Adapting to Unknown Disturbance Autocorrelation in Regression with Long Memory
Adapting to Unknown Disturbance Autocorrelation in Regression with Long Memory
复制标题
适应长记忆回归中的未知干扰自相关
DOI：
10.1111/1468-0262.00341
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发表时间：
2001
期刊：
影响因子：
--
通讯作者：
J. Hidalgo
中科院分区：
文献类型：
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作者：
J. Hidalgo
我们证明，在回归器和扰动都存在长记忆的情况下，通过使用频域广义最小二乘中的平滑非参数谱估计，可以适应时间序列回归中的非参数扰动自相关。当回归量和扰动的集体记忆足够强时，普通最小二乘不仅是渐近低效的，而且是渐近非正态的，并且收敛速度较慢，而广义最小二乘是渐近正态的，并且具有标准收敛速度的高斯马尔可夫效率。尽管谱极点附近的非参数谱估计存在异常行为，但我们能够证明频域广义最小二乘法的标准构造是合理的，先前在短记忆干扰的情况下考虑了这一点。其中包括有限样本性能的小型蒙特卡罗研究。
We show that it is possible to adapt to nonparametric disturbance auto-correlation 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 behaviour 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.