LAUSR

Abstract Multivariate time series contain rich information of corresponding complex systems. This paper proposes a new method to characterize the evolution and transition characteristics of the correlation modes for multivariate time series(ETCCMMTS). Based on ETCCMMTS, the characteristics of energy price systems are analyzed. The results show that energy price correlated modes exhibit co-movement, group-occurrence and the small-world property. The results prove that futures prices have the leading role, the crude oil futures price affects the stability of an energy price system, and the crude oil spot price has the highest clustering coefficient, whereas the heating oil futures price has the largest betweenness coefficient. The topological absorptive is introduced to measure the systemic risk, and the ”risk hopping” phenomenon is revealed. The recursive graph indicates that the fluctuations of energy price display not only short-range correlation for 1–2 months but also long-range correlation for 7–8 years. Additionally, the long-range correlation will lead to high systematic risk. In the course of energy price fluctuations, there is a total of 41 different types of correlation modes. The cumulative time of different correlation modes may result in a “cumulative time jump” and shows a linear growth in general. In addition, the topological structure of energy price correlated modal transition network (EPCMTN) is revealed.