Document describes a moving average process which have regularly varying tail probabilities with index alpha 0. The limit distribution of the sample covariance function is derived in the case that the process has a finite variance but an infinite variance but an infinite fourth moment. Furthermore, in the infinite variance case (0 alpha 2), the sample correlation function is shown to converge in distribution to the ratio of two independent stable random variables with indices alpha and alpha/2, respectively. This result immediately gives the limit distribution for the least squares estimates of the parameters in an autoregressive process. (Author)