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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.

Suggested Citation

  • Onatski, Alexei & Uhlig, Harald, 2009. "Unit Roots in White Noise," MPRA Paper 14057, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:14057
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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. Ulrich K. Müller & Mark W. Watson, 2008. "Testing Models of Low-Frequency Variability," Econometrica, Econometric Society, vol. 76(5), pages 979-1016, September.
    3. 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.
    4. 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.
    5. Saikkonen, Pentti & Lütkepohl, HELMUT, 1996. "Infinite-Order Cointegrated Vector Autoregressive Processes," Econometric Theory, Cambridge University Press, vol. 12(5), pages 814-844, December.
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    Cited by:

    1. James A. Duffy & Jerome R. Simons, 2020. "Cointegration without Unit Roots," Papers 2002.08092, arXiv.org, revised Apr 2023.
    2. Jurgen A. Doornik & Rocco Mosconi & Paolo Paruolo, 2017. "Formula I(1) and I(2): Race Tracks for Likelihood Maximization Algorithms of I(1) and I(2) Cointegrated VAR Models," Econometrics, MDPI, vol. 5(4), pages 1-30, November.
    3. Bruns, Stephan B. & Csereklyei, Zsuzsanna & Stern, David I., 2020. "A multicointegration model of global climate change," Journal of Econometrics, Elsevier, vol. 214(1), pages 175-197.

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    More about this item

    Keywords

    unit roots; unit root; white noise; asymptotics; autoregression; Granger and Jeon; clustering of roots;
    All these keywords.

    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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