Corrigendum: A self-normalized approach to confidence interval construction in time series

Authors

Errata

This article corrects:

  1. A self-normalized approach to confidence interval construction in time series Volume 72, Issue 3, 343–366, Article first published online: 20 May 2010

Xiaofeng Shao, Department of Statistics, University of Illinois at Urbana–Champaign, Champaign, IL 61820, USA.
E-mail: xshao@uiuc.edu

J. R. Statist. Soc. B, 72 (2010), 343–366

Assumptions 1 and 2 in the paper are not sufficient to ensure the validity of theorem 1. Assumption 2 on page 346 should be replaced by the following.

 Assumption 2.  Assume that RN=op(N−1/2) and inline image.

Then theorem 1 holds under assumption 1 and this assumption 2. The problem lies in the derivation of the limiting distribution of WN. Let

image

Note that

image

It is easy to see that I1ND ΔVqΔ follows from assumption 1 and the continuous mapping theorem. Hence it suffices to show that I3N=op(1), as it implies that I2N=op(1) by the Cauchy–Schwarz inequality. It can be shown that the relationship I3N=op(1) is directly implied by assumption 2, but not by the original assumption 2 in the paper, because the following statement is in general false.

image

Consequently, to verify assumption 2 in remark 1 on page 346 for the smooth function model, we need to impose the assumption that inline image and the absolute summability condition on the jth-order cumulants of Yt, j=2,3,4. Furthermore, the assumptions on inline image and inline image in theorem 2 on page 351 should be changed to

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