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Improved HAR Inference

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Author Info
Peter C.B. Phillips () (Cowles Foundation, Yale University)
Yixiao Sun (Dept. Economics, UCLA, San Diego)
Sainan Jin (Guanghua School of Management, Peking University)

Additional information is available for the following registered author(s):

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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Publisher Info
Paper provided by Cowles Foundation, 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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Phone: (203) 432-3702
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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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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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Find related papers by JEL classification:
C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Estimation
C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions
C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Michael Jansson, 2004. "The Error in Rejection Probability of Simple Autocorrelation Robust Tests," Econometrica, Econometric Society, vol. 72(3), pages 937-946, 05. [Downloadable!] (restricted)
  2. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May. [Downloadable!] (restricted)
    Other versions:
  3. Donggyu Sul & Peter C.B. Phillips & Choi, Chi-Young, 2003. "Prewhitening Bias in HAC Estimation," Cowles Foundation Discussion Papers 1436, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
  4. repec:cup:etheor:v:12:y:1996:i:2:p:331-46 is not listed on IDEAS
  5. 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. [Downloadable!]
  6. Phillips, P C B, 1980. "Finite Sample Theory and the Distributions of Alternative Estimators of the Marginal Propensity to Consume," Review of Economic Studies, Blackwell Publishing, vol. 47(1), pages 183-224, January. [Downloadable!] (restricted)
  7. 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, Yale University. [Downloadable!]
    Other versions:
  8. 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. [Downloadable!]
  9. 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.
  10. 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. [Downloadable!]
  11. Andrews, Donald W K & Monahan, J Christopher, 1992. "An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator," Econometrica, Econometric Society, vol. 60(4), pages 953-66, July. [Downloadable!] (restricted)
    Other versions:
  12. Jansson, Michael, 2002. "Consistent Covariance Matrix Estimation For Linear Processes," Econometric Theory, Cambridge University Press, vol. 18(06), pages 1449-1459, December. [Downloadable!]
  13. Peter C. B. Phillips & Yixiao Sun & Sainan Jin, 2003. "Consistent HAC Estimation and Robust Regression Testing Using Sharp Origin Kernels with No Truncation," University of California at San Diego, Economics Working Paper Series 2003-05, Department of Economics, UC San Diego. [Downloadable!]
    Other versions:
  14. Wouter J. den Haan & Andrew Levin, 1996. "A Practitioner's Guide to Robust Covariance Matrix Estimation," University of California at San Diego, Economics Working Paper Series 96-17, Department of Economics, UC San Diego. [Downloadable!]
    Other versions:
  15. Whitney K. Newey & Kenneth D. West, 1986. "A Simple, Positive Semi-Definite, Heteroskedasticity and AutocorrelationConsistent Covariance Matrix," NBER Technical Working Papers 0055, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    Other versions:
  16. 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.
    Other versions:
  17. 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. [Downloadable!]
  18. Yixiao Sun, 2003. "Estimation of the Long-run Average Relationship in Nonstationary Panel Time Series," University of California at San Diego, Economics Working Paper Series 2003-06, Department of Economics, UC San Diego. [Downloadable!]
  19. Hansen, Bruce E, 1992. "Consistent Covariance Matrix Estimation for Dependent Heterogeneous Processes," Econometrica, Econometric Society, vol. 60(4), pages 967-72, July. [Downloadable!] (restricted)
  20. Peter C.B. Phillips, 1990. "Operational Algebra and Regression t-Tests," Cowles Foundation Discussion Papers 948, Cowles Foundation, Yale University. [Downloadable!]
Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Peter Phillips & Yixiao Sun & Sainan Jin, 2004. "Spectral Density Estimation and Robust Hypothesis Testing Using Steep Origin Kernels Without Truncation," University of California at San Diego, Economics Working Paper Series 2004-15, Department of Economics, UC San Diego. [Downloadable!]
    Other versions:
  2. 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," Documents de Travail 194, Banque de France. [Downloadable!]
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