Fig 1.
All the states occurring in the state transfer networks for the fGm and stock market index series.
Segment length is selected to be s = 5. Each state is assigned an identifier number as presented below it.
Fig 2.
State transfer networks for fGms series.
Segment length is selected to be s = 5. Subplots (a1)-(f1) are the original state transfer networks for the fGm series with H = 0.5, 0.6, 0.65, 0.7, 0.75, and 0.8, respectively. The nodes that have self-links are marked with red color. The label x(y) means the state occurs for the first time at the position x along the time series (the x’th segment), and its identifier number is y; (a2)-(f2) The strong state transfer networks constructed by filtering out weak links (less than 25) in the original state transfer networks; (a3)-(f3) Shuffled networks. One can shuffle each original fGm series, and construct from the resulting series a shuffled network. Each displayed shuffled network is an average over 1000 realizations. Weak links also are filtered out. Except in the networks shown in (a1)-(f1), the size of a node indicates the occurring degree of the state. The width of an edge is the link’s weight.
Fig 3.
Degree, degree ratio, and persistent behaviors of motifs for fGm series.
Segment length is selected to be s = 5. (a1)-(e1) show the occurrence degrees of the states in the original and shuffled fGm series with H = 0.6, 0.65, 0.7, 0.75 and 0.8, respectively; (a2)-(e2) present the degree ratios for all the states (visibility graphs) in the series with H = 0.6, 0.65, 0.7, 0.75, and 0.8, respectively; (a3)-(e3) Relations of R/S versus n obtained from occurring position series of the motifs, from which one can find persistent behaviors of the motifs’ occurring along the series.
Fig 4.
State transfer networks for stock markets.
Segment length is selected to be s = 5. (a1) and (b1) display the original state transfer networks for S&P500 and Nasdaq respectively. The label x(y) means the state occurs for the first time at the position x along the time series (the x’th segment), and its identifier number is y; (a2) and (b2) are the strong state transfer networks constructed by filtering out weak links (less than 25) in (a1) and (a2), respectively. While, (a3) and (b3) are the corresponding networks (weak links also are filtered out) constructed from shuffled series. Statistical average is conducted over 1000 realizations. Except in networks shown in (a1) and (b1), the size of a node indicates the occurring degree of the state. The width of an edge is the link’s weight.
Fig 5.
Degree, degree ratio, and persistent behaviors of motifs for the stock markets.
Segment length is selected to be s = 5. (a1)and (b1) show the occurrence degrees of the states in the original and shuffled S&P500 and Nasdaq index series, respectively. From the occurrence degrees one can easily identify hubs in the original and shuffled series; (a2)-(e2) present the degree ratios for all the states in the S&P500 and Nasdaq index series, respectively. From the ratios one can easily find the the motifs. A state being called a motif means that its degree in the original series is significantly larger than that in the shuffled series; (a3)-(e3) Relations of R/S versus n obtained from occurring position series of the motifs, from which one can find persistent behaviors of the motifs’ occurring along the series.
Fig 6.
All the states that turn out to be motifs in the fGm series with H = 0.6, 0.65, 0.7, 0.75, 0.8 (the total number of occurrence states is 132).
Segment length is selected to be s = 6.
Fig 7.
All the states that turn out to be motifs in the stock market index series.
Segment length is selected to be s = 6.
Fig 8.
Degree, degree ratio, and persistent behaviors of motifs for fGm series.
Segment length is selected to be s = 6. (a1)-(e1) show the occurrence degrees of the states in the original and shuffled fGm series with H = 0.6, 0.65, 0.7, 0.75 and 0.8, respectively; (a2)-(e2) present the degree ratios for all the states (visibility graphs) in the series with H = 0.6, 0.65, 0.7, 0.75, and 0.8, respectively; (a3)-(e3) Relations of R/S versus n obtained from occurring position series of the motifs, from which one can find persistent behaviors of the motifs’ occurring along the series.
Fig 9.
Degree, degree ratio, and persistent behaviors of motifs for the stock markets.
Segment length is selected to be s = 6. (a1)and (b1) show the occurrence degrees of the states in the original and shuffled S&P500 and Nasdaq index series, respectively. (a2)-(e2) present the degree ratios for all the states in the S&P500 and Nasdaq index series, respectively; (a3)-(e3) Relations of R/S versus n obtained from occurring position series of the motifs, from which one can find persistent behaviors of the motifs’ occurring along the series.