Adapting to Unknown Disturbance Autocorrelation in Regression with Long Memory
提出在回归量和扰动均存在长记忆的时间序列回归中，使用平滑非参数谱估计的频率域广义最小二乘法，可适应未知扰动自相关，并证明其渐近正态性和有效性，附有蒙特卡洛模拟。
We show that it is possible to adapt to nonparametric disturbance autocorrelation in time series regression in the presence of long memory in both regressors and disturbances by using a smoothed nonparametric spectrum estimate in frequency-domain generalized least squares. When the collective memory in regressors and disturbances is sufficiently strong, ordinary least squares is not only asymptotically inefficient but asymptotically non-normal and has a slow rate of convergence, whereas generalized least squares is asymptotically normal and Gauss-Markov efficient with standard convergence rate. Despite the anomalous behavior of nonparametric spectrum estimates near a spectral pole, we are able to justify a standard construction of frequency-domain generalized least squares, earlier considered in case of short memory disturbances. A small Monte Carlo study of finite sample performance is included. Copyright The Econometric Society 2002.