Forecasting real-time data allowing for data revisions

A modeling approach to real-time forecasting that allows for data revisions is shown. In this approach, an observed time series is decomposed into stochastic trend, data revision, and observation noise in real time. It is assumed that the stochastic trend is defined such that its first difference is specified as an AR model, and that the data revision, obtained only for the latest part of the time series, is also specified as an AR model. The proposed method is applicable to the data set with one vintage. Empirical applications to real-time forecasting of quarterly time series of US real GDP and its eight components are shown to illustrate the usefulness of the proposed approach.