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Alternative HAC covariance matrix estimators with improved finite sample properties

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  • Hartigan, Luke

Abstract

HAC estimators are known to produce test statistics that reject too frequently in finite samples. One neglected reason comes from the OLS residuals used to construct the HAC estimator. If the design matrix contains leverage points, such as from outliers, then the OLS residuals will be downward biased. This makes the OLS residuals smaller than otherwise, thereby reducing their variance. Transformations to offset the bias via inflating the OLS residuals have been available in the related HC literature for some time, but these have been overlooked so far in the HAC literature. Using HC-inspired techniques and a range of simulations, this paper provides strong support for replacing the OLS residual-based HAC estimator with two new alternatives called HAC-PE and HAC-MDE when estimating coefficient standard errors to produce test statistics because they display much less size distortion in practice.

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  • Hartigan, Luke, 2018. "Alternative HAC covariance matrix estimators with improved finite sample properties," Computational Statistics & Data Analysis, Elsevier, vol. 119(C), pages 55-73.
    • Handle: RePEc:eee:csdana:v:119:y:2018:i:c:p:55-73
    DOI: 10.1016/j.csda.2017.09.007
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    1. Chistiano, Lawrence J & den Haan, Wouter J, 1996. "Small-Sample Properties of GMM for Business-Cycle Analysis," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 309-327, July.
    2. Donggyu Sul & Peter C. B. Phillips & Chi‐Young Choi, 2005. "Prewhitening Bias in HAC Estimation," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 67(4), pages 517-546, August.
    3. Francis X. Diebold, 2015. "Comparing Predictive Accuracy, Twenty Years Later: A Personal Perspective on the Use and Abuse of Diebold-Mariano Tests," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(1), pages 1-1, January.
    4. Whitney K. Newey & Kenneth D. West, 1994. "Automatic Lag Selection in Covariance Matrix Estimation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 61(4), pages 631-653.
    5. Francisco Cribari-Neto & Wilton Silva, 2011. "A new heteroskedasticity-consistent covariance matrix estimator for the linear regression model," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 95(2), pages 129-146, June.
    6. Cribari-Neto, Francisco, 2004. "Asymptotic inference under heteroskedasticity of unknown form," Computational Statistics & Data Analysis, Elsevier, vol. 45(2), pages 215-233, March.
    7. Burnside, Craig & Eichenbaum, Martin S, 1996. "Small-Sample Properties of GMM-Based Wald Tests," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 294-308, July.
    8. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
    9. Chesher, Andrew & Austin, Gerard, 1991. "The finite-sample distributions of heteroskedasticity robust Wald statistics," Journal of Econometrics, Elsevier, vol. 47(1), pages 153-173, January.
    10. Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119.
    11. Zeileis, Achim, 2004. "Econometric Computing with HC and HAC Covariance Matrix Estimators," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 11(i10).
    12. Chesher, Andrew & Jewitt, Ian, 1987. "The Bias of a Heteroskedasticity Consistent Covariance Matrix Estimator," Econometrica, Econometric Society, vol. 55(5), pages 1217-1222, September.
    13. Kuan, Chung-Ming & Hsieh, Yu-Wei, 2008. "Improved HAC covariance matrix estimation based on forecast errors," Economics Letters, Elsevier, vol. 99(1), pages 89-92, April.
    14. Keener, Robert W. & Kmenta, Jan & Weber, Neville C., 1991. "Estimation of the Covariance Matrix of the Least-Squares Regression Coefficients When the Disturbance Covariance Matrix Is of Unknown Form," Econometric Theory, Cambridge University Press, vol. 7(1), pages 22-45, March.
    15. Hansen, Bruce E, 1992. "Consistent Covariance Matrix Estimation for Dependent Heterogeneous Processes," Econometrica, Econometric Society, vol. 60(4), pages 967-972, July.
    16. 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.
    17. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-144, January.
    18. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    19. 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.
    20. 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.
    21. MacKinnon, James G. & White, Halbert, 1985. "Some heteroskedasticity-consistent covariance matrix estimators with improved finite sample properties," Journal of Econometrics, Elsevier, vol. 29(3), pages 305-325, September.
    22. Kauermann G. & Carroll R.J., 2001. "A Note on the Efficiency of Sandwich Covariance Matrix Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1387-1396, December.
    23. West, Kenneth D., 1997. "Another heteroskedasticity- and autocorrelation-consistent covariance matrix estimator," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 171-191.
    24. Wouter J. den Haan & Andrew T. Levin, 2000. "Robust Covariance Matrix Estimation with Data-Dependent VAR Prewhitening Order," NBER Technical Working Papers 0255, National Bureau of Economic Research, Inc.
    25. Elliott, Graham & Timmermann, Allan, 2004. "Optimal forecast combinations under general loss functions and forecast error distributions," Journal of Econometrics, Elsevier, vol. 122(1), pages 47-79, September.
    26. Robert M. De Jong & James Davidson, 2000. "Consistency of Kernel Estimators of Heteroscedastic and Autocorrelated Covariance Matrices," Econometrica, Econometric Society, vol. 68(2), pages 407-424, March.
    27. Jansson, Michael, 2002. "Consistent Covariance Matrix Estimation For Linear Processes," Econometric Theory, Cambridge University Press, vol. 18(6), pages 1449-1459, December.
    28. Godfrey, L.G., 2006. "Tests for regression models with heteroskedasticity of unknown form," Computational Statistics & Data Analysis, Elsevier, vol. 50(10), pages 2715-2733, June.
    29. de Jong, Robert M., 2000. "A Strong Consistency Proof For Heteroskedasticity And Autocorrelation Consistent Covariance Matrix Estimators," Econometric Theory, Cambridge University Press, vol. 16(2), pages 262-268, April.
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    Cited by:

    1. Luke Hartigan, 2016. "Testing for Symmetry in Weakly Dependent Time Series," Discussion Papers 2016-18, School of Economics, The University of New South Wales.
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    3. Luke Hartigan & James Morley, 2018. "A Factor Model Analysis of the Effects on Inflation Targeting on the Australian Economy," RBA Annual Conference Volume (Discontinued), in: John Simon & Maxwell Sutton (ed.),Central Bank Frameworks: Evolution or Revolution?, Reserve Bank of Australia.
    4. Luke Hartigan & Michelle Wright, 2023. "Monitoring Financial Conditions and Downside Risk to Economic Activity in Australia," The Economic Record, The Economic Society of Australia, vol. 99(325), pages 253-287, June.

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    More about this item

    Keywords

    Covariance matrix estimation; Finite sample analysis; Leverage points; Hypothesis testing; Monte Carlo simulation; Inference;
    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
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation 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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