A theory of robust long-run variance estimation

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Long-run variance estimation can typically be viewed as the problem of estimating the scale of a limiting continuous time Gaussian process on the unit interval. A natural benchmark model is given by a sample that consists of equally spaced observations of this limiting process. The paper analyzes the asymptotic robustness of long-run variance estimators to contaminations of this benchmark model. It is shown that any equivariant long-run variance estimator that is consistent in the benchmark model is highly fragile: there always exists a sequence of contaminated models with the same limiting behavior as the benchmark model for which the estimator converges in probability to an arbitrary positive value. A class of robust inconsistent long-run variance estimators is derived that optimally trades off asymptotic variance in the benchmark model against the largest asymptotic bias in a specific set of contaminated models.

Original languageEnglish (US)
Pages (from-to)1331-1352
Number of pages22
JournalJournal of Econometrics
Issue number2
StatePublished - Dec 2007

All Science Journal Classification (ASJC) codes

  • Economics and Econometrics


  • Bias
  • Functional central limit theorem
  • Heteroskedasticity and autocorrelation consistent (HAC) variance estimation
  • Qualitative robustness


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