Forecasting time series with long memory and level shifts

It is well known that some economic time series can be described by models which allow for either long memory or for occasional level shifts. In this paper we propose to examine the relative merits of these models by introducing a new model, which jointly captures the two features. We discuss representation and estimation. Using simulations, we demonstrate its forecasting ability, relative to the one-feature models, both in terms of point forecasts and interval forecasts. We illustrate the model for daily S&P500 volatility.