Let {Xk,k∈Z} be a zero mean d-dimensional stationary process, and let Sn,d=(Sn,1,Sn,2,…,Sn,d)T with Sn,h=1n∑k=1nXk,h, where Xk,h denotes the single components of {Xk,k∈Z}. Under a weak dependence condition, we show that the ellipsoid Xd2=max1≤k≤d(2k)−1/2|Sn,kTΓk−1Sn,k−k|...

We study subsampling estimators for the limit variance σ2=V ar(X1)+2∑k=2∞Cov(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...