Read the full paper at: http://www.scirp.org/journal/PaperInformation.aspx?PaperID=49945 DOI: 10.4236/ojs.2014.48058 Author(s) Bernardo Lagos-Álvarez, Guillermo Ferreira, Emilio Porcu ABSTRACT We consider a time series following a simple linear regression with first-order autoregressive errors belonging to the class of heavy-tailed distributions. The proposed model provides a useful generalization of the symmetrical linear regression models with independent error, since the error distribution covers both correlated innovations following a Generalized Exponential distribution. Furthermore, we derive the modified maximum likelihood (MML) estimators as an efficient alternative for estimating model parameters. Finally, we investigate the asymptotic properties of the proposed estimators. Our findings are also illustrated through a simulation study.eww140925gjr KEYWORDS Autoregressive Time Series Model, Maximum Likelihood, Modified Maximum Likelihood, Least Squares,Generalized Exponential