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Properties of etimated characteristic roots

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  • Bent Nielsen

    ()
    (Nuffield College, Oxford University)

  • Heino Bohn Nielsen

    ()
    (University of Copenhagen)

Abstract

Estimated characteristic roots in stationary autoregressions are shown to give rather noisy information about their population equivalents. This is remarkable given the central role of the characteristic roots in the theory of autoregressive processes. In the asymptotic analysis the problems appear when multiple roots are present as this imply a non-differentiability so the d-method does not apply, convergence rates are slow, and the asymptotic distribution is non-normal. In finite samples this has a considerable influence on the finite sample distribution unless the roots are far apart. With increasing order of the autoregressions it becomes increasingly difficult to place the roots far apart giving a very noisy signal from the characteristic roots.

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File URL: http://www.nuffield.ox.ac.uk/economics/papers/2008/w7/NN2008.pdf
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Bibliographic Info

Paper provided by Economics Group, Nuffield College, University of Oxford in its series Economics Papers with number 2008-W07.

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Length: 14 pages
Date of creation: 05 2008
Date of revision:
Handle: RePEc:nuf:econwp:0807

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Web page: http://www.nuff.ox.ac.uk/economics/

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Keywords: Autoregression; Characteristic root.;

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  1. Pantula, Sastry G., 1989. "Testing for Unit Roots in Time Series Data," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 5(02), pages 256-271, August.
  2. Wymer, C R, 1972. "Econometric Estimation of Stochastic Differential Equation Systems," Econometrica, Econometric Society, Econometric Society, vol. 40(3), pages 565-77, May.
  3. Soren JOHANSEN, 2001. "The Asymptotic Variance of the Estimated Roots in a Cointegrated Vector Autoregressive Model," Economics Working Papers, European University Institute ECO2001/01, European University Institute.
  4. Clive W. J. Granger & Yongil Jeon, 2006. "Dynamics of Model Overfitting Measured in terms of Autoregressive Roots," Journal of Time Series Analysis, Wiley Blackwell, Wiley Blackwell, vol. 27(3), pages 347-365, 05.
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Cited by:
  1. Harald Uhlig & Alexei Onatski, 2009. "Unit Roots in White Noise," Working Papers, Becker Friedman Institute for Research In Economics 2009-004, Becker Friedman Institute for Research In Economics.

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