  In this article we study the estimation of the location of jump points in the
first derivative (referred to as kinks) of a regression function \mu in two
random design models with different long-range dependent (LRD) structures. The
method is based on the zero-crossing technique and makes use of high-order
kernels. The rate of convergence of the estimator is contingent on the level of
dependence and the smoothness of the regression function \mu. In one of the
models, the convergence rate is the same as the minimax rate for kink
estimation in the fixed design scenario with i.i.d. errors which suggests that
the method is optimal in the minimax sense.
