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Robust covariance matrix estimation : 'HAC' estimates with long memory/antipersistence correction

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  • Robinson, P. M.

Abstract

Smoothed nonparametric estimates of the spectral density matrix at zero frequency have been widely used in econometric inference, because they can consistently estimate the covariance matrix of a partial sum of a possibly dependent vector process. When elements of the vector process exhibit long memory or antipersistence such estimates are inconsistent. We propose estimates which are still consistent in such circumstances, adapting automatically to memory parameters that can vary across the vector and be unknown.

Suggested Citation

  • Robinson, P. M., 2005. "Robust covariance matrix estimation : 'HAC' estimates with long memory/antipersistence correction," LSE Research Online Documents on Economics 323, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:323
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    File URL: http://eprints.lse.ac.uk/323/
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    Cited by:

    1. Yuanhua Feng & Jan Beran, 2013. "Optimal convergence rates in non-parametric regression with fractional time series errors," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(1), pages 30-39, January.
    2. Ulrich K. Müller & Mark W. Watson, 2021. "Spatial Correlation Robust Inference," Working Papers 2021-61, Princeton University. Economics Department..
    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. Manabu Asai & Michael McAleer, 2017. "A fractionally integrated Wishart stochastic volatility model," Econometric Reviews, Taylor & Francis Journals, vol. 36(1-3), pages 42-59, March.
    5. Ergemen, Yunus Emre & Velasco, Carlos, 2017. "Estimation of fractionally integrated panels with fixed effects and cross-section dependence," Journal of Econometrics, Elsevier, vol. 196(2), pages 248-258.
    6. Gupta, Abhimanyu, 2018. "Autoregressive spatial spectral estimates," Journal of Econometrics, Elsevier, vol. 203(1), pages 80-95.
    7. 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).
    8. 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.
    9. Ulrich K. Müller & Mark W. Watson, 2022. "Spatial Correlation Robust Inference," Econometrica, Econometric Society, vol. 90(6), pages 2901-2935, November.
    10. Peter M Robinson, 2007. "Multiple Local Whittle Estimation in StationarySystems," STICERD - Econometrics Paper Series 525, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    11. 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.
    12. Degui Li & Peter M. Robinson & Han Lin Shang, 2021. "Local Whittle estimation of long‐range dependence for functional time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 42(5-6), pages 685-695, September.
    13. Robinson, Peter M., 2007. "Multiple local whittle estimation in stationary systems," LSE Research Online Documents on Economics 4436, London School of Economics and Political Science, LSE Library.
    14. 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.
    15. Wenger, Kai & Leschinski, Christian & Sibbertsen, Philipp, 2018. "A simple test on structural change in long-memory time series," Economics Letters, Elsevier, vol. 163(C), pages 90-94.
    16. Ulrich K. Muller & Mark W. Watson, 2021. "Spatial Correlation Robust Inference," Papers 2102.09353, arXiv.org.
    17. Fu, Hui & Chen, Wenting & He, Xin-Jiang, 2018. "On a class of estimation and test for long memory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 906-920.
    18. Gannaz, Irène, 2023. "Asymptotic normality of wavelet covariances and multivariate wavelet Whittle estimators," Stochastic Processes and their Applications, Elsevier, vol. 155(C), pages 485-534.
    19. 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.
    20. 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.
    21. Robinson, P.M., 2011. "Asymptotic theory for nonparametric regression with spatial data," Journal of Econometrics, Elsevier, vol. 165(1), pages 5-19.
    22. Sophie Achard & Irène Gannaz, 2016. "Multivariate Wavelet Whittle Estimation in Long-range Dependence," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(4), pages 476-512, July.
    23. Hualde, Javier & Iacone, Fabrizio, 2017. "Revisiting inflation in the euro area allowing for long memory," Economics Letters, Elsevier, vol. 156(C), pages 145-150.

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    JEL classification:

    • J1 - Labor and Demographic Economics - - Demographic Economics

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