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A New Asymptotic Theory for Vector Autoregressive Long-run Variance Estimation and Autocorrelation Robust Testing

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  • Sun, Yixiao
  • Kaplan, David M.

Abstract

We develop a new asymptotic theory for autocorrelation robust tests using a vector autoregressive (VAR) covariance matrix estimator. In contrast to the conventional asymptotics where the VAR order goes to infinity but at a slower rate than the sample size, wehave the VAR order grow at the same rate, as a fixed fraction of the sample size. Under thisfixed-smoothing asymptotic specification, the associated Wald statistic remains asymptot-ically pivotal. On the basis of this asymptotics, we introduce a new and easy-to-use F test that employs a Önite sample corrected Wald statistic and uses critical values from an Fdistribution. We also propose an empirical VAR order selection rule that exploits the connection between VAR variance estimation and kernel variance estimation. Simulations show that the new VAR Ftest with the empirical order selection is much more accuratein size than the conventional chi-square test.

Suggested Citation

  • 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.
    • Handle: RePEc:cdl:ucsdec:qt8cx0t4gc
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    References listed on IDEAS

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    1. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    2. 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.
    3. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    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. Sun, Yixiao & Kim, Min Seong, 2012. "Simple and powerful GMM over-identification tests with accurate size," Journal of Econometrics, Elsevier, vol. 166(2), pages 267-281.
    6. Andrews, Donald W K & Monahan, J Christopher, 1992. "An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator," Econometrica, Econometric Society, vol. 60(4), pages 953-966, July.
    7. 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.
    8. de Jong, Robert M. & Davidson, James, 2000. "The Functional Central Limit Theorem And Weak Convergence To Stochastic Integrals I," Econometric Theory, Cambridge University Press, vol. 16(5), pages 621-642, October.
    9. 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.
    10. 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.
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    Cited by:

    1. Kim, Min Seong & Sun, Yixiao, 2013. "Heteroskedasticity and spatiotemporal dependence robust inference for linear panel models with fixed effects," Journal of Econometrics, Elsevier, vol. 177(1), pages 85-108.
    2. Sun, Yixiao, 2013. "Fixed-smoothing Asymptotics in a Two-step GMM Framework," University of California at San Diego, Economics Working Paper Series qt64x4z265, Department of Economics, UC San Diego.
    3. Kaplan, David M., 2015. "Improved quantile inference via fixed-smoothing asymptotics and Edgeworth expansion," Journal of Econometrics, Elsevier, vol. 185(1), pages 20-32.
    4. 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.

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