IDEAS home Printed from https://ideas.repec.org/a/spr/jotpro/v19y2006i3d10.1007_s10959-006-0029-y.html
   My bibliography  Save this article

On the Weak Invariance Principle for Stationary Sequences under Projective Criteria

Author

Listed:
  • Florence Merlevède

    (Université Paris VI, et C.N.R.S UMR 7599)

  • Magda Peligrad

    (University of Cincinnati)

Abstract

In this paper, we study the central limit theorem and its weak invariance principle for sums of a stationary sequence of random variables, via a martingale decomposition. Our conditions involve the conditional expectation of sums of random variables with respect to the distant past. The results contribute to the clarification of the central limit question for stationary sequences.

Suggested Citation

  • Florence Merlevède & Magda Peligrad, 2006. "On the Weak Invariance Principle for Stationary Sequences under Projective Criteria," Journal of Theoretical Probability, Springer, vol. 19(3), pages 647-689, December.
    • Handle: RePEc:spr:jotpro:v:19:y:2006:i:3:d:10.1007_s10959-006-0029-y
    DOI: 10.1007/s10959-006-0029-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10959-006-0029-y
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10959-006-0029-y?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. Shao, Qi-Man, 1993. "Almost sure invariance principles for mixing sequences of random variables," Stochastic Processes and their Applications, Elsevier, vol. 48(2), pages 319-334, November.
    2. Dedecker, Jérôme & Doukhan, Paul, 2003. "A new covariance inequality and applications," Stochastic Processes and their Applications, Elsevier, vol. 106(1), pages 63-80, July.
    3. Richard C. Bradley, 1997. "On Quantiles and the Central Limit Question for Strongly Mixing Sequences," Journal of Theoretical Probability, Springer, vol. 10(2), pages 507-555, April.
    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. Jérôme Dedecker & Florence Merlevède & Dalibor Volný, 2007. "On the Weak Invariance Principle for Non-Adapted Sequences under Projective Criteria," Journal of Theoretical Probability, Springer, vol. 20(4), pages 971-1004, December.
    2. Yizao Wang, 2014. "An Invariance Principle for Fractional Brownian Sheets," Journal of Theoretical Probability, Springer, vol. 27(4), pages 1124-1139, December.

    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. Jirak, Moritz, 2012. "Change-point analysis in increasing dimension," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 136-159.
    2. Christophe Cuny & Florence Merlevède, 2015. "Strong Invariance Principles with Rate for “Reverse” Martingale Differences and Applications," Journal of Theoretical Probability, Springer, vol. 28(1), pages 137-183, March.
    3. Andrii Babii & Eric Ghysels & Jonas Striaukas, 2022. "Machine Learning Time Series Regressions With an Application to Nowcasting," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(3), pages 1094-1106, June.
    4. J. Dedecker & C. Prieur, 2004. "Coupling for τ-Dependent Sequences and Applications," Journal of Theoretical Probability, Springer, vol. 17(4), pages 861-885, October.
    5. Babii, Andrii & Ball, Ryan T. & Ghysels, Eric & Striaukas, Jonas, 2023. "Machine learning panel data regressions with heavy-tailed dependent data: Theory and application," Journal of Econometrics, Elsevier, vol. 237(2).
    6. Paul Doukhan & Jean-David Fermanian & Gabriel Lang, 2009. "An empirical central limit theorem with applications to copulas under weak dependence," Statistical Inference for Stochastic Processes, Springer, vol. 12(1), pages 65-87, February.
    7. P. Chigansky & Yu. Kutoyants, 2013. "Estimation in threshold autoregressive models with correlated innovations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(5), pages 959-992, October.
    8. Hélène Cossette & Etienne Marceau & Véronique Maume-Deschamps, 2011. "Adjustment Coefficient for Risk Processes in Some Dependent Contexts," Methodology and Computing in Applied Probability, Springer, vol. 13(4), pages 695-721, December.
    9. Ngai Chan & Yury Kutoyants, 2012. "On parameter estimation of threshold autoregressive models," Statistical Inference for Stochastic Processes, Springer, vol. 15(1), pages 81-104, April.
    10. Bashtova, Elena & Shashkin, Alexey, 2022. "Strong Gaussian approximation for cumulative processes," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 1-18.
    11. Doukhan, P. & Pommeret, D. & Reboul, L., 2015. "Data driven smooth test of comparison for dependent sequences," Journal of Multivariate Analysis, Elsevier, vol. 139(C), pages 147-165.
    12. Paul Doukhan & Gilles Teyssière & Pablo Winant, 2005. "A Larch Vector Valued Process," Working Papers 2005-49, Center for Research in Economics and Statistics.
    13. Raluca Balan & Kulik, 2005. "Self-Normalized Weak Invariance Principle for Mixing Sequences," RePAd Working Paper Series lrsp-TRS417, Département des sciences administratives, UQO.
    14. Yannick Hoga, 2023. "The Estimation Risk in Extreme Systemic Risk Forecasts," Papers 2304.10349, arXiv.org.
    15. Galtchouk, L. & Pergamenshchikov, S., 2007. "Uniform concentration inequality for ergodic diffusion processes," Stochastic Processes and their Applications, Elsevier, vol. 117(7), pages 830-839, July.
    16. Emmanuel Rio, 2009. "Moment Inequalities for Sums of Dependent Random Variables under Projective Conditions," Journal of Theoretical Probability, Springer, vol. 22(1), pages 146-163, March.
    17. Hafouta, Yeor, 2023. "An almost sure invariance principle for some classes of non-stationary mixing sequences," Statistics & Probability Letters, Elsevier, vol. 193(C).
    18. Douc, R. & Fort, G. & Moulines, E. & Priouret, P., 2009. "Forgetting the initial distribution for Hidden Markov Models," Stochastic Processes and their Applications, Elsevier, vol. 119(4), pages 1235-1256, April.
    19. Davide Giraudo, 2017. "Holderian Weak Invariance Principle for Stationary Mixing Sequences," Journal of Theoretical Probability, Springer, vol. 30(1), pages 196-211, March.
    20. Paul Doukhan & Olivier Wintenberger, 2005. "An Invariance Principle for New Weakly Dependent Stationary Models using Sharp Moment Assumptions," Working Papers 2005-51, Center for Research in Economics and Statistics.

    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:spr:jotpro:v:19:y:2006:i:3:d:10.1007_s10959-006-0029-y. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.