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Asymptotic Efficiency of the OLS Estimator with Singular Limiting Sample Moment Matrices

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  • Yoshimasa Uematsu

Abstract

This paper presents a time series model that has an asymptotically efficient ordinary least squares (OLS) estimator, irrespective of the singularity of its limiting sample moment matrices. In the literature on stationary time series analysis, Grenander and Rosenblatt's (1957) (G-R) classical result is used to judge the asymptotic efficiency of regression coefficients on deterministic regressors satisfying Grenander's condition. Without this condition, however, it is not obvious that the model is efficient. In this paper, we introduce such a model by proving the efficiency of the model with a slowly varying (SV) regressor under the same condition on error terms constrained in G-R. This kind of regressor is known to display asymptotic singularity in the sample moment matrices, as in Phillips (2007), such that Grenander's condition fails.

Suggested Citation

  • Yoshimasa Uematsu, 2011. "Asymptotic Efficiency of the OLS Estimator with Singular Limiting Sample Moment Matrices," Global COE Hi-Stat Discussion Paper Series gd11-208, Institute of Economic Research, Hitotsubashi University.
  • Handle: RePEc:hst:ghsdps:gd11-208
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    File URL: http://gcoe.ier.hit-u.ac.jp/research/discussion/2008/pdf/gd11-208.pdf
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    References listed on IDEAS

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    1. Shin, Dong Wan & Oh, Man Suk, 2002. "Asymptotic Efficiency Of The Ordinary Least Squares Estimator For Regressions With Unstable Regressors," Econometric Theory, Cambridge University Press, vol. 18(05), pages 1121-1138, October.
    2. Perron, Pierre & Yabu, Tomoyoshi, 2009. "Estimating deterministic trends with an integrated or stationary noise component," Journal of Econometrics, Elsevier, vol. 151(1), pages 56-69, July.
    3. Kramer, Walter & Hassler, Uwe, 1998. "Limiting efficiency of OLS vs. GLS when regressors are fractionally integrated," Economics Letters, Elsevier, vol. 60(3), pages 285-290, September.
    4. Phillips, Peter C.B., 2007. "Regression With Slowly Varying Regressors And Nonlinear Trends," Econometric Theory, Cambridge University Press, vol. 23(04), pages 557-614, August.
    5. Mynbaev, Kairat T., 2009. "Central Limit Theorems For Weighted Sums Of Linear Processes: Lp -Approximability Versus Brownian Motion," Econometric Theory, Cambridge University Press, vol. 25(03), pages 748-763, June.
    6. Timothy J. Vogelsang, 1998. "Trend Function Hypothesis Testing in the Presence of Serial Correlation," Econometrica, Econometric Society, vol. 66(1), pages 123-148, January.
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