Valid Locally Uniform Edgeworth Expansions Under Weak Dependence and Sequences of Smooth Transformations Stelios Arvanitis and Antonis Demos Athens University of Economics and Business March 2012 Abstract In this paper we are concerned with the issue of the existence of locally uniform Edgeworth expansions for the distributions of random vectors. Our motivation resides on the fact that this could enable subsequent uniform approximations of analogous moments and their derivatives. We derive su¢cient conditions either in the case of sto- chastic processes exhibiting weak dependence, or in the case of smooth transformations of such expansions. The combination of the results can lead to the establishment of high order asymptotic properties for estimators of interest. KEYWORDS: Locally uniform Edgeworth expansion, formal Edge- worth distribution, weak dependence, smooth transformations, mo- ment approximations, GMM estimators, Indirect estimators, GARCH model. JEL: C10, C13 1 Introduction In this paper we are concerned with the issue of the approximation of the distributions of a sequence of random vectors by sequences of Edgeworth dis- tributions uniformly with respect to a compact valued Euclidean parameter. Our motivation resides on the fact that this could enable subsequent uniform approximations of analogous moments and their derivatives with respect to the aforementioned parameter. This in turn can facilitate the extraction of higher order asymptotic properties of estimators that are dened by the 1