Abstract

In this study, we prove the strong consistency of the least squares esti-mator in a random sampled linear regression model with long-memory noise and an independent set of random times given by renewal process sampling. Addition-ally, we illustrate how to work with a random number of observations up to time T = 1. A simulation study is provided to illustrate the behavior of the different terms, as well as the performance of the estimator under various values of the Hurst parameter H.