We show that the empirical distribution of the roots of the vector autoregression (VAR) of order <italic>p</italic> fitted to <italic>T</italic> observations of a general stationary or nonstationary process converges to the uniform distribution over the unit circle on the complex plane, when both <italic>T</italic> and <italic>p</italic> tend to infinity so that (ln <italic>T</italic>)/<italic>p</italic> → 0 and <italic>p</italic><sup>3</sup>/<italic>T</italic> → 0. In particular, even if the process is a white noise, nearly all roots of the estimated VAR will converge by absolute value to unity. For fixed <italic>p</italic>, we derive an asymptotic approximation to the expected empirical distribution of the estimated roots as <italic>T</italic> → ∞. The approximation is concentrated in a circular region in the complex plane for various data generating processes and sample sizes.
