Asymptotic expansions for sums of weakly dependent random vectors

Abstract

It is shown that formal Edgeworth expansions are valid for sums of weakly dependent random vectors. The error of approximation has ordero(n −(s−2)/2) if The strong mixing coefficients in (iii) are decreasing at an exponential rate. The above conditions can easily be checked and are often satisfied when the sequence of random vectors is a Gaussian, or a Markov, or an autoregressive process. Explicit formulas are given for the distribution of finite Fourier transforms of a strictly stationary time series.