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Generalized least squares with misspecified serial correlation structures

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  • Sergio G. Koreisha
  • Yue Fang

Abstract

Summary. The regression literature contains hundreds of studies on serially correlated disturbances. Most of these studies assume that the structure of the error covariance matrix Ω is known or can be estimated consistently from data. Surprisingly, few studies investigate the properties of estimated generalized least squares (GLS) procedures when the structure of Ω is incorrectly identified and the parameters are inefficiently estimated. We compare the finite sample efficiencies of ordinary least squares (OLS), GLS and incorrect GLS (IGLS) estimators. We also prove new theorems establishing theoretical efficiency bounds for IGLS relative to GLS and OLS. Results from an exhaustive simulation study are used to evaluate the finite sample performance and to demonstrate the robustness of IGLS estimates vis‐à‐vis OLS and GLS estimates constructed for models with known and estimated (but correctly identified) Ω. Some of our conclusions for finite samples differ from established asymptotic results.

Suggested Citation

  • Sergio G. Koreisha & Yue Fang, 2001. "Generalized least squares with misspecified serial correlation structures," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(3), pages 515-531.
    • Handle: RePEc:bla:jorssb:v:63:y:2001:i:3:p:515-531
    DOI: 10.1111/1467-9868.00296
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    Cited by:

    1. Engelbert Stockhammer & Giorgos Gouzoulis & Rob Calvert Jump, 2019. "Debt-driven business cycles in historical perspective: The cases of the USA (1889-2015) and UK (1882-2010)," Working Papers PKWP1907, Post Keynesian Economics Society (PKES).
    2. Engelbert Stockhammer & Giorgos Gouzoulis, 2023. "Debt-GDP cycles in historical perspective: the case of the USA (1889–2014)," Industrial and Corporate Change, Oxford University Press and the Associazione ICC, vol. 32(2), pages 317-335.
    3. Yue Fang & Sergio G. Koreisha, 2004. "Updating ARMA predictions for temporal aggregates," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 23(4), pages 275-296.
    4. You-Gan Wang & Xu Lin, 2005. "Effects of Variance-Function Misspecification in Analysis of Longitudinal Data," Biometrics, The International Biometric Society, vol. 61(2), pages 413-421, June.
    5. Hines, R.J. O'Hara & Hines, W.G.S., 2010. "Indices for covariance mis-specification in longitudinal data analysis with no missing responses and with MAR drop-outs," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 806-815, April.
    6. O'Hara Hines, R.J. & Hines, W.G.S., 2007. "Covariance miss-specification and the local influence approach in sensitivity analyses of longitudinal data with drop-outs," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 5537-5546, August.

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