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Finite sample performance of a long run variance estimator based on exactly (almost) unbiased autocovariance estimators

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  • Yang, Jingjing
  • Vogelsang, Timothy J.

Abstract

This paper proposes a bias reduced long run variance (LRV) estimator of a univariate time series with unknown mean that addresses well known finite sample bias problems. The LRV estimator is based on the (almost) exactly unbiased autocovariance estimator proposed by Vogelsang and Yang (2016). Whereas using fixed-b critical values is known to correct downward bias in LRV estimates generated by demeaning the data, the approach we take also corrects the classic Parzen bias that is not captured by the fixed-b approach. When applied to the tests of the null hypothesis of the mean in a simple location model, a simulation study shows that the proposed LRV estimator leads to tests with less over-rejections while maintaining power at least as high and often higher as the standard robust t test based on fixed-b critical values. These simulations suggest further theoretical analysis of the bias reduction approach is warranted.

Suggested Citation

  • Yang, Jingjing & Vogelsang, Timothy J., 2018. "Finite sample performance of a long run variance estimator based on exactly (almost) unbiased autocovariance estimators," Economics Letters, Elsevier, vol. 165(C), pages 21-27.
    • Handle: RePEc:eee:ecolet:v:165:y:2018:i:c:p:21-27
    DOI: 10.1016/j.econlet.2018.01.023
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Sun, Yixiao & Kaplan, David M., 2011. "A New Asymptotic Theory for Vector Autoregressive Long-run Variance Estimation and Autocorrelation Robust Testing," University of California at San Diego, Economics Working Paper Series qt8cx0t4gc, Department of Economics, UC San Diego.
    4. Nigar Hashimzade & Timothy J. Vogelsang, 2008. "Fixed‐b asymptotic approximation of the sampling behaviour of nonparametric spectral density estimators," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(1), pages 142-162, January.
    5. Timothy J. Vogelsang & Jingjing Yang, 2016. "Exactly/Nearly Unbiased Estimation of Autocovariances of a Univariate Time Series With Unknown Mean," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(6), pages 723-740, November.
    6. Nicholas M. Kiefer & Timothy J. Vogelsang & Helle Bunzel, 2000. "Simple Robust Testing of Regression Hypotheses," Econometrica, Econometric Society, vol. 68(3), pages 695-714, May.
    7. Kiefer, Nicholas M. & Vogelsang, Timothy J., 2002. "Heteroskedasticity-Autocorrelation Robust Testing Using Bandwidth Equal To Sample Size," Econometric Theory, Cambridge University Press, vol. 18(6), pages 1350-1366, December.
    8. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    9. 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.
    10. Okui, Ryo, 2010. "Asymptotically Unbiased Estimation Of Autocovariances And Autocorrelations With Long Panel Data," Econometric Theory, Cambridge University Press, vol. 26(5), pages 1263-1304, October.
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    Cited by:

    1. Yifan Li & Yao Rao, 2021. "A simple nearly unbiased estimator of cross‐covariances," Journal of Time Series Analysis, Wiley Blackwell, vol. 42(2), pages 240-266, March.
    2. Yifan Li, 2024. "Correcting the bias of the sample cross‐covariance estimator," Journal of Time Series Analysis, Wiley Blackwell, vol. 45(2), pages 214-247, March.
    3. Li, Yifan, 2020. "Nearly unbiased estimation of sample skewness," Economics Letters, Elsevier, vol. 192(C).

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    More about this item

    Keywords

    Long run variance; HAC estimator; Bias correction; Fixed-b asymptotics; Hypothesis testing; Parzen bias;
    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
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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