Subsample-based Estimation under Dynamic Contamination
TLDR
Subsample-based estimation in dynamic time series fails under contamination due to residual propagation, but a new patch removal operator restores consistency.
Key contributions
- Subsample-based estimation is invalid in dynamic time series due to contamination propagating through residual filters.
- Contamination distorts the estimation criterion, making simple removal of outliers insufficient for consistency.
- Introduces a "patch removal operator" to transform index sets, explicitly controlling residual propagation.
- This operator restores consistency for clean-data parameters under contamination while maintaining asymptotic properties.
Why it matters
This paper addresses a fundamental flaw in robust estimation for dynamic models, showing why standard subsampling fails. It introduces a novel solution that ensures valid estimation, crucial for accurate econometric analysis in contaminated time series.
Original Abstract
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.
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