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Second-order least-squares estimation for regression models with autocorrelated errors

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  • Dedi Rosadi
  • Shelton Peiris

Abstract

In their recent paper, Wang and Leblanc (Ann Inst Stat Math 60:883–900, 2008 ) have shown that the second-order least squares estimator (SLSE) is more efficient than the ordinary least squares estimator (OLSE) when the errors are independent and identically distributed with non zero third moments. In this paper, we generalize the theory of SLSE to regression models with autocorrelated errors. Under certain regularity conditions, we establish the consistency and asymptotic normality of the proposed estimator and provide a simulation study to compare its performance with the corresponding OLSE and generalized least square estimator (GLSE). It is shown that the SLSE performs well giving relatively small standard error and bias (or the mean square error) in estimating parameters of such regression models with autocorrelated errors. Based on our study, we conjecture that for less correlated data, the standard errors of SLSE lie between those of the OLSE and GLSE which can be interpreted as adding the second moment information can improve the performance of an estimator. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Dedi Rosadi & Shelton Peiris, 2014. "Second-order least-squares estimation for regression models with autocorrelated errors," Computational Statistics, Springer, vol. 29(5), pages 931-943, October.
    • Handle: RePEc:spr:compst:v:29:y:2014:i:5:p:931-943
    DOI: 10.1007/s00180-013-0470-1
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    References listed on IDEAS

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    1. Krämer, Walter & Marmol, Francesc, 1998. "OLS-based asymptotic inference in linear regression models with trending regressors and AR(p)-disturbances," Technical Reports 1998,43, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    2. Amemiya, Takeshi, 1973. "Regression Analysis when the Dependent Variable is Truncated Normal," Econometrica, Econometric Society, vol. 41(6), pages 997-1016, November.
    3. Liqun Wang & Alexandre Leblanc, 2008. "Second-order nonlinear least squares estimation," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 60(4), pages 883-900, December.
    4. Chipman, John S, 1979. "Efficiency of Least-Squares Estimation of Linear Trend when Residuals are Autocorrelated," Econometrica, Econometric Society, vol. 47(1), pages 115-128, January.
    5. White, Halbert, 1980. "Nonlinear Regression on Cross-Section Data," Econometrica, Econometric Society, vol. 48(3), pages 721-746, April.
    6. A. Ullah & V. K. Srivastava & L. Magee & A. Srivastava, 1983. "Estimation Of Linear Regression Model With Autocorrelated Disturbances," Journal of Time Series Analysis, Wiley Blackwell, vol. 4(2), pages 127-135, March.
    7. White, Halbert & Domowitz, Ian, 1984. "Nonlinear Regression with Dependent Observations," Econometrica, Econometric Society, vol. 52(1), pages 143-161, January.
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    Cited by:

    1. D. Rosadi & P. Filzmoser, 2019. "Robust second-order least-squares estimation for regression models with autoregressive errors," Statistical Papers, Springer, vol. 60(1), pages 105-122, February.
    2. Mustafa Salamh & Liqun Wang, 2021. "Second-Order Least Squares Estimation in Nonlinear Time Series Models with ARCH Errors," Econometrics, MDPI, vol. 9(4), pages 1-17, November.

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