This paper investigates whether the real interest rate parity (RIRP) is valid during the three waves of globalizations that occurred in the last 150 years (1870-1914, 1944-1971, 1989 to the present). If any, these periods should favor RIRP, since globalization is a process where economies and financial markets become increasingly integrated into a global economic system. In contrast to the existing literature, we model the departures from RIRP as a long-term memory process and apply fractional integration methods on a sample of real interest rate differentials of seven developed countries: France, Germany, Holland, Italy, Japan, Spain, and the UK across the three globalization waves paired against the USA. We compute impulse response functions (IRF) to gain further insight into the memory characteristics of the RIRP differential processes and provide half-life estimates. We find that deviations from RIRP are mean reverting, providing robust evidence of real interest rate convergence during the three globalization waves. We shed further light on financial and commodity market integration during the three globalization waves by assessing the memory properties of uncovered interest rate parity (UIP) and relative purchasing power parity (PPP) differential processes. We find that deviations from relative PPP and UIP are not always mean-reverting processes. RIRP, relative PPP, and UIP hold simultaneously only in 7 out of 21 cases; RIRP and UIP hold in 11 out of 21 cases; RIRP hold without the support of relative PPP and UIP in 3 out of 21 cases. Thus, the evidence in favor of real interest rate convergence appears to be driven more by UIP than relative PPP. All these results are, to the authors knowledge, new to the literature.