Xiangyun Gao

Characteristics of the transmission of autoregressive sub-patterns in financial time series

There are many types of autoregressive patterns in financial time series, and they form a transmission process. Here, we define autoregressive patterns quantitatively through an econometrical regression model. We present a computational algorithm that sets the autoregressive patterns as nodes and transmissions between patterns as edges, and then converts the transmission process of autoregressive patterns in a time series into a network. We utilised daily Shanghai (securities) composite index time series to study the transmission characteristics of autoregressive patterns. We found statistically significant evidence that the financial market is not random and that there are similar characteristics between parts and whole time series. A few types of autoregressive sub-patterns and transmission patterns drive the oscillations of the financial market. A clustering effect on fluctuations appears in the transmission process, and certain non-major autoregressive sub-patterns have high media capabilities in the financial time series. Different stock indexes exhibit similar characteristics in the transmission of fluctuation information. This work not only proposes a distinctive perspective for analysing financial time series but also provides important information for investors.

Features of the Correlation Structure of Price Indices

What are the features of the correlation structure of price indices? To answer this question, 5 types of price indices, including 195 specific price indices from 2003 to 2011, were selected as sample data. To build a weighted network of price indices each price index is represented by a vertex, and a positive correlation between two price indices is represented by an edge. We studied the features of the weighted network structure by applying economic theory to the analysis of complex network parameters. We found that the frequency of the price indices follows a normal distribution by counting the weighted degrees of the nodes, and we identified the price indices which have an important impact on the networks structure. We found out small groups in the weighted network by the methods of k-core and k-plex. We discovered structure holes in the network by calculating the hierarchy of the nodes. Finally, we found that the price indices weighted network has a small-world effect by calculating the shortest path. These results provide a scientific basis for macroeconomic control policies.

The Multiscale Conformation Evolution of the Financial Time Series

Fluctuations of the nonlinear time series are driven by the traverses of multiscale conformations from one state to another. Aiming to characterize the evolution of multiscale conformations with changes in time and frequency domains, we present an algorithm that combines the wavelet transform and the complex network. Based on defining the multiscale conformation using a set of fluctuation states from different frequency components at each time point rather than the single observable value, we construct the conformational evolution complex network. To illustrate, using data of Shanghai’s composition index with daily frequency from 1991 to 2014 as an example, we find that a few major conformations are the main contributors of evolution progress, the whole conformational evolution network has a clustering effect, and there is a turning point when the size of the chain of multiscale conformations is 14. This work presents a refined perspective into underlying fluctuation features of financial markets.

Reconstructing complex network for characterizing the time-varying causality evolution behavior of multivariate time series

In order to explore the characteristics of the evolution behavior of the time-varying relationships between multivariate time series, this paper proposes an algorithm to transfer this evolution process to a complex network. We take the causality patterns as nodes and the succeeding sequence relations between patterns as edges. We used four time series as sample data. The results of the analysis reveal some statistical evidences that the causalities between time series is in a dynamic process. It implicates that stationary long-term causalities are not suitable for some special situations. Some short-term causalities that our model recognized can be referenced to the dynamic adjustment of the decisions. The results also show that weighted degree of the nodes obeys power law distribution. This implies that a few types of causality patterns play a major role in the process of the transition and that international crude oil market is statistically significantly not random. The clustering effect appears in the transition process and different clusters have different transition characteristics which provide probability information for predicting the evolution of the causality. The approach presents a potential to analyze multivariate time series and provides important information for investors and decision makers.

Multiscale Fluctuation Features of the Dynamic Correlation between Bivariate Time Series

The fluctuation of the dynamic correlation between bivariate time series has some special features on the time-frequency domain. In order to study these fluctuation features, this paper built the dynamic correlation network models using two kinds of time series as sample data. After studying the dynamic correlation networks at different time-scales, we found that the correlation between time series is a dynamic process. The correlation is strong and stable in the long term, but it is weak and unstable in the short and medium term. There are key correlation modes which can effectively indicate the trend of the correlation. The transmission characteristics of correlation modes show that it is easier to judge the trend of the fluctuation of the correlation between time series from the short term to long term. The evolution of media capability of the correlation modes shows that the transmission media in the long term have higher value to predict the trend of correlation. This work does not only propose a new perspective to analyze the correlation between time series but also provide important information for investors and decision makers.

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.

Modelling cointegration and Granger causality network to detect long-term equilibrium and diffusion paths in the financial system

Microscopic factors are the basis of macroscopic phenomena. We proposed a network analysis paradigm to study the macroscopic financial system from a microstructure perspective. We built the cointegration network model and the Granger causality network model based on econometrics and complex network theory and chose stock price time series of the real estate industry and its upstream and downstream industries as empirical sample data. Then, we analysed the cointegration network for understanding the steady long-term equilibrium relationships and analysed the Granger causality network for identifying the diffusion paths of the potential risks in the system. The results showed that the influence from a few key stocks can spread conveniently in the system. The cointegration network and Granger causality network are helpful to detect the diffusion path between the industries. We can also identify and intervene in the transmission medium to curb risk diffusion.

Reconstructing time series into a complex network to assess the evolution dynamics of the correlations among energy prices

Abstract Reconstructing a time series into a complex network can help uncover the dynamic information hidden in the time series. Previous studies mainly focused on the long-term relationship between two energy prices, and traditional econometric methods poorly reflect the evolution of correlations among variables from a short-term perspective. Thus, first, we divide natural gas, coal and crude oil price time series into a series of segments via a set of temporal sliding windows and then calculate the correlation coefficients for each pair of energy prices in each segment. Second, we define the correlation modes based on the correlation coefficients and a coarse graining process. Third, we reconstruct the time series into a complex network to assess the evolution dynamics of the correlations among energy prices. The results show that a few major correlation modes and transmission patterns play important roles in the evolution. The evolution of the correlation modes among energy prices exhibits a significant cluster effect. Approximately 30 days is a turning point at which one type of cluster transforms into another type. Then, we improve the betweenness centrality algorithm to measure the media capability of the correlation mode in the evolution process of different clusters. Based on the transmission probabilities between clusters, we can determine the evolution direction of the correlation modes based on energy prices. These results are useful for monitoring fluctuations in energy prices and making decisions for risk avoidance.

Features of Evolutionary Complex Networks in Complex Adaptive Systems

Adaptive behaviours of nodes can cause the evolution of networks. To investigate the characteristics of evolutionary complex networks that result from the interactions between agents in complex adaptive systems, we construct a complex network model of heat-bug interactions by drawing on statistical physics methods based on the heat-bug experiment. The networks of interactions between heat bugs show the following: that the degree distribution evolves from the Gamma distribution to the Gaussian distribution, that the average local density is high, and the average path length is short, and that the dynamics of clusters in the networks changes from creation to combination and then to separation, and the members of the clusters change continuously, but the number of clusters remains stable. Based on the micro perspective, these results provide a good alternative to explain emerging complex phenomena by elucidating the characteristics of evolutionary complex networks.