In this article we model the log of the U.S. and the U.K. real oil prices in terms of fractionally integrated processes with a mean shift. We use different versions of the tests of Robinson (1994), which have standard null and local limit distributions. The results indicate that if we model the series without a mean shift, they are both nonstationary I(1). However, allowing for a mean shift during the oil crises, they become fractionally integrated with an order of integration smaller than one and thus, showing mean reverting behaviour.
long memory fractional integration mean shift real oil prices