Jirak, Moritz - In: Stochastic Processes and their Applications 123 (2013) 6, pp. 1922-1946
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|...