Linear Regression Analysis with Random Times and Long Memory Noise

In this work, we present the least square estimator for the drift parameter in a regression model driven by the increment of a fractional Brownian motion. For two different random sampling times, jittered sampling and renewal process, consistency of the estimator is shown. Simulations of the estimator, under different values of H, are provided in order to show theperformance of the proposed method for both cases.