: In this thesis, we present an expanded account of stable time series based on an article by Feigin and Resnick (1993). The most important problem for considering behavior of a time series is fitting an appropariate model to it. In dir=ltr In type="#_x0000_t75" is Gaussian or non-gaussian with finite variance then given large values with loss probability. But in this case, { has infinite variance . Same as type="#_x0000_t75" There exist variation in usual methods foe dir=ltr Also a natural model to attempt to fit to time series data is an autoregression of order p, where p itself is often determind from the data. Several methods of parameter estimation for heavy tailed autoregressions have been considered, including Yule-Walker estimation, linear programming estimators and periodogram based estimators. We investigate the statistical pitfalls of the first two methods when the models are mis-specified either completely or due to the presence of outliers. So a warning is sounded against the assumption that autoregressions will be an applicable dir=ltr The structure of this thesis is as follows. A brief history of stable time series are gathered in chapter one. In chapter two explain an introduction of time series and in chapter three, introduction of stable random variables are studied. In chapter four explain LP estimators and in chapter five discus the stable time series . Finally in chapter six using R, Splus and Lingo softwares, examples of stable time series are simulated.