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Article Dans Une Revue Statistical Inference for Stochastic Processes Année : 2008

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

Résumé

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.
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Dates et versions

hal-00126530 , version 1 (25-01-2007)

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Jean-Marc Bardet, Paul Doukhan, José Rafael León. A functional limit theorem for η -weakly dependent processes and its applications. Statistical Inference for Stochastic Processes, 2008, 11 (3), pp.265-280. ⟨10.1007/s11203-007-9015-y⟩. ⟨hal-00126530⟩
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