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

Toward optimal model averaging in regression models with time series errors