Establish asymptotic negligibility of score demeaning

Establish that centering the sample score and the associated sample autocovariances has asymptotically negligible effects on the HAC long-run variance estimator under the paper’s stated assumptions.

Background

The HAC estimator is defined using uncentered sample autocovariances of a truncated score process, although standard HAC procedures commonly center the score. The paper provides an order calculation suggesting that the difference between centered and uncentered versions vanishes asymptotically.

The authors explicitly label this conclusion as a conjecture rather than proving it. Resolving it would clarify whether the uncentered implementation and the centered conventional HAC estimator are asymptotically equivalent in this framework.

References

We conjecture that both types of sample de-meaning have negligible effects asymptotically under our assumptions (see \cref{sec:est-var}).

— Limited-Information Estimation of Heterogeneous Agent Models  (2608.13953 - Liu et al., 14 Aug 2026) in Appendix B, Section “Asymptotic variance estimation,” subsection “HAC”