A functional limit theorem for η -weakly dependent processes and its applications

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1 SAMOS - Statistique Appliquée et MOdélisation Stochastique 2 CES - Centre d-économie de la Sorbonne 3 Universidad Central de Venezuela

Abstract : We prove a general functional central limit theorem for weak dependent time series. A very large variety of models, for instance, causal or non causal linear, ARCH$\infty$, bilinear, Volterra processes, satisfies this theorem. Moreover, it provides numerous application as well for bounding the distance between the empirical mean and the Gaussian measure than for obtaining central limit theorem for sample moments and cumulants.

Keywords : Central limit theorem Weakly dependent processes Sample moments and cumulants

Autor: Jean-Marc Bardet - Paul Doukhan - José Rafael León -

Fuente: https://hal.archives-ouvertes.fr/

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