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Biases of Correlograms and of AR Representations of Stationary Series

Author

Listed:
  • Abadir Karim M.

    (Imperial College London)

  • Larsson Rolf

    (Uppsala University)

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

  • Abadir Karim M. & Larsson Rolf, 2012. "Biases of Correlograms and of AR Representations of Stationary Series," Journal of Time Series Econometrics, De Gruyter, vol. 4(1), pages 1-11, May.
    • Handle: RePEc:bpj:jtsmet:v:4:y:2012:i:1:n:1
    DOI: 10.1515/1941-1928.1130
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    References listed on IDEAS

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    5. Abadir,Karim M. & Magnus,Jan R., 2005. "Matrix Algebra," Cambridge Books, Cambridge University Press, number 9780521537469, October.
    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.
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    More about this item

    Keywords

    Auto-correlation function (ACF) and correlogram; auto-regressive (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

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