A Useful Transformation for the Calculation of the Feasible Generalized Least Squares Estimator

Let Rt be the matrix obtained by inserting p into the right-hand side of

(5.2.10) . Then we have by (5.2.14) fip = (X’ft’&X^X’RJRj. Thus fip can be obtained by least squares after transforming all the variables by Rt. An­other, somewhat simpler transformation is defined by eliminating the first row of R,. This is called the Cochrane-Orcutt transformation (Cochrane and

Orcutt, 1949). The resulting estimator is slightly different from FGLS but has the same asymptotic distribution.

If {u,} follow AR(2) defined by (5.2.16), the relevant transformation is given by (5.2.27), where a’s are determined by solving V(axux) = a2, У(а2щ + a3u2) = a2, and Е[ахщ{а2щ + a3u2)] = 0. A generalization of the Cochrane-Orcutt transformation is obtained by eliminating the first two rows of R2. Higher-order autoregressive processes can be similarly handled.

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