- freely available
Entropy 2013, 15(5), 1643-1662; https://doi.org/10.3390/e15051643
2. Data and Methodology
2.1. Data Set
|Africa||Egyptian Pound||EGP||Europe||Romanian New Leo||RON|
|South Africa Rand||ZAR||Russian Rubles||RUB|
|Asia||Chinese Renminbi||CNY||Swedish Krona||SEK|
|Indian Rupee||INR||Swiss Franc||CHF|
|Indonesian Rupiah||IDR||Turkish New Lira||TRY|
|Japanese Yen||JPY||Latin America||Argentinian Peso||ARS|
|Malaysian Ringgit||MYR||Brazilian Real||BRL|
|Pakistani Rupee||PKR||Chilean Pesos||CLP|
|Philippines Peso||PHP||Colombian Peso||COP|
|Singapore Dollar||SGD||Panamanian Balboas||PAB|
|South Korean Won||KRW||Peruvian New Sole||PEN|
|Sri Lankan Rupee||LKR||Mexican Peso||MXN|
|Taiwan Dollar||TWD||Venezuelan Bolívar Fuerte||VEF|
|Thai Baht||THB||Middle East||Israeli New Shekel||ILS|
|Vietnamese Dong||VND||Jordanian Dinar||JOD|
|Vietnamese Dong||British Pound||GBP||Kuwaiti Dinar||KWD|
|Czech Koruna||CZK||Saudi Arabian Riyal||SAR|
|European Euros||EUR||United Arab Emirates Dirham||AED|
|Hungarian Forint||HUF||North America||Canadian Dollar||CAD|
|Icelandic Krona||ISK||US Dollar||USD|
|Norwegian Krone||NOK||Pacific Ocean||Australian Dollar||AUD|
|Polish Zloty||PLN||New Zealand Dollar||NZD|
3. Empirical Results and Analysis
3.1. Statistics of Cross-Correlation Coefficients
3.2. MST Results
- The international cluster with USD as its center becomes smaller than those of the former two scales, and only five currencies directly link to USD.
- The Asia cluster splits into two small clusters: one is the linear-linked group in the MST, which is composed of INR, THB, PHP, and PKR, and the other is the triangle-linked group, which is composed of SGD, TWD, and MYR.
- Compared with Figure 4, the Latin America cluster has appeared again but with BRL as its center.
- Although the European cluster still exists in the MST, the center is changed to PLN.
- The Commonwealth cluster is separated into two units by KRW but the five currencies (i.e., GBP, NZD, AUD, ZAR, and CAD) are still on a line.
- Both the international cluster and the European cluster exist in the MSTs for three different time scales, which confirms that USD and EUR are the predominant currencies in the FX market and suggests that the currencies can be clustered by the geographical criterion or the trade criterion.
- Another stable cluster in the three MSTs is the Middle East cluster with AED as its center, which consists of AED, JOD, SAR, and KWD. Three countries of them are the members of the Organization of the Petroleum Exporting Countries (OPEC), which causes their currencies to have a strong relationship with USD because the U.S. is the largest importer and consumer of oil in the world at present and USD is the main currency of payment.
- The Asia and Latin America clusters are not stable, which indicates that countries in these areas need more cooperation such as in the fields of trade, policy, economy, and currency.
- An interesting finding is that the Commonwealth cluster appears in our study. This phenomenon suggests that the shared values and the shared trade links of the Commonwealth of Nations are beneficial to the formation of the monetary cluster.
- Five currencies (i.e., CNY, PAB, VND, AED, and EGP) always connect to USD as their center. There are two possible origins to explain the connections: on the one hand, the country is one of the main trading partners of America or the opposite, such as China; on the other hand, the currency may be pegged to USD, such as PAB.
3.3. Statistical Properties of MSTs at Different Time Scales
3.3.1. Four Evaluation Criteria
3.3.2. Distribution of Vertex Degrees
3.3.3. Single-Step Survival Ratio
- Based on the analysis of statistical properties of cross-correlation coefficients, we find that the cross-correlation coefficients of the FX market in the period of 2007–2012 are fat-tailed.
- From the three MSTs in Section 3.2, we draw some conclusions. For instance, USD and EUR are confirmed as the predominant world currencies in the three MSTs. The Asian cluster and the Latin America cluster are not stable while the Middle East cluster is very stable in the MSTs. It is interesting to note that the Commonwealth cluster is found in the MSTs.
- By analyzing the 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 (or power-law) behavior is also found in the FX network at most of time scales.
- Through quantifying the single-step survival ratio of the MSTs at different time scales, we conclude that a great majority of links in the FX network survive from one time scale to the next.
- Our analysis based on the two methods of DCCA coefficient and MST can be employed to analyze the statistical properties of other financial markets at different time scales, such as stock markets and commodity markets.
- The DCCA coefficient method also can be combined with other correlation network-based approaches to study the topology of the networks at different time scales, such as PMFG, and correlation threshold methods.
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