Network Analysis of Cross-Correlations on Forex Market during Crises. Globalisation on Forex Market
Abstract
:1. Introduction
2. Methods
Example of Application
- when the correlation strength is smaller than zero—the distance between time series is decreasing, the time series are converging.
- when the correlation strength is greater than zero—the distance between time series is increasing, and the time series are diverging.
- converging time series networks, i.e., only the nodes (representing the currency time series) with a correlation strength smaller than one are connected, and
- diverging time series network, i.e., only the nodes with a correlation strength greater than one are connected.
- Clique size evolution is obtained by calculating the size of the biggest clique for each of the generated networks. The clique size evolution illustrates a process of unification of the market. Indeed, if the giant clique is observed, then one type of correlation is dominating on the market and, on the contrary, if the size of the biggest cluster is small, then the correlation matrix consists of a variety of correlation type.
- Community number is obtained by measuring the number of community structure partitions that group nodes, such that there is a higher density of edges within the community than between them. This parameter is weaker than the clique number, but still allows observing grouping on Forex market.
- The frequency of connection on the graph is the measure where the frequency of being connected on the graph is analysed. The most important feature of this measure is the ability to distinguish the most stable connections in the considered period.
- Node rank distribution is the analysis where the most detailed information regarding the graph is obtained. The rank of nodes is an important feature allowing for observing the hierarchy of a network and is often used to determine network type [49,50,51]. This measure gives very detailed information regarding the graph. It may be considered as a quick overview of the network main features, e.g., if it is densely connected or whether each node is only connected with a small number of links.
- Rank node entropy is the Shannon entropy that is defined in the standard way (Equation (1)), where the evolution of the entropy of node rank is calculated.
3. Data
3.1. Data Source
3.2. Descriptive Statistics of the Series
4. Results
4.1. Month Time Window
4.2. Quarter Time Window
4.3. Half Year Time Window
5. Conclusions
Funding
Institutional Review Board Statement
Informed Consent Statement
Conflicts of Interest
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Currency | Mean | Median | Std | Max | Min | Skewness | Kurtosis |
---|---|---|---|---|---|---|---|
AR | 9.087 | 3.836 | 1.413 | 0.403 | −0.126 | 11.147 | 261.7 |
CZK | −0.471 | −0.740 | 0.486 | 0.093 | −0.064 | 1.291 | 41.6 |
AUD | 0.324 | −2.245 | 0.760 | 0.079 | −0.050 | 0.743 | 10.8 |
DKK | 0.053 | 0 | 0.048 | 0.079 | −0.009 | −0.560 | 84.1 |
BGN | 1.393 | 0.452 | 0.845 | 0.063 | −0.060 | 0.324 | 6.4 |
EGP | 3.513 | 0.665 | 1.261 | 0.586 | −0.075 | 21.336 | 961.4 |
BRL | 3.334 | −0.718 | 1.182 | 0.129 | −0.1108 | 0.513 | 15.8 |
HKD | −0.079 | 0 | 0.663 | 0.055 | −0.070 | −0.094 | 8.4 |
CAD | −0.140 | −1.480 | 0.674 | 0.044 | −0.043 | 0.201 | 5.7 |
HRK | 0.351 | 0.135 | 0.492 | 0.049 | −0.053 | 0.092 | 18.2 |
CHF | −0.629 | 0 | 0.468 | 0.088 | −0.159 | −6.186 | 304.3 |
HUF | 1.335 | 0.289 | 0.595 | 0.070 | −0.062 | 1.174 | 20.1 |
IDR | 4.849 | 0 | 1.802 | 0.462 | −0.207 | 5.287 | 134.0 |
CNY | −0.313 | 0.329 | 0.834 | 0.050 | −0.062 | −0.102 | 8.4 |
ISK | 1.392 | −0.991 | 0.876 | 0.145 | −0.133 | 1.199 | 71.2 |
JPY | 0.061 | 2.313 | 0.849 | 0.083 | −0.116 | −0.606 | 17.0 |
KRW | 1.050 | −1.545 | 1.084 | 0.158 | −0.232 | −0.678 | 78.1 |
MXN | 1.944 | 0 | 0.904 | 0.068 | −0.091 | 0.221 | 10.1 |
MYR | 1.033 | −0.253 | 0.773 | 0.068 | −0.070 | 0.129 | 13.0 |
NAD | 2.782 | −0.375 | 1.100 | 0.184 | −0.101 | 1.500 | 25.9 |
NOK | 0.585 | −0.937 | 0.530 | 0.050 | −0.082 | −0.350 | 23.5 |
NZD | 0.162 | −3.306 | 0.783 | 0.057 | −0.051 | 0.341 | 6.3 |
PHP | 1.367 | 1.125 | 0.799 | 0.111 | −0.130 | −0.039 | 29.5 |
PLN | 0.615 | −1.442 | 0.642 | 0.057 | −0.048 | 0.609 | 9.6 |
RON | 5.452 | 0.675 | 0.908 | 0.192 | −0.096 | 3.521 | 76.2 |
RUB | 6.074 | 1.393 | 1.651 | 0.347 | −0.282 | 4.050 | 124.6 |
SEK | 0.570 | −0.450 | 0.475 | 0.036 | −0.039 | 0.228 | 8.4 |
SGD | −0.159 | 0 | 0.595 | 0.043 | −0.052 | −0.154 | 7.0 |
THB | 0.412 | 0.367 | 1.016 | 0.171 | −0.067 | 1.045 | 25.0 |
TRY | 9.005 | 4.949 | 1.177 | 0.267 | −0.086 | 4.395 | 89.3 |
TWD | 0.09 | −0.232 | 0.654 | 0.068 | −0.069 | 0.079 | 9.6 |
UAH | 6.469 | 0 | 1.732 | 0.554 | −0.215 | 8.250 | 258.0 |
USD | −0.082 | 0 | 0.672 | 0.077 | −0.077 | −0.046 | 11.6 |
ZAR | 2.768 | −1.856 | 1.113 | 0.121 | −0.143 | 0.259 | 18.1 |
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Miśkiewicz, J. Network Analysis of Cross-Correlations on Forex Market during Crises. Globalisation on Forex Market. Entropy 2021, 23, 352. https://doi.org/10.3390/e23030352
Miśkiewicz J. Network Analysis of Cross-Correlations on Forex Market during Crises. Globalisation on Forex Market. Entropy. 2021; 23(3):352. https://doi.org/10.3390/e23030352
Chicago/Turabian StyleMiśkiewicz, Janusz. 2021. "Network Analysis of Cross-Correlations on Forex Market during Crises. Globalisation on Forex Market" Entropy 23, no. 3: 352. https://doi.org/10.3390/e23030352
APA StyleMiśkiewicz, J. (2021). Network Analysis of Cross-Correlations on Forex Market during Crises. Globalisation on Forex Market. Entropy, 23(3), 352. https://doi.org/10.3390/e23030352