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Finite sample comparisons of the distributions of the ols and gls estimators in regression with an integrated regsorad correlated errors

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  • K. Maekawa
  • J. L. Knight
  • H. Hisamatsu

Abstract

We compare the finite sample distributional properties of the OLS and GT,S mtinialors 11 a rcgrassior wilh arl inl,cgrd,ctl rcgrtssor ant1 corrctifical errors of the form of AR(1) and MA(1) processes. The approach is one of first deriving the joint characteristic function of the quadratic forms in the clefiriit,on of t,hc est,irrial,ors and then rurrierically inverting these 1.0 find the distributions. When the characteristic functions are intractable, Monte Carlo integration is employed. We find substantial differences in the finite jarriplc ditributiorls of OLS ant1 C:LS dthough lsynlptotically thee distributions are equivalent.

Suggested Citation

  • K. Maekawa & J. L. Knight & H. Hisamatsu, 1998. "Finite sample comparisons of the distributions of the ols and gls estimators in regression with an integrated regsorad correlated errors," Econometric Reviews, Taylor & Francis Journals, vol. 17(4), pages 387-413.
    • Handle: RePEc:taf:emetrv:v:17:y:1998:i:4:p:387-413
    DOI: 10.1080/07474939808800424
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    References listed on IDEAS

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    1. Perron, Pierre, 1996. "The adequacy of asymptotic approximations in the near-integrated autoregressive model with dependent errors," Journal of Econometrics, Elsevier, vol. 70(2), pages 317-350, February.
    2. P. C. B. Phillips & S. N. Durlauf, 1986. "Multiple Time Series Regression with Integrated Processes," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(4), pages 473-495.
    3. Phillips, P. C. B., 1987. "Asymptotic Expansions in Nonstationary Vector Autoregressions," Econometric Theory, Cambridge University Press, vol. 3(1), pages 45-68, February.
    4. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    5. Srivastava, V. K. & Maekawa, Koichi, 1995. "Efficiency properties of feasible generalized least squares estimators in SURE models under non-normal disturbances," Journal of Econometrics, Elsevier, vol. 66(1-2), pages 99-121.
    6. Hisamatsu, H. & Knight, J.L. & Maekawa, K., 1995. "The exact distribution of the OLS and GLS estimators in regression with an integrated regressor and correlated errors — comparison of numerical and Monte Carlo integration," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 39(3), pages 273-277.
    7. Perron, Pierre, 1989. "The Calculation of the Limiting Distribution of the Least-Squares Estimator in a Near-Integrated Model," Econometric Theory, Cambridge University Press, vol. 5(2), pages 241-255, August.
    8. Knight, J.L. & Satchell, S.E., 1993. "Asymptotic Expansions for Random Walks with Normal Errors," Econometric Theory, Cambridge University Press, vol. 9(3), pages 363-376, June.
    9. Park, Joon Y. & Phillips, Peter C.B., 1988. "Statistical Inference in Regressions with Integrated Processes: Part 1," Econometric Theory, Cambridge University Press, vol. 4(3), pages 468-497, December.
    10. Hisamatsu, Hiroyuki & Maekawa, Koichi, 1994. "The distribution of the Durbin-Watson statistic in integrated and near-integrated models," Journal of Econometrics, Elsevier, vol. 61(2), pages 367-382, April.
    11. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
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    1. Hisamatsu, H. & Knight, J.L. & Maekawa, K., 1995. "The exact distribution of the OLS and GLS estimators in regression with an integrated regressor and correlated errors — comparison of numerical and Monte Carlo integration," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 39(3), pages 273-277.
    2. Shin, Dong Wan & Song, Seuck Heun, 2000. "Asymptotic efficiency of the OLSE for polynomial regression models with spatially correlated errors," Statistics & Probability Letters, Elsevier, vol. 47(1), pages 1-10, March.

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