Weighted-Average Least Squares (WALS): Confidence and Prediction Intervals

Giuseppe Luca (), Jan R. Magnus and Franco Peracchi
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Giuseppe Luca: University of Palermo
Jan R. Magnus: Vrije Universiteit Amsterdam and Tinbergen Institute

Computational Economics, 2023, vol. 61, issue 4, No 12, 1637-1664

Abstract: Abstract We consider inference for linear regression models estimated by weighted-average least squares (WALS), a frequentist model averaging approach with a Bayesian flavor. We propose a new simulation method that yields re-centered confidence and prediction intervals by exploiting the bias-corrected posterior mean as a frequentist estimator of a normal location parameter. We investigate the performance of WALS and several alternative estimators in an extensive set of Monte Carlo experiments that allow for increasing complexity of the model space and heteroskedastic, skewed, and thick-tailed regression errors. In addition to WALS, we include unrestricted and fully restricted least squares, two post-selection estimators based on classical information criteria, a penalization estimator, and Mallows and jackknife model averaging estimators. We show that, compared to the other approaches, WALS performs well in terms of the mean squared error of point estimates, and also in terms of coverage errors and lengths of confidence and prediction intervals.

Keywords: Linear model; WALS; Confidence intervals; Prediction intervals; Monte Carlo simulations (search for similar items in EconPapers)
JEL-codes: C11 C12 C18 C21 C52 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10614-022-10255-5

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