IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v119y2009i9p3006-3041.html
   My bibliography  Save this article

Central limit theorems for arrays of decimated linear processes

Author

Listed:
  • Roueff, F.
  • Taqqu, M.S.

Abstract

Linear processes are defined as a discrete-time convolution between a kernel and an infinite sequence of i.i.d. random variables. We modify this convolution by introducing decimation, that is, by stretching time accordingly. We then establish central limit theorems for arrays of squares of such decimated processes. These theorems are used to obtain the asymptotic behavior of estimators of the spectral density at specific frequencies. Another application, treated elsewhere, concerns the estimation of the long-memory parameter in time series, using wavelets.

Suggested Citation

  • Roueff, F. & Taqqu, M.S., 2009. "Central limit theorems for arrays of decimated linear processes," Stochastic Processes and their Applications, Elsevier, vol. 119(9), pages 3006-3041, September.
    • Handle: RePEc:eee:spapps:v:119:y:2009:i:9:p:3006-3041
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(09)00073-8
    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. E. Moulines & F. Roueff & M. S. Taqqu, 2007. "On the Spectral Density of the Wavelet Coefficients of Long‐Memory Time Series with Application to the Log‐Regression Estimation of the Memory Parameter," Journal of Time Series Analysis, Wiley Blackwell, vol. 28(2), pages 155-187, March.
    2. Gabriel Lang & Philippe Soulier, 2000. "Convergence de mesures spectrales aléatoires et applications à des principes d'invariance," Statistical Inference for Stochastic Processes, Springer, vol. 3(1), pages 41-51, January.
    3. Bhansali, R.J. & Giraitis, L. & Kokoszka, P.S., 2007. "Approximations and limit theory for quadratic forms of linear processes," Stochastic Processes and their Applications, Elsevier, vol. 117(1), pages 71-95, January.
    4. Faÿ, Gilles & Moulines, Eric & Roueff, François & Taqqu, Murad S., 2009. "Estimators of long-memory: Fourier versus wavelets," Journal of Econometrics, Elsevier, vol. 151(2), pages 159-177, August.
    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. 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.
    2. Roueff, François & von Sachs, Rainer, 2011. "Locally stationary long memory estimation," Stochastic Processes and their Applications, Elsevier, vol. 121(4), pages 813-844, April.
    3. F. Roueff & M. S. Taqqu, 2009. "Asymptotic normality of wavelet estimators of the memory parameter for linear processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(5), pages 534-558, September.

    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. 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.
    2. F. Roueff & M. S. Taqqu, 2009. "Asymptotic normality of wavelet estimators of the memory parameter for linear processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(5), pages 534-558, September.
    3. Roueff, François & von Sachs, Rainer, 2011. "Locally stationary long memory estimation," Stochastic Processes and their Applications, Elsevier, vol. 121(4), pages 813-844, April.
    4. Kei Nanamiya, 2014. "Modelling For The Wavelet Coefficients Of Arfima Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(4), pages 341-356, July.
    5. Dominique Guegan & Zhiping Lu & Beijia Zhu, 2012. "Comparaison of Several Estimation Procedures for Long Term Behavior," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00673934, HAL.
    6. Marie Busch & Philipp Sibbertsen, 2018. "An Overview of Modified Semiparametric Memory Estimation Methods," Econometrics, MDPI, vol. 6(1), pages 1-21, March.
    7. Jean-Christophe Breton & Jean-François Coeurjolly, 2012. "Confidence intervals for the Hurst parameter of a fractional Brownian motion based on finite sample size," Statistical Inference for Stochastic Processes, Springer, vol. 15(1), pages 1-26, April.
    8. Michis, Antonis A., 2014. "Time scale evaluation of economic forecasts," Economics Letters, Elsevier, vol. 123(3), pages 279-281.
    9. Anne Philippe & Donata Puplinskaite & Donatas Surgailis, 2014. "Contemporaneous Aggregation Of Triangular Array Of Random-Coefficient Ar(1) Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(1), pages 16-39, January.
    10. Barunik, Jozef & Barunikova, Michaela, 2015. "Revisiting the long memory dynamics of implied-realized volatility relation: A new evidence from wavelet band spectrum regression," FinMaP-Working Papers 43, Collaborative EU Project FinMaP - Financial Distortions and Macroeconomic Performance: Expectations, Constraints and Interaction of Agents.
    11. Cheung, Ying Lun, 2020. "Nonstationarity-extended Whittle estimation with discontinuity: A correction," Economics Letters, Elsevier, vol. 187(C).
    12. Baruník, Jozef & Kočenda, Evžen & Vácha, Lukáš, 2016. "Gold, oil, and stocks: Dynamic correlations," International Review of Economics & Finance, Elsevier, vol. 42(C), pages 186-201.
    13. Jozef Barunik & Michaela Barunikova, 2012. "Revisiting the fractional cointegrating dynamics of implied-realized volatility relation with wavelet band spectrum regression," Papers 1208.4831, arXiv.org, revised Feb 2013.
    14. Mynbayev, Kairat & Darkenbayeva, Gulsim, 2017. "Weak convergence of linear and quadratic forms and related statements on Lp-approximability," MPRA Paper 101686, University Library of Munich, Germany, revised Dec 2018.
    15. Baruník, Jozef & Hlínková, Michaela, 2016. "Revisiting the long memory dynamics of the implied–realized volatility relationship: New evidence from the wavelet regression," Economic Modelling, Elsevier, vol. 54(C), pages 503-514.
    16. Atchadé, Yves F. & Cattaneo, Matias D., 2014. "A martingale decomposition for quadratic forms of Markov chains (with applications)," Stochastic Processes and their Applications, Elsevier, vol. 124(1), pages 646-677.
    17. Antonis A. Michis, 2022. "Multiscale Partial Correlation Clustering of Stock Market Returns," JRFM, MDPI, vol. 15(1), pages 1-22, January.
    18. Faÿ, Gilles & Moulines, Eric & Roueff, François & Taqqu, Murad S., 2009. "Estimators of long-memory: Fourier versus wavelets," Journal of Econometrics, Elsevier, vol. 151(2), pages 159-177, August.
    19. Linyuan Li & Kewei Lu, 2013. "On rate-optimal nonparametric wavelet regression with long memory moving average errors," Statistical Inference for Stochastic Processes, Springer, vol. 16(2), pages 127-145, July.
    20. Yizao Wang, 2014. "An Invariance Principle for Fractional Brownian Sheets," Journal of Theoretical Probability, Springer, vol. 27(4), pages 1124-1139, December.

    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:119:y:2009:i:9:p:3006-3041. 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.