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Unit Roots in White Noise

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  • Onatski, Alexei
  • Uhlig, Harald

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 n^3/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://mpra.ub.uni-muenchen.de/14057/
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File URL: http://mpra.ub.uni-muenchen.de/14060/
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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 14057.

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Date of creation: 08 Mar 2009
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Handle: RePEc:pra:mprapa:14057

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Keywords: unit roots; unit root; white noise; asymptotics; autoregression; Granger and Jeon; clustering of roots;

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  1. 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.
  2. Soren JOHANSEN, 2001. "The Asymptotic Variance of the Estimated Roots in a Cointegrated Vector Autoregressive Model," Economics Working Papers ECO2001/01, European University Institute.
  3. Ulrich K. Müller & Mark W. Watson, 2008. "Testing Models of Low-Frequency Variability," Econometrica, Econometric Society, vol. 76(5), pages 979-1016, 09.
  4. Bent Nielsen & Heino Bohn Nielsen, 2008. "Properties of estimated characteristic roots," Economics Series Working Papers 2008-WO7, University of Oxford, Department of Economics.
  5. 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.
  6. Saikkonen, Pentti & Lütkepohl, HELMUT, 1996. "Infinite-Order Cointegrated Vector Autoregressive Processes," Econometric Theory, Cambridge University Press, vol. 12(05), pages 814-844, December.
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