Toward optimal model averaging in regression models with time series errors

TL;DR

This paper develops a feasible model averaging method for regression models with time series errors, using consistent estimators of the inverse covariance matrix to optimize weights and improve prediction accuracy.

Contribution

It introduces a new feasible autocovariance-corrected Mallows criterion for optimal weight selection in model averaging with time series errors.

Findings

Asymptotic equivalence to the minimum generalized squared error loss

Inclusion of Hansen (2007) weight set as a subset

Consistent estimator of inverse covariance matrix improves model averaging

Abstract

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.