Subsample-based estimation is a standard tool for achieving robustness to outliers in econometric models. This paper shows that, in dynamic time series settings, such procedures are fundamentally invalid under contamination, even under oracle knowledge of contamination locations. The key issue is that contamination propagates through the model's residual filter and distorts the estimation criterion itself. As a result, removing contaminated observations does not, in general, restore the uncontaminated objective or ensure consistency. We characterise this failure as a structural incompatibility between pointwise subsampling and residual propagation. To address it, we propose a propagation-compatible transformation of index sets, formalised through a patch removal operator that removes the residual footprint of contamination. Under suitable conditions, the proposed operator leaves the estimator asymptotically unchanged under the uncontaminated model, while restoring consistency for the clean-data parameter under contamination. The results apply to a broad class of residual-based estimators and show that valid subsample-based estimation in dynamic models requires explicit control of residual propagation.

翻译：基于子样本的估计是计量经济模型中实现稳健性以抵抗异常值的标准工具。本文表明，在动态时间序列设定下，即使已知污染位置，这种程序在污染条件下从根本上无效。关键问题在于污染通过模型的残差过滤器传播，并扭曲了估计准则本身。因此，移除污染观测通常无法恢复无污染目标函数或确保一致性。我们将这种失败刻画为逐点子采样与残差传播之间的结构不兼容性。为解决这一问题，我们提出一种传播兼容的索引集变换，通过一个补丁移除算子形式化实现，该算子可消除污染的残差足迹。在适当条件下，所提出的算子在无污染模型下使估计量渐近不变，同时在污染条件下恢复干净数据参数的一致性。该结果适用于一大类基于残差的估计量，并表明动态模型中的有效子样本估计需要显式控制残差传播。