ASYMPTOTIC EXPANSIONS FOR THE DISTRIBUTIONS OF SERIAL CORRELATIONS
Kamal C. Chanda · Journal of Time Series Analysis · 1987
Abstract. Let X1, …, Xn be a random sample from a population with a distribution function F and let E(X1) = 0, E(X12) < ∞. Let r1=Σt=1n‐1XtXt+1/Σt=1n‐1(Xt2+Xt+12). We derive a proper Edgeworth type expansion for the sampling distribution of r1 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.