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Heteroscedasticity of time series is an important issue addressed in relation to the nonlinearity and complexity of time series. Previous studies have focused on time series heteroscedasticity during a long-term period but have rarely analyzed it from a nonlinear dynamic perspective. This paper proposes a new model for converting a time series into a complex network. Our proposed model can examine not only the heteroscedasticity of a short-term series but also the dynamic evolution process of this heteroscedasticity. Using four typical crude oil time series as sample data, we construct four networks. A network node denotes the types of fluctuation patterns corresponding to the symbolization of the heteroscedastic features of a short-term fluctuation series based on the autoregressive generalized autoregressive conditional heteroscedasticity model, and a weighted edge represents the evolution direction and frequency between two patterns. Our findings show that the choice of the length of a short-term period depends on the diversity of these patterns. The identification of the nodes with greater out-strength or greater betweenness centrality can help us to understand the different roles of fluctuation patterns in the evolution process. We propose a method for predicting the most probable target nodes from a source node. The analysis of clustering effects can help in detecting the fluctuation patterns between different clusters. This paper investigates the evolution dynamic mechanism of the heteroscedastic features of a short-term time series, which can help researchers and investors deeply understand the dynamic process of time series. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Abstract We established a complex network from multivariate financial time series in which one node represents the types of states corresponding to the combination of the fluctuations of the crude oil future prices, the S&P 500 Index, the US Dollar Index, and gold future prices on a given day; one edge denotes the transition time from one node to another; and the weight is the transition frequency between two states. Through analyzing the network's topological structure, we obtain the characteristics of the transitions of these states in financial time series. The results show that nodes' out-strength distribution and betweenness centrality distribution both follow the power-law distribution. A shock to one financial market can be quickly transited to the other three financial markets and a transition probability matrix is proposed to predict the short-term financial market fluctuations. The transition characteristics under volatility clustering of the network that are obtained in this study provide a new perspective to explain financial volatility clustering, which extends the application of complex network theory to financial studies and helps investors understand the financial market. Highlights • We established a complex network for multivariable financial time series. • A node shows the absolute returns of multi variables and the co-movement among them. • We studied the dynamics characteristics of transition process in multivariable time series. • We provided a new perspective for explaining the volatility clustering phenomenon. [ABSTRACT FROM AUTHOR]

The multi-scale method is widely used in analyzing time series of financial markets and it can provide market information for different economic entities who focus on different periods. Through constructing multi-scale networks of price fluctuation correlation in the stock market, we can detect the topological relationship between each time series. Previous research has not addressed the problem that the original fluctuation correlation networks are fully connected networks and more information exists within these networks that is currently being utilized. Here we use listed coal companies as a case study. First, we decompose the original stock price fluctuation series into different time scales. Second, we construct the stock price fluctuation correlation networks at different time scales. Third, we delete the edges of the network based on thresholds and analyze the network indicators. Through combining the multi-scale method with the multi-threshold method, we bring to light the implicit information of fully connected networks. [ABSTRACT FROM AUTHOR]