The study of RMB exchange rate complex networks based on fluctuation mode

• Out degree distributions of fluctuation network follow power-law distribution.
• A frequent mode has a long-range memory characteristic.
• Clustering coefficient and out degree obey approximated negative correlation.
• The transmission route appears partially closed loop, repeat and reversibility.

In the paper, we research on the characteristics of RMB exchange rate time series fluctuation with methods of symbolization and coarse gaining. First, based on fluctuation features of RMB exchange rate, we define the first type of fluctuation mode as one specific foreign currency against RMB in four days’ fluctuating situations, and the second type as four different foreign currencies against RMB in one day’s fluctuating situation. With the transforming method, we construct the unique-currency and multi-currency complex networks.Further, through analyzing the topological features including out-degree, betweenness centrality and clustering coefficient of fluctuation-mode complex networks, we find that the out-degree distribution of both types of fluctuation mode basically follows power-law distributions with exponents between 1 and 2. The further analysis reveals that the out-degree and the clustering coefficient generally obey the approximated negative correlation. With this result, we confirm previous observations showing that the RMB exchange rate exhibits a characteristic of long-range memory.Finally, we analyze the most probable transmission route of fluctuation modes, and provide probability prediction matrix. The transmission route for RMB exchange rate fluctuation modes exhibits the characteristics of partially closed loop, repeat and reversibility, which lays a solid foundation for predicting RMB exchange rate fluctuation patterns with large volume of data.