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Fixed-smoothing Asymptotics and Asymptotic F and t Tests in the Presence of Strong Autocorrelation

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  • Sun, Yixiao

Abstract

New asymptotic approximations are established for the Wald and t statistics in the presence of unknown but strong autocorrelation. The asymptotic theory extends the usual fixed-smoothing asymptotics under weak dependence to allow for near unit root and weak unit root processes. As the locality parameter that characterizes the neighborhood of the autoregressive root increases from zero to infinity, the new fixed-smoothing asymptotic distribution changes smoothly from the unit-root fixed-smoothing asymptotics to the usual fixed-smoothing asymptotics under weak dependence. Simulations show that the new approximation is more accurate than the usual fixed-smoothing approximation.

Suggested Citation

  • Sun, Yixiao, 2014. "Fixed-smoothing Asymptotics and Asymptotic F and t Tests in the Presence of Strong Autocorrelation," University of California at San Diego, Economics Working Paper Series qt8479f4s2, Department of Economics, UC San Diego.
    • Handle: RePEc:cdl:ucsdec:qt8479f4s2
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    References listed on IDEAS

    as
    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 & 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. Park, Joon, 2003. "Weak Unit Roots," Working Papers 2003-17, Rice University, Department of Economics.
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    8. 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.
    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. Whitney Newey & Kenneth West, 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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    12. Phillips, Peter C.B. & Magdalinos, Tassos & Giraitis, Liudas, 2010. "Smoothing local-to-moderate unit root theory," Journal of Econometrics, Elsevier, vol. 158(2), pages 274-279, October.
    13. repec:cdl:ucsdec:qt64x4z265 is not listed on IDEAS
    14. Sun, Yixiao, 2004. "A CONVERGENT t-STATISTIC IN SPURIOUS REGRESSIONS," Econometric Theory, Cambridge University Press, vol. 20(5), pages 943-962, October.
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    Cited by:

    1. Hwang, Jungbin & Sun, Yixiao, 2017. "Asymptotic F and t tests in an efficient GMM setting," Journal of Econometrics, Elsevier, vol. 198(2), pages 277-295.
    2. Martínez-Iriarte, Julián & Sun, Yixiao & Wang, Xuexin, 2020. "Asymptotic F tests under possibly weak identification," Journal of Econometrics, Elsevier, vol. 218(1), pages 140-177.
    3. Kim, Min Seong & Sun, Yixiao & Yang, Jingjing, 2016. "A Fixed-bandwidth View of the Pre-asymptotic Inference for Kernel Smoothing with Time Series Data," University of California at San Diego, Economics Working Paper Series qt2240n3n5, Department of Economics, UC San Diego.
    4. Liu, Cheng & Sun, Yixiao, 2019. "A Simple and Trustworthy Asymptotic t Test in Difference-in-Differences Regressions," University of California at San Diego, Economics Working Paper Series qt0ck2109g, Department of Economics, UC San Diego.
    5. Hwang, Jungbin & Sun, Yixiao, 2015. "Asymptotic F and t Tests in an Efficient GMM Setting," University of California at San Diego, Economics Working Paper Series qt1c62d8xf, Department of Economics, UC San Diego.
    6. Sun, Yixiao & Yang, Jingjing, 2020. "Testing-optimal kernel choice in HAR inference," Journal of Econometrics, Elsevier, vol. 219(1), pages 123-136.
    7. Hwang., Jungbin & Sun, Yixiao, 2017. "Simple, Robust, and Accurate F and t Tests in Cointegrated Systems," University of California at San Diego, Economics Working Paper Series qt83b4q8pk, Department of Economics, UC San Diego.
    8. Liu, Cheng & Sun, Yixiao, 2019. "A simple and trustworthy asymptotic t test in difference-in-differences regressions," Journal of Econometrics, Elsevier, vol. 210(2), pages 327-362.
    9. Martínez-Iriarte, Julián & Sun, Yixiao & Wang, Xuexin, 2019. "Asymptotic F Tests under Possibly Weak Identification," University of California at San Diego, Economics Working Paper Series qt6qk200q8, Department of Economics, UC San Diego.
    10. Kim, Min Seong & Sun, Yixiao & Yang, Jingjing, 2017. "A fixed-bandwidth view of the pre-asymptotic inference for kernel smoothing with time series data," Journal of Econometrics, Elsevier, vol. 197(2), pages 298-322.

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