IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v115y2005i11p1838-1859.html
   My bibliography  Save this article

Decomposition of discrete time periodically correlated and multivariate stationary symmetric stable processes

Author

Listed:
  • Soltani, A.R.
  • Parvardeh, A.

Abstract

The spectral structure of discrete time periodically correlated (as well as multivariate stationary) symmetric [alpha]-stable processes is identified by decomposing such a process uniquely in distribution into one sum of three mutually independent periodically correlated (multivariate stationary) stable processes that are classified as mixed moving average, harmonizable and of a third kind. The techniques are based on presenting the flow and its cocycle that govern the spectral representation of the process, using the Hopf decomposition and specifying the harmonizable component.

Suggested Citation

  • Soltani, A.R. & Parvardeh, A., 2005. "Decomposition of discrete time periodically correlated and multivariate stationary symmetric stable processes," Stochastic Processes and their Applications, Elsevier, vol. 115(11), pages 1838-1859, November.
    • Handle: RePEc:eee:spapps:v:115:y:2005:i:11:p:1838-1859
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(05)00081-5
    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. Hardin, Clyde D., 1982. "On the spectral representation of symmetric stable processes," Journal of Multivariate Analysis, Elsevier, vol. 12(3), pages 385-401, September.
    2. Pipiras, Vladas & Taqqu, Murad S. & Abry, Patrice, 2003. "Can continuous-time stationary stable processes have discrete linear representations?," Statistics & Probability Letters, Elsevier, vol. 64(2), pages 147-157, August.
    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. Arijit Chakrabarty & Parthanil Roy, 2013. "Group-Theoretic Dimension of Stationary Symmetric α-Stable Random Fields," Journal of Theoretical Probability, Springer, vol. 26(1), pages 240-258, March.
    2. Wang, Yizao & Stoev, Stilian A. & Roy, Parthanil, 2012. "Decomposability for stable processes," Stochastic Processes and their Applications, Elsevier, vol. 122(3), pages 1093-1109.
    3. Grassi, Stefano & Santucci de Magistris, Paolo, 2014. "When long memory meets the Kalman filter: A comparative study," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 301-319.
    4. Pipiras, Vladas, 2007. "Nonminimal sets, their projections and integral representations of stable processes," Stochastic Processes and their Applications, Elsevier, vol. 117(9), pages 1285-1302, September.
    5. Sławomir Kolodyński & Jan Rosiński, 2003. "Group Self-Similar Stable Processes in R d," Journal of Theoretical Probability, Springer, vol. 16(4), pages 855-876, October.
    6. Ibragimov, Ildar & Kabluchko, Zakhar & Lifshits, Mikhail, 2019. "Some extensions of linear approximation and prediction problems for stationary processes," Stochastic Processes and their Applications, Elsevier, vol. 129(8), pages 2758-2782.
    7. Pérez-Abreu, Victor & Rocha-Arteaga, Alfonso, 1997. "On stable processes of bounded variation," Statistics & Probability Letters, Elsevier, vol. 33(1), pages 69-77, April.
    8. Rutkowski, Marek, 1995. "Left and right linear innovations for a multivariate S[alpha]S random variable," Statistics & Probability Letters, Elsevier, vol. 22(3), pages 175-184, February.
    9. Stoev, Stilian A., 2008. "On the ergodicity and mixing of max-stable processes," Stochastic Processes and their Applications, Elsevier, vol. 118(9), pages 1679-1705, September.
    10. Vladas Pipiras & Murad S. Taqqu, 2004. "Dilated Fractional Stable Motions," Journal of Theoretical Probability, Springer, vol. 17(1), pages 51-84, January.
    11. Roman Ger & Michael Keane & Jolanta K. Misiewicz, 2000. "On Convolutions and Linear Combinations of Pseudo-Isotropic Distributions," Journal of Theoretical Probability, Springer, vol. 13(4), pages 977-995, October.
    12. Pipiras, Vladas & Taqqu, Murad S. & Abry, Patrice, 2003. "Can continuous-time stationary stable processes have discrete linear representations?," Statistics & Probability Letters, Elsevier, vol. 64(2), pages 147-157, August.
    13. Krzysztof Burnecki, 1998. "Self-similar models in risk theory," HSC Research Reports HSC/98/03, Hugo Steinhaus Center, Wroclaw University of Technology.
    14. Molchanov, Ilga & Schmutz, Michael & Stucki, Kaspar, 2012. "Invariance properties of random vectors and stochastic processes based on the zonoid concept," DES - Working Papers. Statistics and Econometrics. WS ws122014, Universidad Carlos III de Madrid. Departamento de Estadística.
    15. Matsui, Muneya & Takemura, Akimichi, 2009. "Integral representations of one-dimensional projections for multivariate stable densities," Journal of Multivariate Analysis, Elsevier, vol. 100(3), pages 334-344, March.
    16. Parthanil Roy, 2017. "Maxima of stable random fields, nonsingular actions and finitely generated abelian groups: A survey," Indian Journal of Pure and Applied Mathematics, Springer, vol. 48(4), pages 513-540, December.
    17. Parthanil Roy & Gennady Samorodnitsky, 2008. "Stationary Symmetric α-Stable Discrete Parameter Random Fields," Journal of Theoretical Probability, Springer, vol. 21(1), pages 212-233, March.

    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:115:y:2005:i:11:p:1838-1859. 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.