Robustness of Multistep Forecasts and Predictive Regressions at Intermediate and Long Horizons

This paper studies the properties of multi-step projections, and forecasts that are obtained using either iterated or direct methods. The models considered are local asymptotic: they allow for a near unit root and a local to zero drift. We treat short, intermediate and long term forecasting by considering the horizon in relation to the observable sample size. We show the implication of our results for models of predictive regressions used in the financial literature. We show here that direct projection methods at intermediate and long horizons are robust to the potential misspecification of the serial correlation of the regression errors. We therefore recommend, for better global power in predictive regressions, a combination of test statistics with and without autocorrelation correction.