IDEAS home Printed from https://ideas.repec.org/a/bpj/jtsmet/v8y2016i1p21-39n3.html
   My bibliography  Save this article

A Note on the QMLE Limit Theory in the Non-stationary ARCH(1) Model

Author

Listed:
  • Arvanitis Stelios

    (Department of Economics, Athens University of Economics and Business, P.O. Box 10434, Patision Str. 80, Athens, Greece)

  • Louka Alexandros

    (Department of Economics, Athens University of Economics and Business, P.O. Box 10434, Patision Str. 80, Athens, Greece)

Abstract

In this note we extend the standard results for the limit theory of the popular quasi-maximum likelihood estimator (QMLE) in the context of the non-stationary autoregressive conditional heteroskedastic ARCH(1) model by allowing the innovation process not to possess fourth moments. Depending on the value of the index of stability, we either derive α$\alpha $-stable weak limits with non-standard rates or inconsistency and non-tightness. We obtain the limit theory by the derivation of a limit theorem for multiplicative “martingale” transforms with limit mixtures of α$\alpha $-stable distributions for any α∈0,2$\alpha \in \left({0,2} \right]$.

Suggested Citation

  • Arvanitis Stelios & Louka Alexandros, 2016. "A Note on the QMLE Limit Theory in the Non-stationary ARCH(1) Model," Journal of Time Series Econometrics, De Gruyter, vol. 8(1), pages 21-39, January.
    • Handle: RePEc:bpj:jtsmet:v:8:y:2016:i:1:p:21-39:n:3
    DOI: 10.1515/jtse-2014-0034
    as

    Download full text from publisher

    File URL: https://doi.org/10.1515/jtse-2014-0034
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.
    File URL: https://libkey.io/10.1515/jtse-2014-0034?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. Abadir, Karim & Magnus, Jan, 2004. "03.6.1 The Central Limit Theorem for Student's Distribution—Solution," Econometric Theory, Cambridge University Press, vol. 20(6), pages 1261-1263, December.
    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. Buonocore, R.J. & Aste, T. & Di Matteo, T., 2016. "Measuring multiscaling in financial time-series," Chaos, Solitons & Fractals, Elsevier, vol. 88(C), pages 38-47.

    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:bpj:jtsmet:v:8:y:2016:i:1:p:21-39:n:3. 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: Peter Golla (email available below). General contact details of provider: https://www.degruyter.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.