IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v167y2020ics0167715220302054.html
   My bibliography  Save this article

On the empirical process of tempered moving averages

Author

Listed:
  • Beran, Jan
  • Sabzikar, Farzad
  • Surgailis, Donatas
  • Telkmann, Klaus

Abstract

We consider asymptotic properties of the empirical process of tempered moving average with memory parameter d∈[0,1∕2) and tempering parameter λN→0, centered by the marginal distribution function of the corresponding untempered stationary process. We prove that under long memory (0

Suggested Citation

  • Beran, Jan & Sabzikar, Farzad & Surgailis, Donatas & Telkmann, Klaus, 2020. "On the empirical process of tempered moving averages," Statistics & Probability Letters, Elsevier, vol. 167(C).
    • Handle: RePEc:eee:stapro:v:167:y:2020:i:c:s0167715220302054
    DOI: 10.1016/j.spl.2020.108902
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715220302054
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2020.108902?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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. 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).
    2. Sabzikar, Farzad & Surgailis, Donatas, 2018. "Tempered fractional Brownian and stable motions of second kind," Statistics & Probability Letters, Elsevier, vol. 132(C), pages 17-27.
    3. Giraitis, Liudas & Koul, Hira L. & Surgailis, Donatas, 1996. "Asymptotic normality of regression estimators with long memory errors," Statistics & Probability Letters, Elsevier, vol. 29(4), pages 317-335, September.
    4. Sabzikar, Farzad & Surgailis, Donatas, 2018. "Invariance principles for tempered fractionally integrated processes," Stochastic Processes and their Applications, Elsevier, vol. 128(10), pages 3419-3438.
    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. Giraitis, Liudas & Kokoszka, Piotr & Leipus, Remigijus, 2000. "Stationary Arch Models: Dependence Structure And Central Limit Theorem," Econometric Theory, Cambridge University Press, vol. 16(1), pages 3-22, February.
    7. C. W. J. Granger & Roselyne Joyeux, 1980. "An Introduction To Long‐Memory Time Series Models And Fractional Differencing," Journal of Time Series Analysis, Wiley Blackwell, vol. 1(1), pages 15-29, January.
    Full references (including those not matched with items on IDEAS)

    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. Sabzikar, Farzad & Surgailis, Donatas, 2018. "Invariance principles for tempered fractionally integrated processes," Stochastic Processes and their Applications, Elsevier, vol. 128(10), pages 3419-3438.
    2. Kris Brabanter & Farzad Sabzikar, 2021. "Asymptotic theory for regression models with fractional local to unity root errors," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(7), pages 997-1024, October.
    3. Farzad Sabzikar & Qiying Wang & Peter C.B. Phillips, 2018. "Asymptotic Theory for Near Integrated Process Driven by Tempered Linear Process," Cowles Foundation Discussion Papers 2131, Cowles Foundation for Research in Economics, Yale University.
    4. Kunal Saha & Vinodh Madhavan & Chandrashekhar G. R. & David McMillan, 2020. "Pitfalls in long memory research," Cogent Economics & Finance, Taylor & Francis Journals, vol. 8(1), pages 1733280-173, January.
    5. Chaker Aloui & Duc Khuong Nguyen, 2014. "On the detection of extreme movements and persistent behaviour in Mediterranean stock markets: a wavelet-based approach," Applied Economics, Taylor & Francis Journals, vol. 46(22), pages 2611-2622, August.
    6. Ding, Liang & Luo, Yi & Lin, Yan & Huang, Yirong, 2021. "Revisiting the relations between Hurst exponent and fractional differencing parameter for long memory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 566(C).
    7. Fu, Hui, 2012. "On a Class of Estimation and Test for Long Memory," MPRA Paper 47978, University Library of Munich, Germany.
    8. D. Ventosa-Santaulària, 2009. "Spurious Regression," Journal of Probability and Statistics, Hindawi, vol. 2009, pages 1-27, August.
    9. Farzad Sabzikar & Piotr Kokoszka, 2023. "Tempered functional time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 44(3), pages 280-293, May.
    10. Kwan, Wilson & Li, Wai Keung & Li, Guodong, 2012. "On the estimation and diagnostic checking of the ARFIMA–HYGARCH model," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3632-3644.
    11. Lujia Bai & Weichi Wu, 2021. "Detecting long-range dependence for time-varying linear models," Papers 2110.08089, arXiv.org, revised Mar 2023.
    12. Ranjit Kumar Paul & Bishal Gurung & Sandipan Samanta, 2015. "Analyzing the Effect of Dual Long Memory Process in Forecasting Agricultural Prices in Different Markets of India," International Journal of Empirical Finance, Research Academy of Social Sciences, vol. 4(4), pages 235-249.
    13. Robert A. Connolly & Z. Nuray Güner & Kenneth N. Hightower, 2007. "Evidence on the Extent and Potential Sources of Long Memory in U.S. Treasury Security Returns and Yields," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(2‐3), pages 689-702, March.
    14. TEYSSIERE, Gilles, 2003. "Interaction models for common long-range dependence in asset price volatilities," LIDAM Discussion Papers CORE 2003026, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    15. Al-Shboul, Mohammad & Alsharari, Nizar, 2019. "The dynamic behavior of evolving efficiency: Evidence from the UAE stock markets," The Quarterly Review of Economics and Finance, Elsevier, vol. 73(C), pages 119-135.
    16. Berkes, István & Hörmann, Siegfried & Horváth, Lajos, 2008. "The functional central limit theorem for a family of GARCH observations with applications," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2725-2730, November.
    17. Cho, Cheol-Keun & Amsler, Christine & Schmidt, Peter, 2015. "A test of the null of integer integration against the alternative of fractional integration," Journal of Econometrics, Elsevier, vol. 187(1), pages 217-237.
    18. 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.
    19. Sabzikar, Farzad & Wang, Qiying & Phillips, Peter C.B., 2020. "Asymptotic theory for near integrated processes driven by tempered linear processes," Journal of Econometrics, Elsevier, vol. 216(1), pages 192-202.
    20. Beran, Jan, 2006. "On location estimation for LARCH processes," Journal of Multivariate Analysis, Elsevier, vol. 97(8), pages 1766-1782, September.

    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:stapro:v:167:y:2020:i:c:s0167715220302054. 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/622892/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.