Toward optimal model averaging in regression models with time series errors

Tzu Chang F. Cheng, Ching Kang Ing, Shu Hui Yu

Research output: Contribution to journalArticlepeer-review

23 Scopus citations

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.

Original languageEnglish
Pages (from-to)321-334
Number of pages14
JournalJournal of Econometrics
Volume189
Issue number2
DOIs
StatePublished - Dec 2015

Keywords

  • Asymptotic efficiency
  • Autocovariance-corrected Mallows model averaging
  • Banded Cholesky factorization
  • Feasible generalized least squares estimator
  • High-dimensional covariance matrix
  • Time series errors

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