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Biases of correlograms and of AR representations of stationary series

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  • K Abadir
  • R Larsson

Abstract

We derive the relation between the biases of correlograms and of estimates of auto-regressive AR(k) representations of stationary series. We illustrate our approach with a simple AR(2) example, then apply it to the more substantive case of a fractionally-integrated processes where the results have not been derived before. In such a case, k needs to be asymptotically a concave and increasing function of the sample size T. It turns out that the AR representation of I(d) processes leads to biases that are much smaller than for traditional AR models, hence making it an attractive representation.

Suggested Citation

  • K Abadir & R Larsson, "undated". "Biases of correlograms and of AR representations of stationary series," Discussion Papers 05/21, Department of Economics, University of York.
    • Handle: RePEc:yor:yorken:05/21
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    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
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    More about this item

    JEL classification:

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

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