Discrete Dynamics in Nature and Society

Volume 2015, Article ID 641907, 9 pages

http://dx.doi.org/10.1155/2015/641907

## Analysis of Linkage Effects among Currency Networks Using REER Data

College of Finance and Statistics, Hunan University, Changsha 410006, China

Received 8 February 2015; Revised 10 May 2015; Accepted 14 May 2015

Academic Editor: Peng Shi

Copyright © 2015 Haishu Qiao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

We modeled the currency networks through the use of REER (real effective exchange rate) instead of a bilateral exchange rate in order to overcome the confusion in selecting base currencies. Based on the MST (minimum spanning tree) approach and the rolling-window method, we constructed time-varying and correlation-based networks with which we investigate the linkage effects among different currencies. In particular, and as the source of empirical data, we chose the monthly REER data for a set of 61 major currencies during the period from 1994 to 2014. The study demonstrated that obvious linkage effects existed among currency networks and the euro (EUR) was confirmed as the predominant world currency. Additionally, we used the rolling-window method to investigate the stability of linkage effects, doing so by calculating the mean correlations and mean distances as well as the normalized tree length and degrees of those currencies. The results showed that financial crises during the study period had a great effect on the currency network’s topology structure and led to more clustered currency networks. Our results suggested that it is more appropriate to estimate the linkage effects among currency networks through the use of REER data.

#### 1. Introduction

The application of complex network analysis to financial data has attracted considerable interest in recent years [1–4]. Particularly, many scholars have focused their studies on the currency networks by using network-based correlation approaches, given that the foreign-exchange market, as the largest, most influential financial market, could directly or indirectly affect all other financial markets [5–10]. Most studies have employed the physics-derived method—namely, the minimum spanning tree (MST), which is robust but simple—to investigate the topological structure and statistical features of financial markets [11, 12]. Nevertheless, the MST results in the aforementioned investigations differ significantly, one reason being that the way to build correlation coefficient matrices varies to a great extent. Some scholars choose the Pearson correlation coefficient (PCC), which reflects the linear correlation between two stable time series, to build correlation coefficient matrices [13–15]. However, the financial time series usually demonstrate the nonlinear and nonstationary characteristics in real life, for example, the “stylized fact” of fat-tailed distribution in the return series [16]. Hence, other methods (e.g., the time-varying copula approach [10], phase synchronous information approach [9], etc.) to compute correlation coefficients among currencies have been used instead.

The aforementioned research has mainly focused on the use of a novel method to describe the interdependencies among different currencies, but few studies have focused on the confusion that occurs in the selection of base currencies, which is vital to the construction of correlation coefficient matrices. In the relevant literature it is a general problem to choose a numeraire, due to the fact that all currencies are mutually priced, thereby resulting in the absence of an independent numeraire [17]. For example, Mizuno et al. suggested the use of precious metals such as the gold, silver, and platinum, as the numeraire [18]. Nevertheless, other scholars have insisted that precious metals are inappropriate choices due to their high volatilities. Various numeraires besides the precious metals have also been used, such as the dollar, the minor currency, and the SDR [5–7]. Kwapień et al. [8] analyzed the data sets of daily foreign-exchange rates for 63 currencies and observed that there was no absolute correlation structure among the foreign-exchange networks. Instead, they found that its structure was largely dependent on the choice of base currency and the associated reference frame. In other words, the temporal evolution of the global currency system expressed by relevant exchange rates is actually the evolution of the frame in which the base currency rests. To express it simply, the use of bilateral exchange rates to construct foreign-exchange networks may obtain multifarious results because of the different choice of numeraire.

Thus the real effective exchange rate (REER) is considered to be a more important, authentic indicator, as it is able to reflect the real purchasing-power levels for currencies [19, 20]. Moreover, the REER data is calculated as weighted averages of bilateral exchange rates. Hence, there is no need to select a numeraire so all the currencies in our sample can be employed. Additionally, the current research mainly focuses on the topological structure and statistical features, but few studies have been associated with the inherent meaning of the economic phenomena. We therefore aim to use REER to substitute for the bilateral exchange rate and propose a network approach by combining the rolling-window method and the MST method as the means to investigate the topological and statistical natures of currency networks.

This methodology has been applied in two procedures, as follows. First, we collected 61 major currencies’ monthly REER data over the period of 1995 to 2014, in which the world witnessed the Asian crisis of 1997 and the U.S. subprime credit crisis of 2007. The variety of bilateral exchange rates, being reliant on the choice of the base currency as the numeraire leading to the diversification of currency networks, depends entirely on the researchers’ preference. In other words, the selection of a numeraire has no credible scientific foundation. To elaborate, the REER we employed was the average exchange rate of a basket of the foreign trade-weighted currencies adjusted for inflation. It could serve as a reasonable reference value for our research of the structure, topology, and nature of currency networks. Secondly, we used rolling-window methods to construct the dynamic cross-correlation matrices (CMs) of the 61 major currencies [21–24]. We then transformed the CMs into currency networks through the filter method of the MST in order to analyze the linkage effects of currency networks. Correlations in rolling windows were calculated in order to explore the dynamics of linkage effects. From a methodological perspective, these are the main contributions of this paper.

The rest of the paper is organized as follows: Sections 2 and 3 represent the empirical data and methodological issues. We construct currency networks in different window lengths and then present the main empirical results and analyses in Section 4. We then draw conclusions in Section 5.

#### 2. Data

We studied the REER for a set of 61 major currencies from January 1994 to November 2014. The data set we selected included the monthly index offered by the Bank for International Settlements (BIS). An effective exchange rate (EER) offered a better indicator of the financial effects of exchange rates than any single bilateral rate could. A nominal effective exchange rate (NEER) is an index of the weighted averages of bilateral exchange rates. A real effective exchange rate (REER) is the NEER deflated by relative consumer prices. EERs serve various purposes: as a measure of international competitiveness, as components of monetary/financial conditions indices, as gauges of the transmission of external shocks, as intermediate targets for monetary policy, or as an operational target. Because the REER data was calculated as weighted averages of bilateral exchange rates, it was not necessary to select a numeraire and all the currencies in the sample could be used. Moreover, it should be mentioned that the sample in this study is fully consistent with the official data provided by the BIS, thus being more credible and truthful. The 61 currencies in our research and the respective currency symbols are presented in Table 1.