of MST, we find that the FX network is a scale-free network in most of the time. (iv) A great majority of links between currencies in the international FX market survive from one time to the next, and multistep survive rates descend sharply as the time increases.

The authors declare that there is no conflict of interests regarding the publication of this paper.

The authors thank C. Yu who works in the Guosen Securities Co., Ltd., for helpful discussions. This work was supported by the Fundamental Research Funds for the Central Universities of Hunan University, the Hunan Provincial Innovation Foundation for Postgraduate (Grant no. CX2013A006), the Scholarship Award for Excellent Doctoral Student granted by the Ministry of Education of China, the National Natural Science Foundation of China (Grant no. 71373072), the Specialized Research Fund for the Doctoral Program of Higher Education (Grant no. 20130161110031), the China Postdoctoral Science Foundation (Grant no. 2013M530376), and the Foundation for Innovative Research Groups of the National Natural Science Foundation of China (Grant no. 71221001).