A fractionally integrated model with a mean shift for the US and the UK real oil prices

In this article, we have modeled the log of the US and the UK real oil prices in terms of fractionally integrated processes with a mean shift. We used different versions of the tests of Robinson (1994), which have standard null and local limit distributions. The results indicated that if we model the series without a mean shift, then they are both non-stationary I(1). However, by including a mean shift component during the oil crises, they become fractionally integrated with an order of integration smaller than one and, thus, showing mean reverting behavior.