Estimation for Autoregressive Time Series With a Root Near 1
比较了自回归时间序列参数的估计方法，重点关注单位根或根接近1的情况，提出了一种几乎无偏的估计量，其均方误差在单位根情形下仅为普通最小二乘的40%。
AbstractEstimators for the parameters of autoregressive time series are compared, emphasizing processes with a unit root or a root close to 1. The approximate bias of the sum of the autoregressive coefficients is expressed as a function of the test for a unit root. This expression is used to construct an estimator that is nearly unbiased for the parameter of the first-order scalar process. The estimator for the first-order process has a mean squared error that is about 40% of that of ordinary least squares for the process with a unit root and a constant mean, and the mean squared error is smaller than that of ordinary least squares for about half of the parameter space. The maximum loss of efficiency is 6n-1 in the remainder of the parameter space. The estimation procedure is extended to higher-order processes by modifying the estimator of the sum of the autoregressive coefficients. Limiting results are derived for the autoregressive process with a mean that is a linear trend.KEY WORDS: Bias in autoregressionStationary processUnit root