Abstract In this paper, we examine the time-varying causal relationship between green bonds and other assets including US conventional bonds, WilderHill clean energy (equity) index, and CO2 emission allowances price during the period spanning from 30 July 2014 to 10 February 2020. We apply the novel time-varying Granger causality test (Shi et al. 2018) based on the recursive evolving algorithm introduced by Phillips et al. (2015a, 2015b) for controlling financial bubbles to detect real–time causality, detecting possible changes in the causal direction and dating financial turbulences, The study based on this algorithm reveals a significant causality running from the US 10-year Treasury bond index to green bonds starting from the end of the year 2016 until the end of the sample period. Besides, we find that the link CO2 emission allowances price causing green bonds is significant from the beginning of the sample period to the end of the year 2015. Furthermore, by using the recursive-evolving causality algorithm of the Shi et al. (2018) test, we find that the causality running from the clean energy index to green bonds is very limited to the year 2019. On the other hand, there is no significant causality running from green bonds to all considered assets, indicating no predictive power for this asset in its proper domain, which is not yet examined in the literature.