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Unit Roots in White Noise

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Author Info
Onatski, Alexei
Uhlig, Harald

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

Find related papers by JEL classification:
C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions
C01 - Mathematical and Quantitative Methods - - General - - - Econometrics

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References listed on IDEAS
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  1. Søren Johansen, 2003. "The asymptotic variance of the estimated roots in a cointegrated vector autoregressive model," Journal of Time Series Analysis, Blackwell Publishing, vol. 24(6), pages 663-678, November. [Downloadable!] (restricted)
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  2. Bent Nielsen & Heino Bohn Nielsen, 2008. "Properties of Estimated Characteristic Roots," Discussion Papers 08-13, University of Copenhagen. Department of Economics. [Downloadable!]
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  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. [Downloadable!] (restricted)
  4. Ulrich K. Müller & Mark W. Watson, 2008. "Testing Models of Low-Frequency Variability," Econometrica, Econometric Society, vol. 76(5), pages 979-1016, 09. [Downloadable!] (restricted)
  5. Clive W. J. Granger & Yongil Jeon, 2006. "Dynamics of Model Overfitting Measured in terms of Autoregressive Roots," Journal of Time Series Analysis, Blackwell Publishing, vol. 27(3), pages 347-365, 05. [Downloadable!] (restricted)
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This page was last updated on 2009-11-23.

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