IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v80y2009i2p367-377.html
   My bibliography  Save this article

On properties of the second order generalized autoregressive GAR(2) model with index

Author

Listed:
  • Shitan, Mahendran
  • Peiris, Shelton

Abstract

In this paper we consider a new class of time series models generated by a second order autoregressive type operator with an index. Autocorrelation and spectral properties are discussed and some explicit results are derived for a restricted class in the family. The parameter estimation is discussed using the Whittle procedure. Some numerical results are presented to support the theoretical results.

Suggested Citation

  • Shitan, Mahendran & Peiris, Shelton, 2009. "On properties of the second order generalized autoregressive GAR(2) model with index," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(2), pages 367-377.
    • Handle: RePEc:eee:matcom:v:80:y:2009:i:2:p:367-377
    DOI: 10.1016/j.matcom.2009.07.007
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S037847540900233X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2009.07.007?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. Gemai Chen & Bovas Abraham & Shelton Peiris, 1994. "Lag Window Estimation Of The Degree Of Differencing In Fractionally Integrated Time Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 15(5), pages 473-487, September.
    2. Henry L. Gray & Nien‐Fan Zhang & Wayne A. Woodward, 1989. "On Generalized Fractional Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 10(3), pages 233-257, May.
    3. C. W. J. Granger & Roselyne Joyeux, 1980. "An Introduction To Long‐Memory Time Series Models And Fractional Differencing," Journal of Time Series Analysis, Wiley Blackwell, vol. 1(1), pages 15-29, January.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Federico Maddanu, 2023. "Forecasting highly persistent time series with bounded spectrum processes," Statistical Papers, Springer, vol. 64(1), pages 285-319, February.

    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. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
    2. Dissanayake, G.S. & Peiris, M.S. & Proietti, T., 2016. "State space modeling of Gegenbauer processes with long memory," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 115-130.
    3. Erhard Reschenhofer & Manveer K. Mangat, 2021. "Fast computation and practical use of amplitudes at non-Fourier frequencies," Computational Statistics, Springer, vol. 36(3), pages 1755-1773, September.
    4. Rocha Souza, Leonardo & Jorge Soares, Lacir, 2007. "Electricity rationing and public response," Energy Economics, Elsevier, vol. 29(2), pages 296-311, March.
    5. Paramsothy Silvapulle, 2001. "A Score Test For Seasonal Fractional Integration And Cointegration," Econometric Reviews, Taylor & Francis Journals, vol. 20(1), pages 85-104.
    6. Dominique Guegan & Laurent Ferrara, 2008. "Fractional and seasonal filtering," PSE-Ecole d'économie de Paris (Postprint) halshs-00646178, HAL.
    7. Soares, Lacir Jorge & Souza, Leonardo Rocha, 2006. "Forecasting electricity demand using generalized long memory," International Journal of Forecasting, Elsevier, vol. 22(1), pages 17-28.
    8. Dominique Guegan & Bertrand K. Hassani, 2019. "Risk Measurement," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-02119256, HAL.
    9. Luis A. Gil-Alana & Juan Carlos Cuestas, 2012. "A Non-linear Approach with Long Range Dependence based on Chebyshev Polynomials," Faculty Working Papers 14/12, School of Economics and Business Administration, University of Navarra.
    10. Granger, Clive W. J. & Ding, Zhuanxin, 1996. "Varieties of long memory models," Journal of Econometrics, Elsevier, vol. 73(1), pages 61-77, July.
    11. Boubaker, Heni & Sghaier, Nadia, 2015. "Semiparametric generalized long-memory modeling of some mena stock market returns: A wavelet approach," Economic Modelling, Elsevier, vol. 50(C), pages 254-265.
    12. Collet J.J. & Fadili J.M., 2005. "Simulation of Gegenbauer processes using wavelet packets," School of Economics and Finance Discussion Papers and Working Papers Series 190, School of Economics and Finance, Queensland University of Technology.
    13. Laurent Ferrara & Dominique Guégan, 2008. "Business surveys modelling with Seasonal-Cyclical Long Memory models," Economics Bulletin, AccessEcon, vol. 3(29), pages 1-10.
    14. Erhard Reschenhofer & Manveer K. Mangat, 2020. "Reducing the Bias of the Smoothed Log Periodogram Regression for Financial High-Frequency Data," Econometrics, MDPI, vol. 8(4), pages 1-15, October.
    15. Proietti, Tommaso, 2014. "Exponential Smoothing, Long Memory and Volatility Prediction," MPRA Paper 57230, University Library of Munich, Germany.
    16. Martin, Vance L. & Wilkins, Nigel P., 1999. "Indirect estimation of ARFIMA and VARFIMA models," Journal of Econometrics, Elsevier, vol. 93(1), pages 149-175, November.
    17. Richards, Gordon R., 2000. "The fractal structure of exchange rates: measurement and forecasting," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 10(2), pages 163-180, June.
    18. Javier Hidalgo & Philippe Soulier, 2004. "Estimation of the location and exponent of the spectral singularity of a long memory process," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(1), pages 55-81, January.
    19. Sun, Jingwei & Shi, Wendong, 2014. "Aggregation of the generalized fractional processes," Economics Letters, Elsevier, vol. 124(2), pages 258-262.
    20. Aaron D. Smallwood & Paul M. Beaumont, 2002. "An Asymptotic MLE Approach to Modelling Multiple Frequency GARMA Models," Computing in Economics and Finance 2002 285, Society for Computational Economics.

    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:matcom:v:80:y:2009:i:2:p:367-377. 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.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    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.