An invariance principle for weakly dependent stationary general models

Abstract

The aim of this article is to refine a weak invariance principle for stationary sequences given by Doukhan & Louhichi (1999). Since our conditions are not causal our assumptions need to be stronger than the mixing and causal $\theta$-weak dependence assumptions used in Dedecker & Doukhan (2003). Here, if moments of order $>2$ exist, a weak invariance principle and convergence rates in the CLT are obtained; Doukhan & Louhichi (1999) assumed the existence of moments with order $>4$. Besides the previously used $\eta$- and $\kappa$-weak dependence conditions, we introduce a weaker one, $\lambda$, which fits the Bernoulli shifts with dependent inputs.

30 pages

References in corpus (2)

• Invariance principle for stochastic processes with short memory
• Strong invariance principle for dependent random fields

Cited by in corpus (3)

• Augmented GARCH sequences: Dependence structure and asymptotics
• The notion of $\psi$-weak dependence and its applications to bootstrapping time series
• Aggregation of weakly dependent doubly stochastic processes