p.135

Specification of the Disturbance for Efficient Estimation

Robert F. Engle

Abstract

Necessary and sufficient conditions are determined under which a truncated approximation to generalized least squares is more efficient than ordinary least squares. For the general case, the necessary conditions are unlikely to be fulfilled. For a first order Markov model in a second order world, the sufficient conditions are satisfied only when one of the second order roots is very small, and therefore the first order assumption is approximately true. When the class of possible exogenous variables is limited to those typical of economic time series, the sufficient conditions are satisfied for a wider range of cases. Relative efficiencies are computed for a variety of cases.