IDEAS home Printed from https://ideas.repec.org/a/bla/jtsera/v21y2000i2p193-218.html
   My bibliography  Save this article

Data Driven Order Selection for Projection Estimator of the Spectral Density of Time Series with Long Range Dependence

Author

Listed:
  • Eric Moulines
  • Philippe Soulier

Abstract

Fractional exponential (FEXP) models have been introduced by Robinson (1991) and Beran (1993) to model the spectral density of a covariance stationary long‐range dependent process. In this class of models, the spectral density f(x) of the process is decomposed as f(x) = |1 − exp(ix)|−2df*(x), where f*(x) accounts for the short‐memory component. In this contribution, FEXP models are used to construct semi‐parametric estimates of the fractional differencing coefficient and of the spectral density, by considering an infinite Fourier series expansion of log f*(x). A data‐driven order selection procedure, adapted from the Mallows' Cp procedure, is proposed to determine the order of truncation. The optimality of the data‐driven procedure is established, under mild assumptions on the short‐memory component f*(x). A limited Monte‐Carlo experiment is presented to support our claims.

Suggested Citation

  • Eric Moulines & Philippe Soulier, 2000. "Data Driven Order Selection for Projection Estimator of the Spectral Density of Time Series with Long Range Dependence," Journal of Time Series Analysis, Wiley Blackwell, vol. 21(2), pages 193-218, March.
    • Handle: RePEc:bla:jtsera:v:21:y:2000:i:2:p:193-218
    DOI: 10.1111/1467-9892.00181
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/1467-9892.00181
    Download Restriction: no
    File URL: https://libkey.io/10.1111/1467-9892.00181?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
    ---><---

    Citations

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


    Cited by:

    1. Jan Beran & Sucharita Ghosh, 2020. "Estimating the Mean Direction of Strongly Dependent Circular Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(2), pages 210-228, March.
    2. Hurvich, Clifford M., 2002. "Multistep forecasting of long memory series using fractional exponential models," International Journal of Forecasting, Elsevier, vol. 18(2), pages 167-179.
    3. Masaki Narukawa & Yasumasa Matsuda, 2008. "Broadband semiparametric estimation of the long-memory parameter by the likelihood-based FEXP approach," TERG Discussion Papers 239, Graduate School of Economics and Management, Tohoku University.
    4. Bhansali, R.J. & Giraitis, L. & Kokoszka, P.S., 2006. "Estimation of the memory parameter by fitting fractionally differenced autoregressive models," Journal of Multivariate Analysis, Elsevier, vol. 97(10), pages 2101-2130, November.
    5. Uwe Hassler & Marc-Oliver Pohle, 2019. "Forecasting under Long Memory and Nonstationarity," Papers 1910.08202, arXiv.org.

    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:bla:jtsera:v:21:y:2000:i:2:p:193-218. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0143-9782 .

    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.