Onatski, Alexei and Uhlig, Harald (2009): Unit Roots in White Noise.
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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.
|Item Type:||MPRA Paper|
|Original Title:||Unit Roots in White Noise|
|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 - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models
C - Mathematical and Quantitative Methods > C2 - Single Equation Models; Single Variables > C22 - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models
C - Mathematical and Quantitative Methods > C0 - General > C01 - Econometrics
|Depositing User:||Harald Uhlig|
|Date Deposited:||14. Mar 2009 06:55|
|Last Modified:||21. Feb 2013 21:02|
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