Testing and forecasting the degree of integration in the US inflation rate

In this article we model the log of the US inflation rate by means of fractionally integrated processes. We use the tests of Robinson for testing this type of hypothesis, which include, as particular cases, the I(0) and I(1) specifications, and which also, unusually, have standard null and local limit distributions. A model selection criterion is established to determine which may be the best model specification of the series, and the forecasting properties of the selected models are also examined. The results vary substantially depending on how we specify the disturbances. Thus, if they are white noise, the series is I(d) with d fluctuating around 0.25; however, imposing autoregressive disturbances, the log of the US inflation rate seems to be anti-persistent, with an order of integration smaller than zero. Looking at the forecasting properties, those models based on autocorrelated disturbances (with d < 0) predict better over a short horizon, while those based on white noise disturbances (with d > 0) seem to predict better over longer periods of time.