Multivariate financial time series in the light of complex network analysis

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.