Who has mastered exchange rate ups and downs: China or the United States?

•We study the China–US exchange rate bubbles from a nonlinear perspective.•This study quantitatively assesses the determinants of the exchange rate bubbles.•We find two bubble periods in the China–US exchange rate.•The difference in interest rates between the US and China positively impact China–US exchange rate bubbles. This study uses the generalized sup augmented Dickey–Fuller (GSADF) method to study the beginnings and endings of the China–US exchange rate bubbles that occurred during the period 1981–2021 and the factors that affected those exchange rate bubbles from a nonlinear perspective. The contribution of this paper is to quantitatively assess the determinants of these bubbles. We find two bubble periods in the China–US exchange rate, one from January 1985 to December 1986 and the other from August 2005 to August 2015. Our findings suggest that the Chinese interest rate and the difference in interest rates between the US and China positively impact China–US exchange rate bubbles, while the US interest rate has no effect on the exchange rate bubble in bubble periods. Additionally, FDI from China to the US and the subprime crisis negatively influence China–US exchange rate bubbles. The findings of this paper are of value as a reference for maintaining the stability of the RMB exchange rate.