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On a general class of long run variance estimators

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  • Zhang, Xianyang
  • Shao, Xiaofeng

Abstract

This note proposes a class of estimators for estimating the asymptotic covariance matrix of the generalized method of moments (GMM) estimator in the stationary time series models. The proposed estimator is general enough to include the traditional heteroskedasticity and autocorrelation consistent (HAC) covariance estimator and some recently developed estimators, such as the cluster covariance estimator and projection-based covariance estimator, as special cases. We also study the first order asymptotics of the Wald statistics based on the general covariance estimators when the underlying smoothing parameter is held fixed.

Suggested Citation

  • Zhang, Xianyang & Shao, Xiaofeng, 2013. "On a general class of long run variance estimators," Economics Letters, Elsevier, vol. 120(3), pages 437-441.
    • Handle: RePEc:eee:ecolet:v:120:y:2013:i:3:p:437-441
    DOI: 10.1016/j.econlet.2013.05.026
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    References listed on IDEAS

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    1. Phillips, Peter C.B., 2005. "Hac Estimation By Automated Regression," Econometric Theory, Cambridge University Press, vol. 21(1), pages 116-142, February.
    2. Yixiao Sun, 2013. "A heteroskedasticity and autocorrelation robust F test using an orthonormal series variance estimator," Econometrics Journal, Royal Economic Society, vol. 16(1), pages 1-26, February.
    3. Lobato I. N., 2001. "Testing That a Dependent Process Is Uncorrelated," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1066-1076, September.
    4. Xiaofeng Shao, 2010. "Corrigendum: A self‐normalized approach to confidence interval construction in time series," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(5), pages 695-696, November.
    5. Sun, Yixiao, 2011. "Robust trend inference with series variance estimator and testing-optimal smoothing parameter," Journal of Econometrics, Elsevier, vol. 164(2), pages 345-366, October.
    6. Yixiao Sun & Peter C. B. Phillips & Sainan Jin, 2008. "Optimal Bandwidth Selection in Heteroskedasticity-Autocorrelation Robust Testing," Econometrica, Econometric Society, vol. 76(1), pages 175-194, January.
    7. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    8. Xiaofeng Shao, 2010. "A self‐normalized approach to confidence interval construction in time series," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(3), pages 343-366, June.
    9. Kiefer, Nicholas M. & Vogelsang, Timothy J., 2005. "A New Asymptotic Theory For Heteroskedasticity-Autocorrelation Robust Tests," Econometric Theory, Cambridge University Press, vol. 21(6), pages 1130-1164, December.
    10. Kuan, Chung-Ming & Lee, Wei-Ming, 2006. "Robust M Tests Without Consistent Estimation of the Asymptotic Covariance Matrix," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1264-1275, September.
    11. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 33(1), pages 125-132.
    12. Bester, C. Alan & Conley, Timothy G. & Hansen, Christian B., 2011. "Inference with dependent data using cluster covariance estimators," Journal of Econometrics, Elsevier, vol. 165(2), pages 137-151.
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    More about this item

    Keywords

    Fixed-smoothing asymptotics; Generalized method of moments; Long run variance matrix;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

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