IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v71y1997i1p75-90.html
   My bibliography  Save this article

Large deviations for quadratic forms of stationary Gaussian processes

Author

Listed:
  • Bercu, B.
  • Gamboa, F.
  • Rouault, A.

Abstract

A large deviation principle is proved for Toeplitz quadratic forms of centred stationary Gaussian processes. The rate function is obtained by a sharp study of the behaviour of eigenvalues of a product of two Toeplitz matrices. Some statistical applications such as the likelihood ratio test and the estimation of the parameter of an autoregressive Gaussian process are also provided.

Suggested Citation

  • Bercu, B. & Gamboa, F. & Rouault, A., 1997. "Large deviations for quadratic forms of stationary Gaussian processes," Stochastic Processes and their Applications, Elsevier, vol. 71(1), pages 75-90, October.
    • Handle: RePEc:eee:spapps:v:71:y:1997:i:1:p:75-90
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(97)00071-9
    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. Bryc, Wlodzimierz & Smolenski, Wlodzimierz, 1993. "On the large deviation principle for a quadratic functional of the autoregressive process," Statistics & Probability Letters, Elsevier, vol. 17(4), pages 281-285, 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. Macci, Claudio & Pacchiarotti, Barbara, 2017. "Large deviations for estimators of the parameters of a neuronal response latency model," Statistics & Probability Letters, Elsevier, vol. 126(C), pages 65-75.
    2. Zani, Marguerite, 2002. "Large Deviations for Quadratic Forms of Locally Stationary Processes," Journal of Multivariate Analysis, Elsevier, vol. 81(2), pages 205-228, May.
    3. Kakizawa, Yoshihide, 2000. "On Bahadur asymptotic efficiency of the maximum likelihood and quasi-maximum likelihood estimators in Gaussian stationary processes," Stochastic Processes and their Applications, Elsevier, vol. 85(1), pages 29-44, January.
    4. Kakizawa, Yoshihide, 2007. "Moderate deviations for quadratic forms in Gaussian stationary processes," Journal of Multivariate Analysis, Elsevier, vol. 98(5), pages 992-1017, May.
    5. Yu, Miao & Si, Shen, 2009. "Moderate deviation principle for autoregressive processes," Journal of Multivariate Analysis, Elsevier, vol. 100(9), pages 1952-1961, October.
    6. Kley, Tobias & Preuss, Philip & Fryzlewicz, Piotr, 2019. "Predictive, finite-sample model choice for time series under stationarity and non-stationarity," LSE Research Online Documents on Economics 101748, London School of Economics and Political Science, LSE Library.
    7. Worms, Julien, 2001. "Large and moderate deviations upper bounds for the Gaussian autoregressive process," Statistics & Probability Letters, Elsevier, vol. 51(3), pages 235-243, February.
    8. Yu Miao & Yanling Wang & Guangyu Yang, 2015. "Moderate Deviation Principles for Empirical Covariance in the Neighbourhood of the Unit Root," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(1), pages 234-255, March.
    9. Kanaya, Shin & Otsu, Taisuke, 2012. "Large deviations of realized volatility," Stochastic Processes and their Applications, Elsevier, vol. 122(2), pages 546-581.
    10. Gamboa, F. & Rouault, A. & Zani, M., 1999. "A functional large deviations principle for quadratic forms of Gaussian stationary processes," Statistics & Probability Letters, Elsevier, vol. 43(3), pages 299-308, July.
    11. Hacène Djellout & Arnaud Guillin & Yacouba Samoura, 2014. "Large Deviations Of The Realized (Co-)Volatility Vector," Working Papers hal-01082903, HAL.
    12. Hui, Jiang, 2010. "Moderate deviations for estimators of quadratic variational process of diffusion with compound Poisson jumps," Statistics & Probability Letters, Elsevier, vol. 80(17-18), pages 1297-1305, September.
    13. Zani, Marguerite, 2002. "Large deviations for squared radial Ornstein-Uhlenbeck processes," Stochastic Processes and their Applications, Elsevier, vol. 102(1), pages 25-42, November.
    14. Djellout, Hacène & Guillin, Arnaud & Samoura, Yacouba, 2017. "Estimation of the realized (co-)volatility vector: Large deviations approach," Stochastic Processes and their Applications, Elsevier, vol. 127(9), pages 2926-2960.
    15. Miao, Yu & Yin, Qing, 2024. "Cramér’s moderate deviations for the LS estimator of the autoregressive processes in the neighborhood of the unit root," Statistics & Probability Letters, Elsevier, vol. 209(C).
    16. Ginovyan, Mamikon S. & Sahakyan, Artur A., 2013. "On the trace approximations of products of Toeplitz matrices," Statistics & Probability Letters, Elsevier, vol. 83(3), pages 753-760.
    17. Hacène Djellout & Arnaud Guillin & Yacouba Samoura, 2017. "Large Deviations Of The Realized (Co-)Volatility Vector," Post-Print hal-01082903, HAL.

    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. Włodzimierz Bryc & Amir Dembo, 1997. "Large Deviations for Quadratic Functionals of Gaussian Processes," Journal of Theoretical Probability, Springer, vol. 10(2), pages 307-332, April.

    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:71:y:1997:i:1:p:75-90. 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.