Averaging estimators for autoregressions with a near unit root

Abstract

This paper uses local-to-unity theory to evaluate the asymptotic mean-squared error (AMSE) and forecast expected squared error from least-squares estimation of an autoregressive model with a root close to unity. We investigate unconstrained estimation, estimation imposing the unit root constraint, pre-test estimation, model selection estimation, and model average estimation. We find that the asymptotic risk depends only on the local-to-unity parameter, facilitating simple graphical comparisons. Our results strongly caution against pre-testing. Strong evidence supports averaging based on Mallows weights. In particular, our Mallows averaging method has uniformly and substantially smaller risk than the conventional unconstrained estimator, and this holds for autoregressive roots far from unity. Our averaging estimator is a new approach to forecast combination.