Unit Roots in White Noise
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 â†’ 0 and n3/T â†’ 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.
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