This paper deals with the analysis of the inflation rate in Nigeria. We use long range dependence techniques based on fractional integration or I(d) models, incorporating structural breaks in the model. The results indicate that inflation in Nigeria displays long memory behaviour, with an order of integration of about 0.3 in spite of the existence of breaks at different periods. Including the growth rate of money (M1) as an exogenous term, the results indicate that this variable significantly affects inflation two and three periods (quarters) after the initial shock.