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In this paper we consider quantile and Bahadur-Kiefer processes for longrange dependent linear sequences. These processes, unlike in previous studies,are considered on the whole interval $(0,1)$. As it is well-known, quantileprocesses can have very erratic behavior on the tails. We overcome this problemby considering these processes with appropriate weight functions. In this waywe conclude strong approximations that yield some remarkable phenomena that arenot shared with i.i.d. sequences, including weak convergence of theBahadur-Kiefer processes, a different pointwise behavior of the general anduniform Bahadur-Kiefer processes, and a somewhat "strange" behavior of thegeneral quantile process.

Reduction principles for quantile and Bahadur-Kiefer processes of long-range dependent linear sequences