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 C  Mathematical and Quantitative Methods > C2  Single Equation Models; Single Variables > C22  TimeSeries Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models 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:  24. Feb 2013 22:45 
References:  Berk, K. N. (1974),"Consistent autoregressive spectral estimates", Annals of Statistics 2, No3, 489502. Edelman, A. and Kostlan, E. (1995) "How many zeros of a random polynomial are real?", Bulletin of the American Mathematical Society 32, pp. 137. Erdos, P. and Turan, P. (1950) "On the distribution of roots of polynomials" , Annals of Mathematics 51, 105119. Granger, C.W.J. and Y. Jeon (2006) "Dynamics of Model Overfitting Measured in Terms of Autoregressive Roots", Journal of Time Series Analysis 27, 347365. Horn, R.A. and Johnson C.R. (1991) Topics in Matrix Analysis, Cambridge University Press, Cambridge, New York, Port Chester, Melbourne, Sydney. Johansen, S. (2003) "The asymptotic variance of the estimated roots in a cointegrated vector autoregressive model", Journal of Time Series Analysis, 24, 663678. Lewis, R. and G.C. Reinsel (1985) "Prediction of Multivariate Time Series by Autoregressive Model Fitting", Journal of Multivariate Analysis 16, 393411. Muller, Ulrich K. and Mark W. Watson (2008), "Testing Models of LowFrequency Variability", Econometrica 76 (5), 9791016. Nielsen, B. and Nielsen, H. B. (2008) "Properties of Estimated Characteristic Roots", Univ. of Copenhagen Dept. of Economics Discussion Paper No. 0813. Saikkonen, P., and H. Lutkepohl (1996) "InfiniteOrder Cointegrated Vector Autoregressive Processes: Estimation and Inference", Econometric Theory 12, 814844. Shparo, D.I. and M.G. Schur (1962) "On the Distribution of Roots of Random Polynomials", Vestnik Moskovskogo Universiteta, Series 1: Mathematics and Mechanics, no.3, pp. 4043. 
URI:  http://mpra.ub.unimuenchen.de/id/eprint/14060 
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