Weighted-Average Least Squares Prediction

Jan R. Magnus*, Wendun Wang, Xinyu Zhang

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review


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
Issue number6
Publication statusPublished - 2 Jul 2016


  • Bayesian analysis
  • Model averaging
  • Model uncertainty
  • Prediction


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