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Unit Roots in White Noise

Author

Listed:
  • 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.

Suggested Citation

  • Harald Uhlig & Alexei Onatski, 2009. "Unit Roots in White Noise," Working Papers 2009-004, Becker Friedman Institute for Research In Economics.
  • Handle: RePEc:bfi:wpaper:2009-004
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    File URL: https://econresearch.uchicago.edu/sites/econresearch.uchicago.edu/files/BFI_2009-004.pdf
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    References listed on IDEAS

    as
    1. 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.
    2. Litterman, Robert B, 1986. "Forecasting with Bayesian Vector Autoregressions-Five Years of Experience," Journal of Business & Economic Statistics, American Statistical Association, vol. 4(1), pages 25-38, January.
    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, September.
    5. 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, May.
    6. Bent Nielsen & Heino Bohn Nielsen, 2008. "Properties of etimated characteristic roots," Economics Papers 2008-W07, Economics Group, Nuffield College, University of Oxford.
    7. 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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    Cited by:

    1. David I. Stern, 2004. "A Multicointegration Model of Global Climate Change," Rensselaer Working Papers in Economics 0406, Rensselaer Polytechnic Institute, Department of Economics.
    2. repec:gam:jecnmx:v:5:y:2017:i:4:p:49-:d:119536 is not listed on IDEAS

    More about this item

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics

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