Inflation rates; long-memoray, level shifts, or both?

We examine if US inflation rates series can be characterized by a long-memory model, by a model with occasional level shifts or by a new model, which jointly captures the two features. Through simulations we show that this new model can be usefully applied in practice. For 23 inflation rate series we find that generally the long-memory model is best, both in terms of in-sample fit and out-of-sample forecasts.