IDEAS home Printed from https://ideas.repec.org/p/crs/wpaper/2005-51.html
   My bibliography  Save this paper

An Invariance Principle for New Weakly Dependent Stationary Models using Sharp Moment Assumptions

Author

Listed:
  • Paul Doukhan

    (Crest)

  • Olivier Wintenberger

    (Crest)

Abstract

This paper is aimed at sharpen a weak invariance principle for stationary sequences in Doukhan & Louhichi (1999). Our assumption is both beyond mixing and the causal ?-weak dependence in Dedecker and Doukhan (2003); those authors obtained a sharp result which improves on an optimal one in Doukhan {\it et alii} (1995) under strong mixing. We prove this result and we also precise convergence rates under existence of moments with order >2 while Doukhan & Louhichi (1999) assume a moment of order >4. Analogously to those authors, we use a non-causal condition to deal with some general classes of stationary and weakly dependent sequences. Besides the previously used ?- and ?-weak dependence conditions, we introduce a mixed condition, ?, adapted to consider Bernoulli shifts with dependent inputs.

Suggested Citation

  • 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.
    • Handle: RePEc:crs:wpaper:2005-51
    as

    Download full text from publisher

    File URL: http://crest.science/RePEc/wpstorage/2005-51.pdf
    File Function: Crest working paper version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Giraitis, Liudas & Surgailis, Donatas, 0. "ARCH-type bilinear models with double long memory," Stochastic Processes and their Applications, Elsevier, vol. 100(1-2), pages 275-300, July.
    2. Doukhan, Paul & Louhichi, Sana, 1999. "A new weak dependence condition and applications to moment inequalities," Stochastic Processes and their Applications, Elsevier, vol. 84(2), pages 313-342, December.
    3. Dedecker, Jérôme & Doukhan, Paul, 2003. "A new covariance inequality and applications," Stochastic Processes and their Applications, Elsevier, vol. 106(1), pages 63-80, July.
    4. Sana Louhichi & Philippe Soulier, 2000. "Marcinkiewicz–Zygmund Strong Laws for Infinite Variance Time Series," Statistical Inference for Stochastic Processes, Springer, vol. 3(1), pages 31-40, January.
    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. Jean-Marc Bardet & Paul Doukhan & José Rafael Leon_, 2005. "Uniform Limit Theorems for the Integrated Periodogram of Weakly Dependent Time Series and their Applications to Whittle's Estimate," Working Papers 2005-46, Center for Research in Economics and Statistics.

    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. Paul Doukhan & Gilles Teyssière & Pablo Winant, 2005. "A Larch Vector Valued Process," Working Papers 2005-49, Center for Research in Economics and Statistics.
    2. Jean-Marc Bardet & Paul Doukhan & José Rafael Leon_, 2005. "Uniform Limit Theorems for the Integrated Periodogram of Weakly Dependent Time Series and their Applications to Whittle's Estimate," Working Papers 2005-46, Center for Research in Economics and Statistics.
    3. Paul Doukhan & Hélène Madre & Mathieu Rosenbaum, 2005. "Weak Dependence Beyond Mixing for Infinite ARCH-type Bilinear Models," Working Papers 2005-50, Center for Research in Economics and Statistics.
    4. Jean‐Marc Bardet & Paul Doukhan & José Rafael León, 2008. "Uniform limit theorems for the integrated periodogram of weakly dependent time series and their applications to Whittle's estimate," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(5), pages 906-945, September.
    5. Jerôme Dedecker & Paul Doukhan, 2002. "A New Covariance Inequality and Applications," Working Papers 2002-25, Center for Research in Economics and Statistics.
    6. Pierre Perron & Eduardo Zorita & Wen Cao & Clifford Hurvich & Philippe Soulier, 2017. "Drift in Transaction-Level Asset Price Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(5), pages 769-790, September.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. Jean-Marc Bardet & Paul Doukhan & José León, 2008. "A functional limit theorem for η-weakly dependent processes and its applications," Statistical Inference for Stochastic Processes, Springer, vol. 11(3), pages 265-280, October.
    12. Jean-Marc Bardet & Paul Doukhan & José Rafael Leon_, 2005. "A Functional Limit Theorem for weakly Dependent Processes and its Applications," Working Papers 2005-45, Center for Research in Economics and Statistics.
    13. Doukhan, Paul & Fokianos, Konstantinos & Li, Xiaoyin, 2012. "On weak dependence conditions: The case of discrete valued processes," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 1941-1948.
    14. Giuliano-Antonini, R. & Weber, M., 2008. "The theta-dependence coefficient and an Almost Sure Limit Theorem for random iterative models," Statistics & Probability Letters, Elsevier, vol. 78(5), pages 564-575, April.
    15. Manel Kacem & Stéphane Loisel & Véronique Maume-Deschamps, 2016. "Some mixing properties of conditionally independent processes," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(5), pages 1241-1259, March.
    16. Sancetta, Alessio, 2005. "Distance between nonidentically weakly dependent random vectors and Gaussian random vectors under the bounded Lipschitz metric," Statistics & Probability Letters, Elsevier, vol. 75(3), pages 158-168, December.
    17. Rootzén, Holger, 2009. "Weak convergence of the tail empirical process for dependent sequences," Stochastic Processes and their Applications, Elsevier, vol. 119(2), pages 468-490, February.
    18. Doukhan, Paul & Wintenberger, Olivier, 2008. "Weakly dependent chains with infinite memory," Stochastic Processes and their Applications, Elsevier, vol. 118(11), pages 1997-2013, November.
    19. Doukhan, Paul & Neumann, Michael H., 2007. "Probability and moment inequalities for sums of weakly dependent random variables, with applications," Stochastic Processes and their Applications, Elsevier, vol. 117(7), pages 878-903, July.
    20. El Ghouch, Anouar & Genton, Marc G. & Bouezmarni , Taoufik, 2012. "Measuring the Discrepancy of a Parametric Model via Local Polynomial Smoothing," LIDAM Discussion Papers ISBA 2012001, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).

    More about this item

    Statistics

    Access and download 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:crs:wpaper:2005-51. 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: Secretariat General (email available below). General contact details of provider: https://edirc.repec.org/data/crestfr.html .

    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.