This study examines the presence of long-run dependence in a variety of crude and refined energy spot markets during the 1986–2018 period using the time-varying generalised Hurst exponent. Our results indicate that the weak-form efficiency in energy spot markets is clearly time-varying, with USGC(U.S. Gulf Coast Conventional Gasoline) Diesel Fuel the most efficient and Propane the least. An important finding is that after the subprime crisis, the persistence of energy spot market products has increased. Overall, our finding highlights that the time-varying model is preferable to the time-constant one since the former can capture time-varying efficiency, which heavily depends on a country's predominant economic and political conditions.