IDEAS home Printed from https://ideas.repec.org/a/taf/jnlbes/v29y2011i2p250-259.html
   My bibliography  Save this article

Estimation for Non-Negative Lévy-Driven CARMA Processes

Author

Listed:
  • Peter J. Brockwell
  • Richard A. Davis
  • Yu Yang

Abstract

Continuous-time autoregressive moving average (CARMA) processes with a nonnegative kernel and driven by a nondecreasing Lévy process constitute a useful and very general class of stationary, nonnegative continuous-time processes that have been used, in particular, for the modeling of stochastic volatility. Brockwell, Davis, and Yang (2007) derived efficient estimates of the parameters of a nonnegative Lévy-driven CAR(1) process and showed how the realization of the underlying Lévy process can be estimated from closely-spaced observations of the process itself. In this article we show how the ideas of that article can be generalized to higher order CARMA processes with nonnegative kernel, the key idea being the decomposition of the CARMA process into a sum of dependent Ornstein--Uhlenbeck processes.

Suggested Citation

  • Peter J. Brockwell & Richard A. Davis & Yu Yang, 2011. "Estimation for Non-Negative Lévy-Driven CARMA Processes," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(2), pages 250-259, April.
    • Handle: RePEc:taf:jnlbes:v:29:y:2011:i:2:p:250-259
    DOI: 10.1198/jbes.2010.08165
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1198/jbes.2010.08165
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1198/jbes.2010.08165?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.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Pham, Viet Son, 2020. "Lévy-driven causal CARMA random fields," Stochastic Processes and their Applications, Elsevier, vol. 130(12), pages 7547-7574.
    2. Brockwell, Peter J. & Schlemm, Eckhard, 2013. "Parametric estimation of the driving Lévy process of multivariate CARMA processes from discrete observations," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 217-251.
    3. Lorenzo Mercuri & Andrea Perchiazzo & Edit Rroji, 2020. "Finite Mixture Approximation of CARMA(p,q) Models," Papers 2005.10130, arXiv.org, revised May 2020.
    4. Stefano Iacus & Lorenzo Mercuri, 2015. "Implementation of Lévy CARMA model in Yuima package," Computational Statistics, Springer, vol. 30(4), pages 1111-1141, December.
    5. Basse-O’Connor, Andreas & Nielsen, Mikkel Slot & Pedersen, Jan & Rohde, Victor, 2019. "Multivariate stochastic delay differential equations and CAR representations of CARMA processes," Stochastic Processes and their Applications, Elsevier, vol. 129(10), pages 4119-4143.
    6. Asmerilda Hitaj & Lorenzo Mercuri & Edit Rroji, 2019. "Lévy CARMA models for shocks in mortality," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(1), pages 205-227, June.
    7. Benth, Fred Espen & Karbach, Sven, 2023. "Multivariate continuous-time autoregressive moving-average processes on cones," Stochastic Processes and their Applications, Elsevier, vol. 162(C), pages 299-337.
    8. Rowińska, Paulina A. & Veraart, Almut E.D. & Gruet, Pierre, 2021. "A multi-factor approach to modelling the impact of wind energy on electricity spot prices," Energy Economics, Elsevier, vol. 104(C).
    9. Zahra Sokoot & Navideh Modarresi & Farzaneh Niknejad, 2017. "Modeling credit default swap premiums with stochastic recovery rate," Papers 1706.05703, arXiv.org.
    10. Sikora, Grzegorz & Michalak, Anna & Bielak, Łukasz & Miśta, Paweł & Wyłomańska, Agnieszka, 2019. "Stochastic modeling of currency exchange rates with novel validation techniques," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 1202-1215.
    11. Szarek, Dawid & Bielak, Łukasz & Wyłomańska, Agnieszka, 2020. "Long-term prediction of the metals’ prices using non-Gaussian time-inhomogeneous stochastic process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 555(C).
    12. Benth, Fred Espen & Klüppelberg, Claudia & Müller, Gernot & Vos, Linda, 2014. "Futures pricing in electricity markets based on stable CARMA spot models," Energy Economics, Elsevier, vol. 44(C), pages 392-406.

    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:taf:jnlbes:v:29:y:2011:i:2:p:250-259. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/UBES20 .

    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.