  Consider a regression model with infinitely many parameters and time series
errors. We are interested in choosing weights for averaging across generalized
least squares (GLS) estimators obtained from a set of approximating models.
However, GLS estimators, depending on the unknown inverse covariance matrix of
the errors, are usually infeasible. We therefore construct feasible generalized
least squares (FGLS) estimators using a consistent estimator of the unknown
inverse matrix. Based on this inverse covariance matrix estimator and FGLS
estimators, we develop a feasible autocovariance-corrected Mallows model
averaging criterion to select weights, thereby providing an FGLS model
averaging estimator of the true regression function. We show that the
generalized squared error loss of our averaging estimator is asymptotically
equivalent to the minimum one among those of GLS model averaging estimators
with the weight vectors belonging to a continuous set, which includes the
discrete weight set used in Hansen (2007) as its proper subset.
