TY - JOUR

T1 - Toward optimal model averaging in regression models with time series errors

AU - Cheng, Tzu Chang F.

AU - Ing, Ching Kang

AU - Yu, Shu Hui

N1 - Publisher Copyright:
© 2015 Elsevier B.V.

PY - 2015/12

Y1 - 2015/12

N2 - 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.

AB - 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.

KW - Asymptotic efficiency

KW - Autocovariance-corrected Mallows model averaging

KW - Banded Cholesky factorization

KW - Feasible generalized least squares estimator

KW - High-dimensional covariance matrix

KW - Time series errors

UR - http://www.scopus.com/inward/record.url?scp=84945454995&partnerID=8YFLogxK

U2 - 10.1016/j.jeconom.2015.03.026

DO - 10.1016/j.jeconom.2015.03.026

M3 - 期刊論文

AN - SCOPUS:84945454995

SN - 0304-4076

VL - 189

SP - 321

EP - 334

JO - Journal of Econometrics

JF - Journal of Econometrics

IS - 2

ER -