Onatski, Alexei and Uhlig, Harald (2009): Unit Roots in White Noise.
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Abstract
We show that the empirical distribution of the roots of the vector autoregression of order n fitted to T observations of a general stationary or nonstationary 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 autoregression will converge by absolute value to unity.
Item Type:  MPRA Paper 

Original Title:  Unit Roots in White Noise 
Language:  English 
Keywords:  unit roots, unit root, white noise, asymptotics, autoregression, Granger and Jeon, clustering of roots 
Subjects:  C  Mathematical and Quantitative Methods > C3  Multiple or Simultaneous Equation Models ; Multiple Variables > C32  TimeSeries Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes ; State Space Models C  Mathematical and Quantitative Methods > C2  Single Equation Models ; Single Variables > C22  TimeSeries Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes C  Mathematical and Quantitative Methods > C0  General > C01  Econometrics 
Item ID:  14060 
Depositing User:  Harald Uhlig 
Date Deposited:  14 Mar 2009 06:55 
Last Modified:  21 Oct 2019 14:13 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/14060 
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Unit Roots in White Noise. (deposited 14 Mar 2009 06:55)
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