Optimal difference-based variance estimators in time series: A general framework
针对非恒定均值的时间序列，提出一个基于差分统计量的长期方差估计通用框架，涵盖现有估计量，给出一致性的充要条件，并推导出首个渐近最优估计量，该估计量对任意均值结构（包括趋势和间断点）具有不变性。
Variance estimation is important for statistical inference. It becomes nontrivial when observations are masked by serial dependence structures and time-varying mean structures. Existing methods either ignore or sub-optimally handle these nuisance structures. This paper develops a general framework for the estimation of the long-run variance for time series with nonconstant means. The building blocks are difference statistics. The proposed class of estimators is general enough to cover many existing estimators. Necessary and sufficient conditions for consistency are investigated. The first asymptotically optimal estimator is derived. Our proposed estimator is theoretically proven to be invariant to arbitrary mean structures, which may include trends and a possibly divergent number of discontinuities.