IDEAS home Printed from https://ideas.repec.org/a/spr/aistmt/v65y2013i4p703-719.html
   My bibliography  Save this article

Large deviations for posterior distributions on the parameter of a multivariate $$\text{ AR}(p)$$ process

Author

Listed:
  • Claudio Macci
  • Stefano Trapani

Abstract

We prove the large deviation principle for the posterior distributions on the (unknown) parameter of a multivariate autoregressive process with i.i.d. Normal innovations. As a particular case, we recover a previous result for univariate first-order autoregressive processes. We also show that the rate function can be expressed in terms of the divergence between two spectral densities. Copyright The Institute of Statistical Mathematics, Tokyo 2013

Suggested Citation

  • Claudio Macci & Stefano Trapani, 2013. "Large deviations for posterior distributions on the parameter of a multivariate $$\text{ AR}(p)$$ process," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(4), pages 703-719, August.
    • Handle: RePEc:spr:aistmt:v:65:y:2013:i:4:p:703-719
    DOI: 10.1007/s10463-012-0389-2
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10463-012-0389-2
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10463-012-0389-2?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. Mas, André & Menneteau, Ludovic, 2003. "Large and moderate deviations for infinite-dimensional autoregressive processes," Journal of Multivariate Analysis, Elsevier, vol. 87(2), pages 241-260, November.
    2. Claudio Macci, 2010. "Large deviations for estimators of some threshold parameters," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 19(1), pages 63-77, March.
    3. James Fu & Robert Kass, 1988. "The exponential rates of convergence of posterior distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 40(4), pages 683-691, December.
    4. Macci, Claudio, 2011. "Large deviations for estimators of unknown probabilities, with applications in risk theory," Statistics & Probability Letters, Elsevier, vol. 81(1), pages 16-24, 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. Álvarez-Liébana, Javier & Bosq, Denis & Ruiz-Medina, María D., 2016. "Consistency of the plug-in functional predictor of the Ornstein–Uhlenbeck process in Hilbert and Banach spaces," Statistics & Probability Letters, Elsevier, vol. 117(C), pages 12-22.
    2. Claudio Macci, 2010. "Large deviations for estimators of some threshold parameters," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 19(1), pages 63-77, March.
    3. Menneteau, Ludovic, 2005. "Some laws of the iterated logarithm in Hilbertian autoregressive models," Journal of Multivariate Analysis, Elsevier, vol. 92(2), pages 405-425, February.
    4. Mas, André, 2007. "Weak convergence in the functional autoregressive model," Journal of Multivariate Analysis, Elsevier, vol. 98(6), pages 1231-1261, July.
    5. Ganesh, Ayalvadi & O'Connell, Neil, 1999. "An inverse of Sanov's theorem," Statistics & Probability Letters, Elsevier, vol. 42(2), pages 201-206, April.
    6. Mao, Mingzhi, 2014. "The asymptotic behaviors for least square estimation of multi-casting autoregressive processes," Journal of Multivariate Analysis, Elsevier, vol. 129(C), pages 110-124.
    7. Enkelejd Hashorva & Claudio Macci & Barbara Pacchiarotti, 2013. "Large Deviations for Proportions of Observations Which Fall in Random Sets Determined by Order Statistics," Methodology and Computing in Applied Probability, Springer, vol. 15(4), pages 875-896, December.
    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. Chun Yip Yau & Zifeng Zhao, 2016. "Inference for multiple change points in time series via likelihood ratio scan statistics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(4), pages 895-916, September.
    10. Macci, Claudio, 2011. "Large deviations for estimators of unknown probabilities, with applications in risk theory," Statistics & Probability Letters, Elsevier, vol. 81(1), pages 16-24, January.
    11. Yu, Miao & Si, Shen, 2009. "Moderate deviation principle for autoregressive processes," Journal of Multivariate Analysis, Elsevier, vol. 100(9), pages 1952-1961, October.
    12. Álvarez-Liébana, J. & Bosq, D. & Ruiz-Medina, M.D., 2017. "Asymptotic properties of a component-wise ARH(1) plug-in predictor," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 12-34.

    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:aistmt:v:65:y:2013:i:4:p:703-719. 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.