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Inferences from parametric and non-parametric covariance matrix estimation procedures

  • Wouter J. den Haan
  • Andrew T. Levin

We propose a parametric spectral estimation procedure for contructing heteroskedasticity and autocorrelation consistent (HAC) covariance matrices. We establish the consistency of this procedure under very general conditions similar to those considered in previous research. We also perform Monte Carlo simulations to evaluate the performance of this procedure in drawing reliable inferences from linear regression estimates. These simulations indicate that the parametric estimator matches, and in some cases greatly exceeds, the performance of the prewhitened kernel estimator proposed by Andrews and Monahan (1992). These simulations also illustrate the inherent limitations of non-parametric HAC covariance matrix estimation procedures, and highlight the advantages of explicitly modeling the temporal properties of the error terms.

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Paper provided by Board of Governors of the Federal Reserve System (U.S.) in its series International Finance Discussion Papers with number 504.

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Date of creation: 1995
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Handle: RePEc:fip:fedgif:504
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  1. Donald W.K. Andrews, 1988. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Cowles Foundation Discussion Papers 877R, Cowles Foundation for Research in Economics, Yale University, revised Jul 1989.
  2. Perron, Pierre & Ng, Serena, 1996. "Useful Modifications to Some Unit Root Tests with Dependent Errors and Their Local Asymptotic Properties," Review of Economic Studies, Wiley Blackwell, vol. 63(3), pages 435-63, July.
  3. Fama, Eugene F & French, Kenneth R, 1988. "Permanent and Temporary Components of Stock Prices," Journal of Political Economy, University of Chicago Press, vol. 96(2), pages 246-73, April.
  4. 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.
  5. 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.
  6. Kenneth D. West & Whitney K. Newey, 1995. "Automatic Lag Selection in Covariance Matrix Estimation," NBER Technical Working Papers 0144, National Bureau of Economic Research, Inc.
  7. Lawrence J. Christiano & Wouter Den Haan, 1995. "Small sample properties of GMM for business cycle analysis," Staff Report 199, Federal Reserve Bank of Minneapolis.
  8. Athreya, Krishna B. & Pantula, Sastry G., 1986. "A note on strong mixing of ARMA processes," Statistics & Probability Letters, Elsevier, vol. 4(4), pages 187-190, June.
  9. P. M. Robinson, 1998. "Inference-Without-Smoothing in the Presence of Nonparametric Autocorrelation," Econometrica, Econometric Society, vol. 66(5), pages 1163-1182, September.
  10. Kenneth D. West, 1995. "Another Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator," NBER Technical Working Papers 0183, National Bureau of Economic Research, Inc.
  11. James H. Stock & Mark W. Watson, 1991. "A simple estimator of cointegrating vectors in higher order integrated systems," Working Paper Series, Macroeconomic Issues 91-3, Federal Reserve Bank of Chicago.
  12. Lars Peter Hansen & Thomas J. Sargent, 1979. "Formulating and estimating dynamic linear rational expectations models," Working Papers 127, Federal Reserve Bank of Minneapolis.
  13. Ng, S. & Perron, P., 1994. "Unit Root Tests ARMA Models with Data Dependent Methods for the Selection of the Truncation Lag," Cahiers de recherche 9423, Centre interuniversitaire de recherche en ├ęconomie quantitative, CIREQ.
  14. Robinson, P M, 1991. "Automatic Frequency Domain Inference on Semiparametric and Nonparametric Models," Econometrica, Econometric Society, vol. 59(5), pages 1329-63, September.
  15. Craig Burnside & Martin Eichenbaum, 1994. "Small Sample Properties of Generalized Method of Moments Based Wald Tests," NBER Technical Working Papers 0155, National Bureau of Economic Research, Inc.
  16. Andrews, Donald W K & Chen, Hong-Yuan, 1994. "Approximately Median-Unbiased Estimation of Autoregressive Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(2), pages 187-204, April.
  17. Hansen, Bruce E, 1992. "Consistent Covariance Matrix Estimation for Dependent Heterogeneous Processes," Econometrica, Econometric Society, vol. 60(4), pages 967-72, July.
  18. 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.
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