Measuring the persistence of shocks in the oil market is a fundamental challenge in macroeconomic analysis and energy policy. This study aims to examine the degree of persistence and long memory in Brent oil prices, focusing on distinguishing inherent persistence from the effects of structural breaks. Monthly oil price data from January 1992 to February 2026 were used. First, the stationarity of the variable was investigated using the seasonal unit root test and the unit root test with Fourier approximation. Next, the ARFIMA model was used for initial estimation, and finally, by extending this model to ARFIMA-Fourier, the fractional Integration parameter was estimated in the presence of structural breaks. The findings indicate that ignoring structural breaks leads to a negative bias in the estimation of persistence; specifically, with the application of Fourier approximation, the fractional integration parameter (d) increased from 0.471 in the ARFIMA model to 0.499 in the ARFIMA-Fourier model. The coefficient being close to 0.5 indicates that while oil prices exhibit mean reversion properties, the speed of shock dissipation is very slow and gradual. Based on these findings, it is recommended that global actors avoid military tensions and prevent severe supply shocks in oil. Conversely, Iran can leverage long-term price stability as a tool to lift sanctions and ensure sustainable income through active diplomacy, managing market expectations via threats of supply disruption, and creating an Eastern energy bloc using local currencies.