Statistical independence: Suppose that Aj and Bk are the possible outcomes of two successive experiments or the joint outcome of a single experiment. And suppose that it turns out that the probability of the occurrence of outcome Bk simply does not depend at all on which outcome Aj accompanies it. Then we say that the outcomes Aj and Bk are independent. Auto correlation also implies comparison of two signals of same source. Hence for random Gaussian process. Auto correlation also implies statistical independence.