An Invariance Principle for New Weakly Dependent Stationary Models using Sharp Moment Assumptions

Paul Doukhan and Olivier Wintenberger
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No 2005-51, Working Papers from Center for Research in Economics and Statistics

Abstract: This paper is aimed at sharpen a weak invariance principle for stationary sequences in Doukhan & Louhichi (1999). Our assumption is both beyond mixing and the causal ?-weak dependence in Dedecker and Doukhan (2003); those authors obtained a sharp result which improves on an optimal one in Doukhan {\it et alii} (1995) under strong mixing. We prove this result and we also precise convergence rates under existence of moments with order >2 while Doukhan & Louhichi (1999) assume a moment of order >4. Analogously to those authors, we use a non-causal condition to deal with some general classes of stationary and weakly dependent sequences. Besides the previously used ?- and ?-weak dependence conditions, we introduce a mixed condition, ?, adapted to consider Bernoulli shifts with dependent inputs.

Pages: 28
Date: 2005
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