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Exact FGLS Asymptotics for MA Errors

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Abstract

We show under very parsimonious assumptions that FGLS and GLS are asymptotically equivalent when errors follow an invertible MA(1) process. Although the linear regression model with MA errors has been studied for many years, asymptotic equivalence of FGLS and GLS has never been established for this model. We do not require anything beyond a finite second moment of the conditional white noise, uniformly bounded fourth moments and independence of the regressor vectors, consistency of the estimator for the MA parameter, and a finite nonsingular probability limit for the (transformed) averages of the regressors. These assumptions are analogous to assumptions typically used to prove asymptotic equivalence of FGLS and GLS in SUR models, models with AR(p) errors, and models of parametric heteroscedasticity.

Suggested Citation

  • David Mandy & Sandor Fridli, 2004. "Exact FGLS Asymptotics for MA Errors," Working Papers 0405, Department of Economics, University of Missouri, revised 16 Dec 2004.
  • Handle: RePEc:umc:wpaper:0405
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    File URL: https://economics.missouri.edu/working-papers/2004/wp0405_mandy.pdf
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    1. Mandy, David M & Martins-Filho, Carlos, 1994. "A Unified Approach to Asymptotic Equivalence of Aitken and Feasible Aitken Instrumental Variables Estimators," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 35(4), pages 957-979, November.
    2. Mandy, David M & Martins-Filho, Carlos, 1997. "A Note on a Unified Approach to Asymptotic Equivalence of Aitken and Feasible Aitken Instrumental Variables Estimators," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 38(2), pages 479-479, May.
    3. Amemiya, Takeshi, 1973. "Generalized Least Squares with an Estimated Autocovariance Matrix," Econometrica, Econometric Society, vol. 41(4), pages 723-732, July.
    4. West, Kenneth D & Wilcox, David W, 1996. "A Comparison of Alternative Instrumental Variables Estimators of a Dynamic Linear Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 281-293, July.
    5. West, Kenneth D & Wilcox, David W, 1996. "A Comparison of Alternative Instrumental Variables Estimators of a Dynamic Linear Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 281-293, July.
    6. Maddala, G S, 1971. "Generalized Least Squares with an Estimated Variance Covariance Matrix," Econometrica, Econometric Society, vol. 39(1), pages 23-33, January.
    7. Zinde-Walsh, Victoria & Galbraith, John W., 1991. "Estimation of a linear regression model with stationary ARMA(p, q) errors," Journal of Econometrics, Elsevier, vol. 47(2-3), pages 333-357, February.
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    Keywords

    Moving Average; Generalized Least Squares; Asymptotic Distribution;

    JEL classification:

    • L5 - Industrial Organization - - Regulation and Industrial Policy

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