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The effect of a Durbin–Watson pretest on confidence intervals in regression

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  • Paul Kabaila
  • Davide Farchione
  • Samer Alhelli
  • Nathan Bragg

Abstract

Consider a linear regression model and suppose that our aim is to find a confidence interval for a specified linear combination of the regression parameters. In practice, it is common to perform a Durbin–Watson pretest of the null hypothesis of zero first‐order autocorrelation of the random errors against the alternative hypothesis of positive first‐order autocorrelation. If this null hypothesis is accepted then the confidence interval centered on the ordinary least squares estimator is used; otherwise the confidence interval centered on the feasible generalized least squares estimator is used. For any given design matrix and parameter of interest, we compare the confidence interval resulting from this two‐stage procedure and the confidence interval that is always centered on the feasible generalized least squares estimator, as follows. First, we compare the coverage probability functions of these confidence intervals. Second, we compute the scaled expected length of the confidence interval resulting from the two‐stage procedure, where the scaling is with respect to the expected length of the confidence interval centered on the feasible generalized least squares estimator, with the same minimum coverage probability. These comparisons are used to choose the better confidence interval, prior to any examination of the observed response vector.

Suggested Citation

  • Paul Kabaila & Davide Farchione & Samer Alhelli & Nathan Bragg, 2021. "The effect of a Durbin–Watson pretest on confidence intervals in regression," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 75(1), pages 4-23, February.
    • Handle: RePEc:bla:stanee:v:75:y:2021:i:1:p:4-23
    DOI: 10.1111/stan.12222
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    References listed on IDEAS

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    1. Paul Kabaila, 2009. "The Coverage Properties of Confidence Regions After Model Selection," International Statistical Review, International Statistical Institute, vol. 77(3), pages 405-414, December.
    2. Griffiths, W.E. & Beesley, P.A.A., 1984. "The small-sample properties of some preliminary test estimators in a linear model with autocorrelated errors," Journal of Econometrics, Elsevier, vol. 25(1-2), pages 49-61.
    3. Paul Kabaila & Rheanna Mainzer & Davide Farchione, 2017. "Conditional assessment of the impact of a Hausman pretest on confidence intervals," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 71(4), pages 240-262, November.
    4. Kabaila, Paul & Mainzer, Rheanna & Farchione, Davide, 2015. "The impact of a Hausman pretest, applied to panel data, on the coverage probability of confidence intervals," Economics Letters, Elsevier, vol. 131(C), pages 12-15.
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