Known Moving-Average Transformations and Autoregressive Processes

Abstract

The errors in the linear models which are used so widely by economists may be generated by mixed moving-average autoregressive processes. If errors on an aggregative equation are generated by a mixed moving-average autoregressive process and the weights of the moving-average component of this process are known, then the least-squares procedure can yield consistent estimators of both signal and autoregressive parameters if two adjustments are made to the equation. The autoregressive transformation is combined with pre-multiplication by a Moore-Penrose inverse based on the known weights of the moving-average component.