The Autocorrelation Function (ACF) was originally studied as a tool for analyzing dependence for Gaussian time series and linear models. The consistent ACF estimator (the sample autocorrelation) is commonly used. A well known theorem defines the asymptotical behavior of the estimator for a white noise process. Nevertheless, this result does not hold when the ACF estimator is computed for the squares of the process. In the present work we present the results of the analysis of the estimated ACF computed for different white noise processes and their squares such as the Student’s t, the exponential power white noise and the mixture of Gaussian white noises.