IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v80y1999i1p1-24.html
   My bibliography  Save this article

Variance-type estimation of long memory

Author

Listed:
  • Giraitis, Liudas
  • Robinson, Peter M.
  • Surgailis, Donatas

Abstract

The aggregation procedure when a sample of length N is divided into blocks of length m=o(N), m-->[infinity] and observations in each block are replaced by their sample mean, is widely used in statistical inference. Taqqu et al. (1995, Fractals, 3, 785-798), and Teverovsky and Taqqu (1997, J. Time Ser. Anal., 18, 279-304) introduced an aggregated variance estimator of the long-memory parameter of a stationary sequence with long range dependence and studied its empirical performance. With respect to autocovariance structure and marginal distribution, the aggregated series is closer to Gaussian fractional noise than the initial series. However, the variance type estimator based on aggregated data is seriously biased. A refined estimator, which employs least-squares regression across varying levels of aggregation, has much smaller bias, permitting deriviation of limiting distributional properties of suitably centered estimates, as well as of a minimum-mean squared error choice of bandwidth m. The results vary considerably with the actual value of the memory parameter.

Suggested Citation

  • Giraitis, Liudas & Robinson, Peter M. & Surgailis, Donatas, 1999. "Variance-type estimation of long memory," Stochastic Processes and their Applications, Elsevier, vol. 80(1), pages 1-24, March.
    • Handle: RePEc:eee:spapps:v:80:y:1999:i:1:p:1-24
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(98)00062-3
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Andrew Harvey (ed.), 1994. "Time Series," Books, Edward Elgar Publishing, volume 0, number 599.
    2. Breuer, Péter & Major, Péter, 1983. "Central limit theorems for non-linear functionals of Gaussian fields," Journal of Multivariate Analysis, Elsevier, vol. 13(3), pages 425-441, September.
    3. Lobato, I. & Robinson, P. M., 1996. "Averaged periodogram estimation of long memory," Journal of Econometrics, Elsevier, vol. 73(1), pages 303-324, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Ting Zhang & Hwai-Chung Ho & Martin Wendler & Wei Biao Wu, 2013. "Block Sampling under Strong Dependence," Papers 1312.5807, arXiv.org.
    2. Jennifer Brown & Les Oxley & William Rea & Marco Reale, 2008. "The Empirical Properties of Some Popular Estimators of Long Memory Processes," Working Papers in Economics 08/13, University of Canterbury, Department of Economics and Finance.
    3. Kang, Taegyu & Kim, Young Min & Im, Jongho, 2021. "A note on stationary bootstrap variance estimator under long-range dependence," Statistics & Probability Letters, Elsevier, vol. 169(C).
    4. Rea, William & Oxley, Les & Reale, Marco & Brown, Jennifer, 2013. "Not all estimators are born equal: The empirical properties of some estimators of long memory," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 93(C), pages 29-42.
    5. Dima, Bogdan & Dima, Ştefana Maria, 2017. "Mutual information and persistence in the stochastic volatility of market returns: An emergent market example," International Review of Economics & Finance, Elsevier, vol. 51(C), pages 36-59.
    6. Marco Dozzi & Yuliya Mishura & Georgiy Shevchenko, 2015. "Asymptotic behavior of mixed power variations and statistical estimation in mixed models," Statistical Inference for Stochastic Processes, Springer, vol. 18(2), pages 151-175, July.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Liudas Giraitis & Peter M Robinson, 1998. "Variance-Type Estimation of Long Memory - (Now published in Stochastic Processes and their Applications, 29 (1999), pp.1-24.)," STICERD - Econometrics Paper Series 363, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    2. Giraitis, Liudas & Robinson, Peter M., 1998. "Variance-type estimation of long memory," LSE Research Online Documents on Economics 2327, London School of Economics and Political Science, LSE Library.
    3. Kerstin Gärtner & Mark Podolskij, 2014. "On non-standard limits of Brownian semi-stationary," CREATES Research Papers 2014-50, Department of Economics and Business Economics, Aarhus University.
    4. Matthew Higgins & Daniel Levy & Andrew T. Young, 2003. "Growth and Convergence across the US: Evidence from County-Level Data," Working Papers 2003-03, Bar-Ilan University, Department of Economics.
    5. Ørregaard Nielsen, Morten, 2004. "Local empirical spectral measure of multivariate processes with long range dependence," Stochastic Processes and their Applications, Elsevier, vol. 109(1), pages 145-166, January.
    6. Catherine Kyrtsou & Michel Terraza, 2003. "Is it Possible to Study Chaotic and ARCH Behaviour Jointly? Application of a Noisy Mackey–Glass Equation with Heteroskedastic Errors to the Paris Stock Exchange Returns Series," Computational Economics, Springer;Society for Computational Economics, vol. 21(3), pages 257-276, June.
    7. Surgailis, Donatas & Teyssière, Gilles & Vaiciulis, Marijus, 2008. "The increment ratio statistic," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 510-541, March.
    8. Bai, Shuyang & Taqqu, Murad S. & Zhang, Ting, 2016. "A unified approach to self-normalized block sampling," Stochastic Processes and their Applications, Elsevier, vol. 126(8), pages 2465-2493.
    9. Shuyang Bai & Murad S. Taqqu, 2013. "Multivariate Limit Theorems In The Context Of Long-Range Dependence," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(6), pages 717-743, November.
    10. Christiane Baumeister & James D. Hamilton, 2015. "Sign Restrictions, Structural Vector Autoregressions, and Useful Prior Information," Econometrica, Econometric Society, vol. 83(5), pages 1963-1999, September.
    11. Claudio Morana & Andrea Beltratti, 2006. "Structural breaks and common factors in the volatility of the Fama-French factor portfolios," Applied Financial Economics, Taylor & Francis Journals, vol. 16(14), pages 1059-1073.
    12. Thierry Chauveau & Sylvain Friederich & Jérôme Héricourt & Emmanuel Jurczenko & Catherine Lubochinsky & Bertrand Maillet & Christophe Moussu & Bogdan Négréa & Hélène Raymond-Feingold, 2004. "La volatilité des marchés augmente-t-elle ?," Revue d'Économie Financière, Programme National Persée, vol. 74(1), pages 17-44.
    13. Brannas, Kurt, 1995. "Prediction and control for a time-series count data model," International Journal of Forecasting, Elsevier, vol. 11(2), pages 263-270, June.
    14. Miguel A. Arcones, 1999. "The Law of the Iterated Logarithm over a Stationary Gaussian Sequence of Random Vectors," Journal of Theoretical Probability, Springer, vol. 12(3), pages 615-641, July.
    15. Hualde, J. & Robinson, P.M., 2010. "Semiparametric inference in multivariate fractionally cointegrated systems," Journal of Econometrics, Elsevier, vol. 157(2), pages 492-511, August.
    16. Robinson, Peter M., 2004. "Robust covariance matrix estimation : HAC estimates with long memory/antipersistence correction," LSE Research Online Documents on Economics 2157, London School of Economics and Political Science, LSE Library.
    17. Hamilton, James D. & Wu, Jing Cynthia, 2014. "Testable implications of affine term structure models," Journal of Econometrics, Elsevier, vol. 178(P2), pages 231-242.
    18. P. M. Robinson & M. Gerolimetto, 2006. "Instrumental variables estimation of stationary and non-stationary cointegrating regressions," Econometrics Journal, Royal Economic Society, vol. 9(2), pages 291-306, July.
    19. James D. Hamilton, 2009. "Understanding Crude Oil Prices," The Energy Journal, International Association for Energy Economics, vol. 0(Number 2), pages 179-206.
    20. James D. Hamilton, 2008. "Assessing monetary policy effects using daily federal funds futures contracts," Review, Federal Reserve Bank of St. Louis, vol. 90(Jul), pages 377-394.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:spapps:v:80:y:1999:i:1:p:1-24. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.