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Unit Roots in White Noise

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  • Harald Uhlig

    (University of Chicago)

  • Alexei Onatski

    ()
    (University of Cambridge)

Abstract

We show that the empirical distribution of the roots of the vector auto-regression of order n fitted to T observations of a general stationary or non-stationary process, converges to the uniform distribution over the unit circle on the complex plane, when both T and n tend to infinity so that (ln T ) /n → 0 and n3/T → 0. In particular, even if the process is a white noise, the roots of the estimated vector auto-regression will converge by absolute value to unity.

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File URL: http://econresearch.uchicago.edu/sites/econresearch.uchicago.edu/files/BFI_2009-004.pdf
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Bibliographic Info

Paper provided by Becker Friedman Institute for Research In Economics in its series Working Papers with number 2009-004.

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Date of creation: 2009
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Handle: RePEc:bfi:wpaper:2009-004

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Web page: http://bfi.uchicago.edu/
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  1. Saikkonen, Pentti & Lütkepohl, HELMUT, 1996. "Infinite-Order Cointegrated Vector Autoregressive Processes," Econometric Theory, Cambridge University Press, vol. 12(05), pages 814-844, December.
  2. Bent Nielsen & Heino Bohn Nielsen, 2008. "Properties of etimated characteristic roots," Economics Papers 2008-W07, Economics Group, Nuffield College, University of Oxford.
  3. Lewis, Richard & Reinsel, Gregory C., 1985. "Prediction of multivariate time series by autoregressive model fitting," Journal of Multivariate Analysis, Elsevier, vol. 16(3), pages 393-411, June.
  4. Ulrich K. Müller & Mark W. Watson, 2008. "Testing Models of Low-Frequency Variability," Econometrica, Econometric Society, vol. 76(5), pages 979-1016, 09.
  5. Søren Johansen, 2003. "The asymptotic variance of the estimated roots in a cointegrated vector autoregressive model," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(6), pages 663-678, November.
  6. Clive W. J. Granger & Yongil Jeon, 2006. "Dynamics of Model Overfitting Measured in terms of Autoregressive Roots," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(3), pages 347-365, 05.
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