IDEAS home Printed from https://ideas.repec.org/p/rim/rimwps/24_12.html
   My bibliography  Save this paper

Biases of Correlograms and of AR Representations of Stationary Series

Author

Listed:
  • Karim M. Abadir

    (Imperial College London, UK)

  • Rolf Larsson

    (Uppsala University, Sweden)

Abstract

We derive the relation between the biases of correlograms and of estimates of auto-regressive AR(k) representations of stationary series, and we illustrate it with a simple AR example. The new relation allows for k to vary with the sample size, which is a representation that can be used for most stationary processes. As a result, the biases of the estimators of such processes can now be quantified explicitly and in a unified way.

Suggested Citation

  • Karim M. Abadir & Rolf Larsson, 2012. "Biases of Correlograms and of AR Representations of Stationary Series," Working Paper series 24_12, Rimini Centre for Economic Analysis.
    • Handle: RePEc:rim:rimwps:24_12
    as

    Download full text from publisher

    File URL: http://www.rcea.org/RePEc/pdf/wp24_12.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Karim M. Abadir & Jan R. Magnus, 2002. "Notation in econometrics: a proposal for a standard," Econometrics Journal, Royal Economic Society, vol. 5(1), pages 76-90, June.
    2. Hidalgo, Javier, 2005. "Semiparametric estimation for stationary processes whose spectra have an unknown pole," LSE Research Online Documents on Economics 6842, London School of Economics and Political Science, LSE Library.
    3. Giraitis, L & Hidalgo, J & Robinson, Peter M., 2001. "Gaussian estimation of parametric spectral density with unknown pole," LSE Research Online Documents on Economics 297, London School of Economics and Political Science, LSE Library.
    4. Giraitis, Liudas & Hidalgo, Javier & Robinson, Peter, 2001. "Gaussian estimation of parametric spectral density with unknown pole," LSE Research Online Documents on Economics 2182, London School of Economics and Political Science, LSE Library.
    5. Abadir,Karim M. & Magnus,Jan R., 2005. "Matrix Algebra," Cambridge Books, Cambridge University Press, number 9780521537469.
    6. Liudas Giraitis & Javier Hidalgo & Peter M Robinson, 2001. "Gaussian Estimation of Parametric Spectral Density with Unknown Pole," STICERD - Econometrics Paper Series 424, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    7. Rolf Larsson, 1997. "On the Asymptotic Expectations of Some Unit Root Tests in a First Order Autoregressive Process in the Presence of Trend," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 49(3), pages 585-599, September.
    8. Kiviet, Jan F. & Phillips, Garry D. A., 1994. "Bias assessment and reduction in linear error-correction models," Journal of Econometrics, Elsevier, vol. 63(1), pages 215-243, July.
    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. Abadir, Karim M., 1993. "Ols Bias in a Nonstationary Autoregression," Econometric Theory, Cambridge University Press, vol. 9(1), pages 81-93, January.
    11. repec:cup:cbooks:9780521822893 is not listed on IDEAS
    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. Abadir, Karim M. & Caggiano, Giovanni & Talmain, Gabriel, 2013. "Nelson–Plosser revisited: The ACF approach," Journal of Econometrics, Elsevier, vol. 175(1), pages 22-34.
    2. Richard Hunt & Shelton Peiris & Neville Weber, 2022. "Estimation methods for stationary Gegenbauer processes," Statistical Papers, Springer, vol. 63(6), pages 1707-1741, December.
    3. 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.
    4. Gil-Alana, Luis A. & Aye, Goodness C. & Gupta, Rangan, 2015. "Trends and cycles in historical gold and silver prices," Journal of International Money and Finance, Elsevier, vol. 58(C), pages 98-109.
    5. Hassler, Uwe, 2011. "Estimation of fractional integration under temporal aggregation," Journal of Econometrics, Elsevier, vol. 162(2), pages 240-247, June.
    6. Javier Haulde & Morten Ørregaard Nielsen, 2022. "Fractional integration and cointegration," CREATES Research Papers 2022-02, Department of Economics and Business Economics, Aarhus University.
    7. repec:hal:journl:peer-00815563 is not listed on IDEAS
    8. Beaumont, Paul & Smallwood, Aaron, 2019. "Inference for likelihood-based estimators of generalized long-memory processes," MPRA Paper 96313, University Library of Munich, Germany.
    9. Giovanni Caggiano & Efrem Castelnuovo, 2008. "Long Memory and Non-Linearities in International Inflation," "Marco Fanno" Working Papers 0076, Dipartimento di Scienze Economiche "Marco Fanno".
    10. 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.
    11. Beaumont, Paul & Smallwood, Aaron, 2019. "Conditional Sum of Squares Estimation of Multiple Frequency Long Memory Models," MPRA Paper 96314, University Library of Munich, Germany.
    12. Proietti, Tommaso & Maddanu, Federico, 2024. "Modelling cycles in climate series: The fractional sinusoidal waveform process," Journal of Econometrics, Elsevier, vol. 239(1).
    13. Violetta Dalla & Javier Hidalgo, 2005. "A Parametric Bootstrap Test for Cycles," STICERD - Econometrics Paper Series 486, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    14. Gil-Alana, Luis A. & Gupta, Rangan, 2014. "Persistence and cycles in historical oil price data," Energy Economics, Elsevier, vol. 45(C), pages 511-516.
    15. Kouamé, Euloge F. & Hili, Ouagnina, 2008. "Minimum distance estimation of k-factors GARMA processes," Statistics & Probability Letters, Elsevier, vol. 78(18), pages 3254-3261, December.
    16. Wilfredo Palma & Ngai Hang Chan, 2005. "Efficient Estimation of Seasonal Long‐Range‐Dependent Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(6), pages 863-892, November.
    17. 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.
    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. Alex Gonzaga & Michael Hauser, 2011. "A wavelet Whittle estimator of generalized long-memory stochastic volatility," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 20(1), pages 23-48, March.
    20. Caporale, Guglielmo Maria & Gil-Alana, Luis A., 2017. "Persistence and cycles in the us federal funds rate," International Review of Financial Analysis, Elsevier, vol. 52(C), pages 1-8.
    21. Hidalgo, Javier, 2005. "Semiparametric estimation for stationary processes whose spectra have an unknown pole," LSE Research Online Documents on Economics 6842, London School of Economics and Political Science, LSE Library.

    More about this item

    Keywords

    Auto-correlation function (ACF) and correlogram; autoregressive (AR) representation; least-squares bias;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:rim:rimwps:24_12. 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: Marco Savioli (email available below). General contact details of provider: https://edirc.repec.org/data/rcfeait.html .

    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.