The Evolution of the Linkage Among Geopolitical Risk, the US Dollar Index, Crude Oil Prices, and Gold Prices at Multiple Scales: A Wavelet Transform-Based Dynamic Transfer Entropy Network Method

In recent years, the correlation mechanisms between geopolitical risks and financial markets have drawn considerable attention from both academic circles and investment communities. However, their multiscale, nonlinear interactive characteristics still require further investigation. To address this, this paper proposes a dynamic nonlinear causal information network combined with a wavelet transform model and the transfer entropy method. We select the geopolitical risk index, the US dollar index, Brent and WTI crude oil prices, COMEX gold futures, and London gold prices time series as the research objects. The results suggest that the network's structure changes with time at different time scales. On the one hand, COMEX gold (London gold) acts as the major causal information transmitter (receiver) at all scales; both of their highest values appear at the mid-scale. The US dollar index plays a bridging role in information transmission, and this mediating ability decreases with increasing time scales. On the other hand, the fastest speed of causal information transmission is at the short scale, and the slowest speed is at the mid-scale. The complexity and systematic risk of causal network decrease with increasing time scales. Importantly, at the short-scale (D1), the information transmission speed slowed during the Russian-Ukrainian conflict and further decreased after the start of the Israel-Hamas conflict. Systematic risk has increased annually since 2018. This study provides a multiscale perspective to study the nonlinear causal relationship between geopolitical risk and financial markets and serves as a reference for policy-makers and investors.