Araya, HéctorBahamonde, NataliaFermín, Lisandro JavierRoa, TaniaTorres, Soledad2022-11-302022-11-302023http://repositoriobibliotecas.uv.cl/handle/uvscl/7222In numerous applications, data are observed at random times. Our main purpose is to study a model observed at random times that incorporates a long-memory noise process with a fractional Brownian Hurst exponent H. We propose a least squares estimator in a linear regression model with long-memory noise and a random sampling time called “jittered sampling”. Specifically, there is a fixed sampling rate 1/N, contaminated by an additive noise (the jitter) and governed by a probability density function supported in [0, 1/N]. The strong consistency of the estimator is established, with a convergence rate depending on N and the Hurst exponent. A Monte Carlo analysis supports the relevance of the theory and produces additional insights, with several levels of long-range dependence (varying the Hurst index) and two different jitter densities.LONG-MEMORY NOISELEAST SQUARES ESTIMATORRANDOM TIMESREGRESSION MODEL.Articulo10.5705/ss.202020.0323