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Convergency of Sample Autocovariance Function in Symmetric a-stable Processes

There are some classes of strictly stationary processes in which the sample autocovariance function (ACVF) and the sample autocorrelation (ACF) do not converge to the autocovariance and autocorrelation function of process, respectively. In this article. the growth rate of ACVF and ACF are discussed for the stationary symmetric ft-stable processes. A mixed symmetric a-stable process is introduced and it was shown that its ACF grows convergency is weaker than the stationary symmetric a-stable process.