Weighted-Average Least Squares Prediction

Jan R. Magnus, Wendun Wang, Xinyu Zhang

Research output: Contribution to JournalArticleAcademicpeer-review

Abstract

Prediction under model uncertainty is an important and difficult issue. Traditional prediction methods (such as pretesting) are based on model selection followed by prediction in the selected model, but the reported prediction and the reported prediction variance ignore the uncertainty from the selection procedure. This article proposes a weighted-average least squares (WALS) prediction procedure that is not conditional on the selected model. Taking both model and error uncertainty into account, we also propose an appropriate estimate of the variance of the WALS predictor. Correlations among the random errors are explicitly allowed. Compared to other prediction averaging methods, the WALS predictor has important advantages both theoretically and computationally. Simulation studies show that the WALS predictor generally produces lower mean squared prediction errors than its competitors, and that the proposed estimator for the prediction variance performs particularly well when model uncertainty increases.

Original languageEnglish
Pages (from-to)1040-1074
Number of pages35
JournalEconometric Reviews
Volume35
Issue number6
DOIs
Publication statusPublished - 2 Jul 2016

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Least squares
Prediction
Predictors
Model uncertainty
Uncertainty
Model selection
Prediction error
Simulation study
Estimator
Random error
Competitors

Keywords

  • Bayesian analysis
  • Model averaging
  • Model uncertainty
  • Prediction

Cite this

Magnus, Jan R. ; Wang, Wendun ; Zhang, Xinyu. / Weighted-Average Least Squares Prediction. In: Econometric Reviews. 2016 ; Vol. 35, No. 6. pp. 1040-1074.
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Weighted-Average Least Squares Prediction. / Magnus, Jan R.; Wang, Wendun; Zhang, Xinyu.

In: Econometric Reviews, Vol. 35, No. 6, 02.07.2016, p. 1040-1074.

Research output: Contribution to JournalArticleAcademicpeer-review

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