On the consistency of the least squares estimator in models sampled at random times driven by long memory noise: the renewal case.

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