Characteristics of the co-fluctuation matrix transmission network based on financial multi-time series

The co-fluctuation of two time series has often been studied by analysing the correlation coefficient over a selected period. However, in both domestic and global financial markets, there are more than two active time series that fluctuate constantly as a result of various factors, including geographic locations, information communications and so on. In addition to correlation relationships over longer periods, daily co-fluctuation relationships and their transmission features are also important, since they can present the co-movement patterns of multi-time series in detail. To capture and analyse the features of the daily co-movements of multiple financial time series and their transmission characteristics, we propose a new term—“the co-fluctuation relation matrix”—which can reveal the co-fluctuation relationships of multi-time series directly. Here, based on complex network theory, we construct a multi-time series co-fluctuation relation matrix transmission network for financial markets by taking each matrix as a node and the succeeding time sequence as an edge. To reveal the process more clearly, we utilize daily time series data for four well-known stock indices—the NASDAQ Composite (COMP), the S&P 500 Index, the Dow Jones Industrial Average and the Russell 1000 Index—from 22 January 2003 to 21 January 2015, to examine the concentration of the transmission networks and the roles of each matrix—in addition to the transmission relationships between the matrices—based on a variety of coefficients. We then compare our results with the statistical features of the stock indices and find that there are not many discernible patterns of co-fluctuation matrices over the 12-year period, and few of these play important roles in the transmission network. However, the conductibility of the few dominant nodes is different and reveals certain novel features that cannot be obtained by traditional statistical analysis, such as the “all positive co-fluctuation matrix”, which is the most important node, although one stock index has negative correlation with the other three. This research therefore provides a novel method for analysing the co-movement behaviour of multiple financial time series, which can help researchers obtain the roles and relations of co-fluctuation patterns both over short and long terms. The findings also provide an important basis for further investigations into financial market simulations and the fluctuation of multiple financial time series.