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Two estimators of the long-run variance: Beyond short memory

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Author Info

  • Abadir, Karim M.
  • Distaso, Walter
  • Giraitis, Liudas

Abstract

This paper deals with the estimation of the long-run variance of a stationary sequence. We extend the usual Bartlett-kernel heteroskedasticity and autocorrelation consistent (HAC) estimator to deal with long memory and antipersistence. We then derive asymptotic expansions for this estimator and the memory and autocorrelation consistent (MAC) estimator introduced by Robinson [Robinson, P. M., 2005. Robust covariance matrix estimation: HAC estimates with long memory/antipersistence correction. Econometric Theory 21, 171-180]. We offer a theoretical explanation for the sensitivity of HAC to the bandwidth choice, a feature which has been observed in the special case of short memory. Using these analytical results, we determine the MSE-optimal bandwidth rates for each estimator. We analyze by simulations the finite-sample performance of HAC and MAC estimators, and the coverage probabilities for the studentized sample mean, giving practical recommendations for the choice of bandwidths.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 150 (2009)
Issue (Month): 1 (May)
Pages: 56-70

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Handle: RePEc:eee:econom:v:150:y:2009:i:1:p:56-70

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Web page: http://www.elsevier.com/locate/jeconom

Related research

Keywords: Long-run variance Long memory Heteroskedasticity and autocorrelation consistent (HAC) estimator Memory and autocorrelation consistent (MAC) estimator;

References

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  1. Velasco, Carlos & Robinson, Peter M., . "Edgeworth expansions for spectral density estimates and studentized sample mean," Open Access publications from Universidad Carlos III de Madrid info:hdl:10016/4373, Universidad Carlos III de Madrid.
  2. Newey, Whitney K & West, Kenneth D, 1987. "A Simple, Positive Semi-definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix," Econometrica, Econometric Society, vol. 55(3), pages 703-08, May.
  3. Giraitis, Liudas & Kokoszka, Piotr & Leipus, Remigijus & Teyssiere, Gilles, 2003. "Rescaled variance and related tests for long memory in volatility and levels," Journal of Econometrics, Elsevier, vol. 112(2), pages 265-294, February.
  4. Violetta Dalla & Liudas Giraitis & Javier Hidalgo, 2006. "Consistent estimation of the memory parameterfor nonlinear time series," STICERD - Econometrics Paper Series /2006/497, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  5. Abadir, Karim & Talmain, Gabriel, 2002. "Aggregation, Persistence and Volatility in a Macro Model," Review of Economic Studies, Wiley Blackwell, vol. 69(4), pages 749-79, October.
  6. Giuseppe Cavaliere, 2001. "Testing the unit root hypothesis using generalized range statistics," Econometrics Journal, Royal Economic Society, vol. 4(1), pages 39.
  7. Francis X. Diebold & Glenn D. Rudebusch, 1988. "Long memory and persistence in aggregate output," Finance and Economics Discussion Series 7, Board of Governors of the Federal Reserve System (U.S.).
  8. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-38, May.
  9. Robinson, P. M., 2005. "Robust covariance matrix estimation : 'HAC' estimates with long memory/antipersistence correction," Open Access publications from London School of Economics and Political Science http://eprints.lse.ac.uk/, London School of Economics and Political Science.
  10. Chambers, Marcus J, 1998. "Long Memory and Aggregation in Macroeconomic Time Series," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 1053-72, November.
  11. Gil-Alana, L. A. & Robinson, P. M., 1997. "Testing of unit root and other nonstationary hypotheses in macroeconomic time series," Journal of Econometrics, Elsevier, vol. 80(2), pages 241-268, October.
  12. Abadir, Karim M. & Distaso, Walter & Giraitis, Liudas, 2007. "Nonstationarity-extended local Whittle estimation," Journal of Econometrics, Elsevier, vol. 141(2), pages 1353-1384, December.
  13. Robinson, P.M., 2005. "Robust Covariance Matrix Estimation: Hac Estimates With Long Memory/Antipersistence Correction," Econometric Theory, Cambridge University Press, vol. 21(01), pages 171-180, February.
  14. 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.
  15. Baillie, R.T. & Bollerslev, T., 1993. "Cointegration, Fractional Cointegration, and Exchange RAte Dynamics," Papers 9103, Michigan State - Econometrics and Economic Theory.
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Cited by:
  1. Lavancier, Frédéric & Philippe, Anne & Surgailis, Donatas, 2010. "A two-sample test for comparison of long memory parameters," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 2118-2136, October.

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