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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.

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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1513.

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Length: 51 pages
Date of creation: Jun 2005
Date of revision:
Handle: RePEc:cwl:cwldpp:1513

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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

Related research

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;

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References

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  1. Peter C.B. Phillips, 1990. "Operational Algebra and Regression t-Tests," Cowles Foundation Discussion Papers 948, Cowles Foundation for Research in Economics, Yale University.
  2. Sainan Jin & Peter Phillips & Yixiao Sun, 2004. "Consistent HAC Estimation and Robust Regression Testing Using Sharp Origin Kernels with No Truncation," Econometric Society 2004 North American Winter Meetings 299, Econometric Society.
  3. repec:cup:etheor:v:12:y:1996:i:2:p:331-46 is not listed on IDEAS
  4. Peter C.B. Phillips & Sainan Jin & Yixiao Sun, 2004. "Long Run Variance Estimation Using Steep Origin Kernels Without Truncation," Yale School of Management Working Papers ysm427, Yale School of Management.
  5. 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.
  6. 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.
  7. Jansson, Michael, 2002. "Consistent Covariance Matrix Estimation For Linear Processes," Econometric Theory, Cambridge University Press, vol. 18(06), pages 1449-1459, December.
  8. Peter C.B. Phillips, 2004. "HAC Estimation by Automated Regression," Cowles Foundation Discussion Papers 1470, Cowles Foundation for Research in Economics, Yale University.
  9. Donald W.K. Andrews & Christopher J. Monahan, 1990. "An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator," Cowles Foundation Discussion Papers 942, Cowles Foundation for Research in Economics, Yale University.
  10. Wouter J. Den Haan & Andrew T. Levin, 1996. "A Practitioner's Guide to Robust Covariance Matrix Estimation," NBER Technical Working Papers 0197, National Bureau of Economic Research, Inc.
  11. Peter M Robinson & Carlos Velasco, 2000. "Edgeworth Expansions for Spectral Density Estimates and Studentized Sample Mean - (Now published in Economic Theory, 17 (2001), pp.497-539," STICERD - Econometrics Paper Series /2000/390, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  12. 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.
  13. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May.
  14. 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.
  15. Donggyu Sul & Peter C.B. Phillips & Choi, Chi-Young, 2003. "Prewhitening Bias in HAC Estimation," Cowles Foundation Discussion Papers 1436, Cowles Foundation for Research in Economics, Yale University.
  16. Phillips, P C B, 1980. "Finite Sample Theory and the Distributions of Alternative Estimators of the Marginal Propensity to Consume," Review of Economic Studies, Wiley Blackwell, vol. 47(1), pages 183-224, January.
  17. Jong, R.M. de & Davidson, J., 1996. "Consistency of Kernel Estimators of Heteroscedastic and Autocorrelated Covariance Matrices," Discussion Paper 1996-52, Tilburg University, Center for Economic Research.
  18. Peter M. Robinson & Carlos Velasco, 2000. "Edgeworth expansions for spectral density estimates and studentized sample mean," LSE Research Online Documents on Economics 2148, London School of Economics and Political Science, LSE Library.
  19. Michael Jansson, 2004. "The Error in Rejection Probability of Simple Autocorrelation Robust Tests," Econometrica, Econometric Society, vol. 72(3), pages 937-946, 05.
  20. Hansen, Bruce E, 1992. "Consistent Covariance Matrix Estimation for Dependent Heterogeneous Processes," Econometrica, Econometric Society, vol. 60(4), pages 967-72, July.
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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.

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