At present, the rapid development of digital finance is closely related to the economic development of urban agglomerations. An urban agglomeration provides conditions for digital finance to form a spatial relevancy network. Exploring the development of digital finance in the urban agglomeration of the Pearl River Delta (PRD), which is the bellwether of China's economy, can provide important practical experience for the economic construction of coastal areas and even the whole country. In this study, using the urban digital finance index issued by the Guangzhou Institute of International Finance, we measured the intensity and direction of the spatial relevancy of digital finance in the PRD urban agglomeration by applying the gravity model, modified in the calculation of distance between cities. Then, we examined the influencing factors of the spatial network of digital finance through the quadratic assignment procedure (QAP) approach. The achieved results are as follows. First, although the overall density is low, the network is tightly connected and stable. Second, in terms of individual characteristics of the network, Guangzhou, Shenzhen, Foshan still play the leading roles in the spatial network of digital finance. Third, the digital finance network does not have bidirectional spillover block. The links between segments are relatively loose. Fourth, economic level, degree of opening up, Internet level and geographical location are important factors in driving the formation of spatial relevancy of digital finance in the PRD urban agglomeration.

Crude oil markets have become increasingly uncertain. To study them, we first employ the decomposition-ensemble framework based on the variational mode decomposition (VMD) and Lempel–Ziv algorithms to assess the crude oil dual attributes. Three steps are involved: 1) conditional autoregressive value at risk measures the crude oil risk; 2) they are decomposed by the VMD algorithm into submodes; 3) the Lempel–Ziv algorithm is applied to analyze the crude oil risk for each, thereby identifying the oil commodity or oil financial risks. The results of the empirical analysis reveal significantly different amplitudes for the high- and low-frequency crude oil risk. By summarizing the crude oil risk components, we also conclude that the mean value for the oil commodity risk is 0.04, while that for the oil financial risk is 0. What is more, the oil commodity risk is highly related to downward trends in oil prices, while the oil financial risk exerts the same clustering effect as oil returns.