Ols Bias in a Nonstationary Autoregression
推导出单位根过程中自回归参数OLS估计量有限样本偏误的解析公式，发现偏误下降速度慢于一致性速率，并给出偏误随样本量增大的特例。
An analytical formula is derived to approximate the finite sample bias of the ordinary least-squares (OLS) estimator of the autoregressive parameter when the underlying process has a unit root. It is found that the bias is expressible in terms of parabolic cylinder functions which are easy to compute. Numerical evaluation of the formula reveals that the approximation is very accurate. The derived formula inspires a heuristic approximation, obtained by leastsquares fitting of the asymptotic bias. More importantly, the formula proves analytically that the bias declines at a rate which is slower than the consistency rate, thus explaining some previous simulation findings. A case where the bias increases with the sample size is also given.