Direct and iterated multistep AR methods for difference stationary processes

The paper focuses on the comparison of the direct and iterated AR predictors for difference stationary processes. In particular, it provides new methods for comparing the efficiency of the two predictors and for extracting the trend from macroeconomic time series using the two methods. The methods are based on an encompassing representation for the two predictors which enables to derive their properties quite easily under a maintained model. The paper provides an analytic expression for the mean square forecast error of the two predictors and derives useful recursive formulae for computing the direct and iterated coefficients. From the empirical standpoint, we propose estimators of the AR coefficients based on the tapered Yule- Walker estimates; we also provide a test of equal forecast accuracy which is very simple to implement and whose critical values are obtained with the bootstrap method.