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Improved HAR Inference

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Abstract

Employing power kernels suggested in earlier work by the authors (2003), this paper shows how to re.ne methods of robust inference on the mean in a time series that rely on families of untruncated kernel estimates of the long-run parameters. The new methods improve the size properties of heteroskedastic and autocorrelation robust (HAR) tests in comparison with conventional methods that employ consistent HAC estimates, and they raise test power in comparison with other tests that are based on untruncated kernel estimates. Large power parameter (rho) asymptotic expansions of the nonstandard limit theory are developed in terms of the usual limiting chi-squared distribution, and corresponding large sample size and large rho asymptotic expansions of the finite sample distribution of Wald tests are developed to justify the new approach. Exact finite sample distributions are given using operational techniques. The paper further shows that the optimal rho that minimizes a weighted sum of type I and II errors has an expansion rate of at most O(T^{1/2}) and can even be O(1) for certain loss functions, and is therefore slower than the O(T^{2/3}) rate which minimizes the asymptotic mean squared error of the corresponding long run variance estimator. A new plug-in procedure for implementing the optimal rho is suggested. Simulations show that the new plug-in procedure works well in finite samples.

Suggested Citation

  • Peter C.B. Phillips & Yixiao Sun & Sainan Jin, 2005. "Improved HAR Inference," Cowles Foundation Discussion Papers 1513, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:1513
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    File URL: http://cowles.yale.edu/sites/default/files/files/pub/d15/d1513.pdf
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    References listed on IDEAS

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    1. Phillips, Peter C.B., 2005. "Hac Estimation By Automated Regression," Econometric Theory, Cambridge University Press, vol. 21(01), pages 116-142, February.
    2. Michael Jansson, 2004. "The Error in Rejection Probability of Simple Autocorrelation Robust Tests," Econometrica, Econometric Society, vol. 72(3), pages 937-946, May.
    3. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 33(1), pages 125-132.
    4. 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.
    5. repec:cup:etheor:v:12:y:1996:i:2:p:331-46 is not listed on IDEAS
    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. repec:wop:calsdi:96-17 is not listed on IDEAS
    8. Peter C.B. Phillips & Yixiao Sun & Sainan Jin, 2003. "Consistent HAC Estimation and Robust Regression Testing Using Sharp Origin Kernels with No Truncation," Cowles Foundation Discussion Papers 1407, Cowles Foundation for Research in Economics, Yale University.
    9. P. C. B. Phillips, 1980. "Finite Sample Theory and the Distributions of Alternative Estimators of the Marginal Propensity to Consume," Review of Economic Studies, Oxford University Press, vol. 47(1), pages 183-224.
    10. Wouter Denhaan & Andrew T. Levin, 1996. "VARHAC Covariance Matrix Estimator (GAUSS)," QM&RBC Codes 64, Quantitative Macroeconomics & Real Business Cycles.
    11. 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.
    12. Velasco, Carlos & Robinson, Peter M., 2001. "Edgeworth Expansions For Spectral Density Estimates And Studentized Sample Mean," Econometric Theory, Cambridge University Press, vol. 17(03), pages 497-539, June.
    13. Hansen, Bruce E, 1992. "Consistent Covariance Matrix Estimation for Dependent Heterogeneous Processes," Econometrica, Econometric Society, vol. 60(4), pages 967-972, July.
    14. Peter C.B. Phillips, 1990. "Operational Algebra and Regression t-Tests," Cowles Foundation Discussion Papers 948, Cowles Foundation for Research in Economics, Yale University.
    15. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    16. Sun, Yixiao, 2004. "Estimation Of The Long-Run Average Relationship In Nonstationary Panel Time Series," Econometric Theory, Cambridge University Press, vol. 20(06), pages 1227-1260, December.
    17. Peter C.B. Phillips & Yixiao Sun & Sainan Jin, 2003. "Long Run Variance Estimation Using Steep Origin Kernels without Truncation," Cowles Foundation Discussion Papers 1437, Cowles Foundation for Research in Economics, Yale University.
    18. Kiefer, Nicholas M. & Vogelsang, Timothy J., 2002. "Heteroskedasticity-Autocorrelation Robust Testing Using Bandwidth Equal To Sample Size," Econometric Theory, Cambridge University Press, vol. 18(06), pages 1350-1366, December.
    19. 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.
    20. Jansson, Michael, 2002. "Consistent Covariance Matrix Estimation For Linear Processes," Econometric Theory, Cambridge University Press, vol. 18(06), pages 1449-1459, December.
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    Cited by:

    1. Barbier de la Serre, A. & Frappa, S. & Montornès, J. & Murez, M., 2008. "La transmission des taux de marché aux taux bancaires : une estimation sur données individuelles françaises," Working papers 194, Banque de France.

    More about this item

    Keywords

    Asymptotic expansion; consistent HAC estimation; data-determined kernel estimation; exact distribution; HAR inference; large rho asymptotics; long run variance; loss function; power parameter; sharp origin kernel;

    JEL classification:

    • 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
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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