For a stationary process , the sample auto covariance function (ACVF) and sample autocorrelation function (ACF) are basic quantities used for inference. When the variance of is finite, ACVF and ACF converge to auto covariance function and autocorrelation function respectively almost surely. However, the behavior can be quite different in the heavy tailed. In thesis this behavior for symmetric - stable random process is considered. Specially a null recurrent Markov chain is associated whit a stationary mixing rocess. The resulting process exhibit such strong dependence that ACVF grows at a surprising rate which is slows than one would expect and ACF converges to non random limit.
