IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v390y2011i1p8-17.html
   My bibliography  Save this article

Empirical aspects of the Whittle-based maximum likelihood method in jointly estimating seasonal and non-seasonal fractional integration parameters

Author

Listed:
  • Marques, G.O.L.C.

Abstract

This paper addresses the efficiency of the maximum likelihood (ML) method in jointly estimating the fractional integration parameters ds and d, respectively associated with seasonal and non-seasonal long-memory components in discrete stochastic processes. The influence of the size of non-seasonal parameter over seasonal parameter estimation, and vice versa, was analyzed in the space d×ds∈(0,1)×(0,1) by using mean squared error statistics MSE(dˆs) and MSE(dˆ). This study was based on Monte Carlo simulation experiments using the ML estimator with Whittle’s approximation in the frequency domain. Numerical results revealed that efficiency in jointly estimating each integration parameter is affected in different ways by their sizes: as ds and d increase simultaneously to 1, MSE(dˆs) and MSE(dˆ) become larger; however, effects on MSE(dˆs) are much stronger than the effects on MSE(dˆ). Moreover, as each parameter tends individually to 1, MSE(dˆ) becomes larger, but MSE(dˆs) is barely influenced.

Suggested Citation

  • Marques, G.O.L.C., 2011. "Empirical aspects of the Whittle-based maximum likelihood method in jointly estimating seasonal and non-seasonal fractional integration parameters," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(1), pages 8-17.
    • Handle: RePEc:eee:phsmap:v:390:y:2011:i:1:p:8-17
    DOI: 10.1016/j.physa.2010.09.007
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437110007879
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2010.09.007?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. Power, Gabriel J. & Turvey, Calum G., 2010. "Long-range dependence in the volatility of commodity futures prices: Wavelet-based evidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(1), pages 79-90.
    2. Seater, John J, 1993. "World Temperature-Trend Uncertainties and Their Implications for Economic Policy," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(3), pages 265-277, July.
    3. Lopes, S.R.C. & Nunes, M.A., 2006. "Long memory analysis in DNA sequences," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 361(2), pages 569-588.
    4. Josu Arteche & Peter M. Robinson, 2000. "Semiparametric Inference in Seasonal and Cyclical Long Memory Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 21(1), pages 1-25, January.
    5. Cajueiro, Daniel O. & Tabak, Benjamin M., 2007. "Time-varying long-range dependence in US interest rates," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 360-367.
    6. Reisen, Valderio Anselmo & Rodrigues, Alexandre L. & Palma, Wilfredo, 2006. "Estimation of seasonal fractionally integrated processes," Computational Statistics & Data Analysis, Elsevier, vol. 50(2), pages 568-582, January.
    7. Barbara Olbermann & Sílvia Lopes & Valdério Reisen, 2006. "Invariance of the first difference in ARFIMA models," Computational Statistics, Springer, vol. 21(3), pages 445-461, December.
    8. Mohamed Boutahar & Velayoudom Marimoutou & Leila Nouira, 2007. "Estimation Methods of the Long Memory Parameter: Monte Carlo Analysis and Application," Journal of Applied Statistics, Taylor & Francis Journals, vol. 34(3), pages 261-301.
    9. 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.
    10. Davidson James E. H. & Peel David A & Byers J. David, 2006. "Support for Governments and Leaders: Fractional Cointegration Analysis of Poll Evidence from the UK, 1960-2004," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 10(1), pages 1-23, March.
    11. Gilles Teyssière & Alan P. Kirman (ed.), 2007. "Long Memory in Economics," Springer Books, Springer, number 978-3-540-34625-8, April.
    12. Diongue, Abdou Kâ & Diop, Aliou & Ndongo, Mor, 2008. "Seasonal fractional ARIMA with stable innovations," Statistics & Probability Letters, Elsevier, vol. 78(12), pages 1404-1411, September.
    13. Barbosa, S.M. & Fernandes, M.J. & Silva, M.E., 2006. "Long-range dependence in North Atlantic sea level," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 371(2), pages 725-731.
    14. 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. Reisen, Valdério A. & Zamprogno, Bartolomeu & Palma, Wilfredo & Arteche, Josu, 2014. "A semiparametric approach to estimate two seasonal fractional parameters in the SARFIMA model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 98(C), pages 1-17.
    2. Ye, Xunyu & Gao, Ping & Li, Handong, 2015. "Improving estimation of the fractionally differencing parameter in the SARFIMA model using tapered periodogram," Economic Modelling, Elsevier, vol. 46(C), pages 167-179.

    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. Javier Hualde & Morten {O}rregaard Nielsen, 2022. "Fractional integration and cointegration," Papers 2211.10235, arXiv.org.
    2. Dominique Guegan & Laurent Ferrara, 2008. "Fractional and seasonal filtering," PSE-Ecole d'économie de Paris (Postprint) halshs-00646178, HAL.
    3. Rosa Espejo & Nikolai Leonenko & Andriy Olenko & María Ruiz-Medina, 2015. "On a class of minimum contrast estimators for Gegenbauer random fields," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(4), pages 657-680, December.
    4. 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.
    5. Voges, Michelle & Sibbertsen, Philipp, 2021. "Cyclical fractional cointegration," Econometrics and Statistics, Elsevier, vol. 19(C), pages 114-129.
    6. Reisen, Valdério A. & Zamprogno, Bartolomeu & Palma, Wilfredo & Arteche, Josu, 2014. "A semiparametric approach to estimate two seasonal fractional parameters in the SARFIMA model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 98(C), pages 1-17.
    7. Laurent Ferrara & Dominique Guégan, 2008. "Business surveys modelling with Seasonal-Cyclical Long Memory models," Economics Bulletin, AccessEcon, vol. 3(29), pages 1-10.
    8. 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.
    9. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
    10. Federico Maddanu, 2022. "A harmonically weighted filter for cyclical long memory processes," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 106(1), pages 49-78, March.
    11. Arteche, Josu, 2004. "Gaussian semiparametric estimation in long memory in stochastic volatility and signal plus noise models," Journal of Econometrics, Elsevier, vol. 119(1), pages 131-154, March.
    12. Nicholas Apergis & Andrea Mervar & James E. Payne, 2017. "Forecasting disaggregated tourist arrivals in Croatia," Tourism Economics, , vol. 23(1), pages 78-98, February.
    13. Beaumont, Paul & Smallwood, Aaron, 2019. "Inference for likelihood-based estimators of generalized long-memory processes," MPRA Paper 96313, University Library of Munich, Germany.
    14. repec:ebl:ecbull:v:3:y:2008:i:29:p:1-10 is not listed on IDEAS
    15. Leschinski, Christian & Sibbertsen, Philipp, 2014. "Model Order Selection in Seasonal/Cyclical Long Memory Models," Hannover Economic Papers (HEP) dp-535, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    16. Rocha Souza, Leonardo & Jorge Soares, Lacir, 2007. "Electricity rationing and public response," Energy Economics, Elsevier, vol. 29(2), pages 296-311, March.
    17. Aaron D. Smallwood & Stefan C. Norrbin, 2006. "Generalized long memory processes, failure of cointegration tests and exchange rate dynamics," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(4), pages 409-417, May.
    18. Paramsothy Silvapulle, 2001. "A Score Test For Seasonal Fractional Integration And Cointegration," Econometric Reviews, Taylor & Francis Journals, vol. 20(1), pages 85-104.
    19. Bhandari, Avishek, 2020. "Long Memory and Correlation Structures of Select Stock Returns Using Novel Wavelet and Fractal Connectivity Networks," MPRA Paper 101946, University Library of Munich, Germany.
    20. Voges, Michelle & Leschinski, Christian & Sibbertsen, Philipp, 2017. "Seasonal long memory in intraday volatility and trading volume of Dow Jones stocks," Hannover Economic Papers (HEP) dp-599, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    21. Guglielmo Maria Caporale & Juncal Cuñado & Luis A. Gil-Alana, 2013. "Modelling long-run trends and cycles in financial time series data," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(3), pages 405-421, May.

    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:phsmap:v:390:y:2011:i:1:p:8-17. 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/physica-a-statistical-mechpplications/ .

    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.