UNIT ROOTS IN WHITE NOISE
研究发现，当阶数p和样本量T都趋于无穷且满足特定条件时，拟合的VAR模型根的分布会收敛到复平面上的单位圆均匀分布，即使数据是白噪声，几乎所有估计根都会趋近于单位圆。
We show that the empirical distribution of the roots of the vector autoregression (VAR) of order p 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 p tend to infinity so that (ln T )/ p → 0 and p 3 / T → 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 p , we derive an asymptotic approximation to the expected empirical distribution of the estimated roots as T → ∞. The approximation is concentrated in a circular region in the complex plane for various data generating processes and sample sizes.