In this paper we specify a multi-factor long-memory process that enables us to estimate the fractional differencing parameters at each frequency separately, and adopt this framework to model quarterly prices in three European countries (France, Italy and the UK). The empirical results suggest that inflation in France and Italy is nonstationary. However, while for the former country this applies both to the zero and the seasonal frequencies, in the case of Italy the nonstationarity comes exclusively from the long-run or zero frequency. In the UK, inflation seems to be stationary with a component of long memory at both the zero and the semi-annual frequencies, especially at the former. In all cases, we find evidence of mean reversion, implying that the effects of exogenous shocks on inflation are transitory and activist policies are not required in response to them. This process is slower in the case of France and Italy compared with the UK.