Econ Papers Daily / 期刊论文
时间序列回归的可行广义最小二乘法
Feasible GLS for time series regression
摘要
We consider GLS and OLS estimation in a linear regression model with serially correlated errors, and we provide the following contributions. First, we clarify when OLS is consistent or not. Second, we give sufficient conditions such that GLS is valid without the assumption of exogenous regressors (uncorrelated with past innovations). Third, we devise a feasible GLS procedure valid whether or not the regressors are exogenous, and which achieves a MSE close to that of the correctly specified infeasible GLS. Fourth, we derive the asymptotic distribution of this feasible GLS estimate: with exogenous regressors, the limit distribution is the same as that of the infeasible GLS estimator. However, with non-exogenous regressors, an additional term is present in the asymptotic variance. We provide a variance estimator, free of tuning parameters, which delivers confidence intervals with asymptotically correct coverage in both cases. We also illustrate how GLS can be more robust than OLS when the regressors are exogenous, even when GLS is based on an incorrect correction. The main assumptions are: a) the regressors are pre-determined (uncorrelated with future innovations); b) the errors are stationary thereby admitting a Wold representation in terms of some unpredictable innovations; c) the moving-average representation of the errors is invertible and implies a short-memory process. We also briefly address issues related to heteroskedastic errors.
中文摘要
我们考虑在误差项存在序列相关的线性回归模型中的GLS和OLS估计，并提供以下贡献。第一，我们阐明OLS何时一致或不一致。第二，我们给出充分条件，使得GLS在无需外生回归元（与过去新息不相关）假设的情况下仍然有效。第三，我们设计一种可行的GLS程序，无论回归元是否为外生均有效，并且其MSE接近正确设定的不可行GLS的MSE。第四，我们推导该可行GLS估计的渐近分布：在回归元为外生时，极限分布与不可行GLS估计量的极限分布相同。然而，在回归元非外生时，渐近方差中会出现一个额外项。我们提供一个无需调优参数的方差估计量，它在两种情形下都能给出渐近正确覆盖率的置信区间。我们还说明，当回归元为外生时，即使GLS基于不正确的修正，GLS也可能比OLS更稳健。主要假设为：a）回归元是预定的（与未来新息不相关）；b）误差是平稳的，从而允许以某些不可预测的新息表示Wold表示；c）误差的移动平均表示可逆，并意味着短记忆过程。我们还简要讨论与异方差误差相关的问题。