Revisiting inflation in the euro area allowing for long memory

•We analyse inflation and inflation differentials in the euro area allowing for long memory.•Evidence based on the short memory assumption and standard normal asymptotics may be spurious.•Inflation differentials between “core” and “peripheral” countries are strongly persistent.•“Core” economies have less persistent differentials and may be more integrated.•“Peripheral” countries with high inflation may find themselves under competitive pressure for a long time.

We analyse inflation and inflation differentials in the euro area allowing for long memory and a new type of limiting theory denoted fixed-bandwidth. Our results differ from those based on standard normal asymptotics and the short memory assumption, and we also find that the inflation differentials between “core” and “peripheral” countries are strongly persistent. “Core” economies appear to have less persistent differentials and may be more integrated, while “peripheral” countries with high inflation may find themselves under competitive pressure for a long time.