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Block Bootstrap Hac Robust Tests: The Sophistication Of The Naive Bootstrap

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  • Gonçalves, Sílvia
  • Vogelsang, Timothy J.

Abstract

This paper studies the properties of naive block bootstrap tests that are scaled by zero frequency spectral density estimators (long-run variance estimators). The naive bootstrap is a bootstrap where the formula used in the bootstrap world to compute standard errors is the same as the formula used on the original data. Simulation evidence shows that the naive bootstrap can be much more accurate than the standard normal approximation. The larger the HAC bandwidth, the greater the improvement. This improvement holds for a large number of popular kernels, including the Bartlett kernel, and it holds when the independent and identically distributed (i.i.d.) bootstrap is used and yet the data are serially correlated. Using recently developed fixed-b asymptotics for HAC robust tests, we provide theoretical results that can explain the finite sample patterns. We show that the block bootstrap, including the special case of the i.i.d. bootstrap, has the same limiting distribution as the fixed-b asymptotic distribution. For the special case of a location model, we provide theoretical results that suggest the naive bootstrap can be more accurate than the standard normal approximation depending on the choice of the bandwidth and the number of finite moments in the data. Our theoretical results lay the foundation for a bootstrap asymptotic theory that is an alternative to the traditional approach based on Edgeworth expansions.

Suggested Citation

  • Gonçalves, Sílvia & Vogelsang, Timothy J., 2011. "Block Bootstrap Hac Robust Tests: The Sophistication Of The Naive Bootstrap," Econometric Theory, Cambridge University Press, vol. 27(4), pages 745-791, August.
    • Handle: RePEc:cup:etheor:v:27:y:2011:i:04:p:745-791_00
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    Cited by:

    1. Marian Vavra, 2015. "On a Bootstrap Test for Forecast Evaluations," Working and Discussion Papers WP 5/2015, Research Department, National Bank of Slovakia.
    2. Robin Greenwood & Samuel G. Hanson, 2013. "Issuer Quality and Corporate Bond Returns," The Review of Financial Studies, Society for Financial Studies, vol. 26(6), pages 1483-1525.
    3. Zhang, Xianyang, 2016. "Fixed-smoothing asymptotics in the generalized empirical likelihood estimation framework," Journal of Econometrics, Elsevier, vol. 193(1), pages 123-146.
    4. Timothy Conley & Silvia Gonçalves & Christian Hansen, 2018. "Inference with Dependent Data in Accounting and Finance Applications," Journal of Accounting Research, Wiley Blackwell, vol. 56(4), pages 1139-1203, September.
    5. 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.
    6. Stephan Smeekes & Joakim Westerlund, 2019. "Robust block bootstrap panel predictability tests," Econometric Reviews, Taylor & Francis Journals, vol. 38(9), pages 1089-1107, October.
    7. Ulrich K. Müller & Mark W. Watson, 2015. "Low-Frequency Econometrics," NBER Working Papers 21564, National Bureau of Economic Research, Inc.
    8. Adamek, Robert & Smeekes, Stephan & Wilms, Ines, 2023. "Lasso inference for high-dimensional time series," Journal of Econometrics, Elsevier, vol. 235(2), pages 1114-1143.
    9. Coroneo, Laura & Iacone, Fabrizio & Paccagnini, Alessia & Santos Monteiro, Paulo, 2023. "Testing the predictive accuracy of COVID-19 forecasts," International Journal of Forecasting, Elsevier, vol. 39(2), pages 606-622.
    10. Ross McKitrick & Timothy Vogelsang, 2011. "Multivariate trend comparisons between autocorrelated climate series with general trend regressors," Working Papers 1109, University of Guelph, Department of Economics and Finance.
    11. Karavias, Yiannis & Symeonides, Spyridon D. & Tzavalis, Elias, 2018. "Higher order expansions for error variance matrix estimates in the Gaussian AR(1) linear regression model," Statistics & Probability Letters, Elsevier, vol. 135(C), pages 54-59.
    12. Laura Coroneo & Fabrizio Iacone, 2020. "Comparing predictive accuracy in small samples using fixed‐smoothing asymptotics," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 35(4), pages 391-409, June.
    13. Xiaoqing Ye & Yixiao Sun, 2018. "Heteroskedasticity- and autocorrelation-robust F and t tests in Stata," Stata Journal, StataCorp LP, vol. 18(4), pages 951-980, December.
    14. Cheol-Keun Cho & Timothy J. Vogelsang, 2016. "Fixed- b Inference for Testing Structural Change in a Time Series Regression," Econometrics, MDPI, vol. 5(1), pages 1-26, December.
    15. Surajit Ray & N. E. Savin, 2008. "The performance of heteroskedasticity and autocorrelation robust tests: a Monte Carlo study with an application to the three-factor Fama-French asset-pricing model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 23(1), pages 91-109.
    16. James G. MacKinnon & Morten Ørregaard Nielsen & Matthew D. Webb, 2021. "Wild Bootstrap and Asymptotic Inference With Multiway Clustering," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(2), pages 505-519, March.
    17. Kim, Min Seong & Sun, Yixiao, 2011. "Spatial heteroskedasticity and autocorrelation consistent estimation of covariance matrix," Journal of Econometrics, Elsevier, vol. 160(2), pages 349-371, February.
    18. Andrea Fracasso & Giuseppe Vittucci Marzetti, 2014. "International R&D Spillovers, Absorptive Capacity and Relative Backwardness: A Panel Smooth Transition Regression Model," International Economic Journal, Taylor & Francis Journals, vol. 28(1), pages 137-160, March.
    19. Federico Belotti & Alessandro Casini & Leopoldo Catania & Stefano Grassi & Pierre Perron, 2023. "Simultaneous bandwidths determination for DK-HAC estimators and long-run variance estimation in nonparametric settings," Econometric Reviews, Taylor & Francis Journals, vol. 42(3), pages 281-306, February.
    20. Matei Demetrescu & Christoph Hanck & Robinson Kruse, 2016. "Fixed-b Inference in the Presence of Time-Varying Volatility," CREATES Research Papers 2016-01, Department of Economics and Business Economics, Aarhus University.
    21. Rho, Seunghwa & Vogelsang, Timothy J., 2021. "Inference in time series models using smoothed-clustered standard errors," Journal of Econometrics, Elsevier, vol. 224(1), pages 113-133.
    22. 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.
    23. Hwang, Jungbin & Sun, Yixiao, 2018. "Should we go one step further? An accurate comparison of one-step and two-step procedures in a generalized method of moments framework," Journal of Econometrics, Elsevier, vol. 207(2), pages 381-405.
    24. Xianyang Zhang & Xiaofeng Shao, 2016. "On the coverage bound problem of empirical likelihood methods for time series," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(2), pages 395-421, March.

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