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

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  • 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.

Suggested Citation

  • Abadir, Karim M. & Distaso, Walter & Giraitis, Liudas, 2009. "Two estimators of the long-run variance: Beyond short memory," Journal of Econometrics, Elsevier, vol. 150(1), pages 56-70, May.
    • Handle: RePEc:eee:econom:v:150:y:2009:i:1:p:56-70
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    1. Velasco, Carlos & Robinson, Peter M., 2001. "Edgeworth Expansions For Spectral Density Estimates And Studentized Sample Mean," Econometric Theory, Cambridge University Press, vol. 17(3), pages 497-539, June.
    2. Karim M. Abadir & A. M. Robert Taylor, 1999. "On the Definitions of (Co‐)integration," Journal of Time Series Analysis, Wiley Blackwell, vol. 20(2), pages 129-137, March.
    3. 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.
    4. Baillie, Richard T & Bollerslev, Tim, 1994. "Cointegration, Fractional Cointegration, and Exchange Rate Dynamics," Journal of Finance, American Finance Association, vol. 49(2), pages 737-745, June.
    5. 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.
    6. Giuseppe Cavaliere, 2001. "Testing the unit root hypothesis using generalized range statistics," Econometrics Journal, Royal Economic Society, vol. 4(1), pages 1-39.
    7. Violetta Dalla & Liudas Giraitis & Javier Hidalgo, 2006. "Consistent estimation of the memory parameter for nonlinear time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(2), pages 211-251, March.
    8. Dalla, Violetta & Giraitis, Liudas & Hidalgo, Javier, 2006. "Consistent estimation of the memory parameter for nonlinear time series," LSE Research Online Documents on Economics 6813, London School of Economics and Political Science, LSE Library.
    9. R J Bhansali & L Giraitis & P Kokoszka, "undated". "Decomposition and asymptotic properties of quadratic forms in linear variables," Discussion Papers 05/18, Department of Economics, University of York.
    10. 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.
    11. GIRAITIS, Liudas & KOKOSZKA, Piotr & LEIPUS, Remigijus & TEYSSIÈRE, Gilles, 2003. "Rescaled variance and related tests for long memory in volatility and levels," LIDAM Reprints CORE 1594, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    12. Diebold, Francis X. & Rudebusch, Glenn D., 1989. "Long memory and persistence in aggregate output," Journal of Monetary Economics, Elsevier, vol. 24(2), pages 189-209, September.
    13. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
    14. 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 1053-1072, November.
    15. Abadir, Karim M. & Distaso, Walter & Giraitis, Liudas, 2007. "Nonstationarity-extended local Whittle estimation," Journal of Econometrics, Elsevier, vol. 141(2), pages 1353-1384, December.
    16. Karim Abadir & Gabriel Talmain, 2002. "Aggregation, Persistence and Volatility in a Macro Model," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 69(4), pages 749-779.
    17. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 33(1), pages 125-132.
    18. Robinson, P.M., 2005. "Robust Covariance Matrix Estimation: Hac Estimates With Long Memory/Antipersistence Correction," Econometric Theory, Cambridge University Press, vol. 21(1), pages 171-180, February.
    19. Violetta Dalla & Liudas Giraitis & Javier Hidalgo, 2006. "Consistent estimation of the memory parameterfor nonlinear time series," STICERD - Econometrics Paper Series 497, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
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    2. Mohamedou Ould Haye & Anne Philippe & Caroline Robet, 2024. "Inference for continuous-time long memory randomly sampled processes," Statistical Papers, Springer, vol. 65(5), pages 3111-3134, July.
    3. Kruse, Robinson & Leschinski, Christian & Will, Michael, 2016. "Comparing Predictive Accuracy under Long Memory - With an Application to Volatility Forecasting," Hannover Economic Papers (HEP) dp-571, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    4. Jannik Kreye & Philipp Sibbertsen, 2024. "Testing for a Forecast Accuracy Breakdown under Long Memory," Papers 2409.07087, arXiv.org.
    5. Qunyong Wang & Na Wu, 2012. "Long-run covariance and its applications in cointegration regression," Stata Journal, StataCorp LP, vol. 12(3), pages 525-542, September.
    6. Becker, Janis & Leschinski, Christian, 2018. "The Bias of Realized Volatility," Hannover Economic Papers (HEP) dp-642, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    7. McElroy, Tucker & Politis, Dimitris N., 2013. "Distribution theory for the studentized mean for long, short, and negative memory time series," Journal of Econometrics, Elsevier, vol. 177(1), pages 60-74.
    8. 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.
    9. Wingert, Simon & Mboya, Mwasi Paza & Sibbertsen, Philipp, 2020. "Distinguishing between breaks in the mean and breaks in persistence under long memory," Economics Letters, Elsevier, vol. 193(C).
    10. Fu, Hui, 2012. "On a Class of Estimation and Test for Long Memory," MPRA Paper 47978, University Library of Munich, Germany.
    11. Masoud M. Nasari & Mohamedou Ould-Haye, 2022. "Confidence intervals with higher accuracy for short and long-memory linear processes," Statistical Papers, Springer, vol. 63(4), pages 1187-1220, August.
    12. Zhihao Xu & Clifford M. Hurvich, 2021. "A Unified Frequency Domain Cross-Validatory Approach to HAC Standard Error Estimation," Papers 2108.06093, arXiv.org, revised Jun 2023.
    13. Hirukawa, Masayuki, 2023. "Robust Covariance Matrix Estimation in Time Series: A Review," Econometrics and Statistics, Elsevier, vol. 27(C), pages 36-61.
    14. Hualde, Javier & Iacone, Fabrizio, 2017. "Fixed bandwidth asymptotics for the studentized mean of fractionally integrated processes," Economics Letters, Elsevier, vol. 150(C), pages 39-43.
    15. Javier Hualde & Fabrizio Iacone, 2015. "Autocorrelation robust inference using the Daniell kernel with fixed bandwidth," Discussion Papers 15/14, Department of Economics, University of York.
    16. Hira Koul & Nao Mimoto & Donatas Surgailis, 2016. "A goodness-of-fit test for marginal distribution of linear random fields with long memory," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(2), pages 165-193, February.
    17. Violetta Dalla & Liudas Giraitis & Hira L. Koul, 2014. "Studentizing Weighted Sums Of Linear Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(2), pages 151-172, March.
    18. Daniel Borup & Bent Jesper Christensen & Yunus Emre Ergemen, 2019. "Assessing predictive accuracy in panel data models with long-range dependence," CREATES Research Papers 2019-04, Department of Economics and Business Economics, Aarhus University.
    19. Kai Wenger & Christian Leschinski & Philipp Sibbertsen, 2019. "Change-in-mean tests in long-memory time series: a review of recent developments," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 103(2), pages 237-256, June.

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