In this talk 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 so called zero-crossing technique and makes use of a high-order kernel smoothing approach. 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. Time permitting, the Wavelet-Deconvolution approach to a similar problem will be discussed which has potential for further applications by estimating the location of jumps in higher order derivatives of $\mu$ (not just the first derivative).