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Two estimators of the long-run variance

Author

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  • K Abadir
  • W Distaso
  • L Giraitis

Abstract

We deal with the important question of estimating the long-run variance of a stationary sequence. We derive the asymptotic properties of a generalized Newey-West type of estimator in the case of a linear I(d) process. The results show that the bias and asymptotic distribution of the generalized Newey-West estimator depend on the memory parameter d. If the series has long memory then the estimator might even have a non-Gaussian limit distribution. The optimal bandwidth parameter q minimising MSE is derived. Theoretical results explain the large bias observed in simulation studies with arbitrarily chosen q. An alternative estimator is suggested. It has an asymptotic Gaussian distribution and bias which do not depend on d. The estimator is easy to apply and can be used to construct confidence intervals. Simulations confirm the theoretical findings.

Suggested Citation

  • K Abadir & W Distaso & L Giraitis, "undated". "Two estimators of the long-run variance," Discussion Papers 05/19, Department of Economics, University of York.
    • Handle: RePEc:yor:yorken:05/19
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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. 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).
    4. 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.
    5. 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.
    6. Leïla Nouira & Mohamed Boutahar & Vêlayoudom Marimoutou, 2009. "The effect of tapering on the semiparametric estimators for nonstationary long memory processes," Statistical Papers, Springer, vol. 50(2), pages 225-248, March.
    7. 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.
    8. 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.
    9. 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.
    10. Nasari, Masoud M. & Ould-Haye, Mohamedou, 2021. "A consistent estimator for skewness of partial sums of dependent data," Statistics & Probability Letters, Elsevier, vol. 171(C).
    11. Karim M. Abadir & Gabriel Talmain, 2008. "Macro and Financial Markets: The Memory of an Elephant?," Working Paper series 17_08, Rimini Centre for Economic Analysis.
    12. 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.
    13. Becker, Janis & Leschinski, Christian, 2018. "The Bias of Realized Volatility," Hannover Economic Papers (HEP) dp-642, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    14. 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.
    15. 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.
    16. 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.

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