Estimation of the Variance of Partial Sums of Dependent Processes

Daniel Vogel, Herold Dehling, Roland Fried, Olimjon Sharipov, Max Wornowizki

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)


We study subsampling estimators for the limit variance σ2=V ar(X1)+2∑∞k=2Cov(X1,Xk) of partial sums of a stationary stochastic process (Xk)k≥1. We establish L2-consistency of a non-overlapping block resampling method. Our results apply to processes that can be represented as functionals of strongly mixing processes. Motivated by recent applications to rank tests, we also study estimators for the series V ar(F(X1))+2∑∞k=2Cov(F(X1),F(Xk)), where F is the distribution function of X1. Simulations illustrate the usefulness of the proposed estimators and of a mean squared error optimal rule for the choice of the block length.
Original languageEnglish
Pages (from-to)141-147
Number of pages7
JournalStatistics and Probability Letters
Issue number1
Early online date23 Aug 2012
Publication statusPublished - Jan 2013

Bibliographical note

The authors were supported in part by the Collaborative Research Grant 823, Project C3 Analysis of Structural Change in Dynamic Processes, of the German Research Foundation.


  • Variance extimation
  • Weakly dependent Processes
  • Subsampling techniques
  • Central limit theorem
  • Functionals of mixing processes


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