The Asymptotic Locations of the Maximum and Minimum of Stationary Sequences

Journal of Statistical Planning and Inference, 104(2) (2002), 287-295
http://dx.doi.org/10.1016/S0378-3758(01)00259-2

We show that the normalized first location of the maximum of a stationary sequence satisfying a long-range dependence condition converges to a uniform variable on [0,1] and is asymptotically independent of the height of the maximum. Additional conditions are given in order to obtain the asymptotic independence of the locations of maximum and minimum.