Kink estimation with correlated noise

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 f in the presence of noise that exhibits long-range dependence (LRD). The method is based on the zero-crossing technique and makes use of high-order kernels. The effect of LRD is seen to be detrimental to the rate of convergence. Using a fractional integration operator we draw a parallel with certain inverse problems which suggests optimality of our approach. The kink location and estimation technique is demonstrated on some simulated data and the detrimental effect of LRD is shown. We also apply our kink analysis on Australian temperature data.