Corrigendum: A self-normalized approach to confidence interval construction in time series
Article first published online: 12 OCT 2010
© 2010 Royal Statistical Society
Journal of the Royal Statistical Society: Series B (Statistical Methodology)
Volume 72, Issue 5, pages 695–696, November 2010
How to Cite
Shao, X. (2010), Corrigendum: A self-normalized approach to confidence interval construction in time series. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 72: 695–696. doi: 10.1111/j.1467-9868.2010.00754.x
- Issue published online: 12 OCT 2010
- Article first published online: 12 OCT 2010
Vol. 72, Issue 3, 343–366, Article first published online: 20 MAY 2010
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 .
Then theorem 1 holds under assumption 1 and this assumption 2. The problem lies in the derivation of the limiting distribution of WN. Let
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.
Consequently, to verify assumption 2 in remark 1 on page 346 for the smooth function model, we need to impose the assumption that and the absolute summability condition on the jth-order cumulants of Yt, j=2,3,4. Furthermore, the assumptions on and in theorem 2 on page 351 should be changed to
- (a)Rnn=op(n−1/2) and and
- (b)and respectively. A revised version of the manuscript can be found at http://arxiv.org/PS_cache/arxiv/pdf/1005/1005.2137v1.pdf.