Abstract: | Abstract. Let X 1, …, X n be a random sample from a population with a distribution function F and let E ( X 1) = 0, E ( X 12) < ∞. Let r 1=Σ t =1 n -1 X t X t +1/Σ t =1 n -1( X t 2+ X t +12). We derive a proper Edgeworth type expansion for the sampling distribution of r 1 under the assumption that F is a mixture of Gaussian distributions of one of two given types. The result can easily be extended to the sampling distributions of serial correlations of arbitrary lag s . |