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


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(∞), LARCH(∞), Volterra processes, satisfies this theorem. Moreover, it provides numerous applications 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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Author information

Correspondence to Jean-Marc Bardet.

Additional information

C. José Rafael León—Partially supported by the program ECOS-NORD of Fonacit, Venezuela.

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Bardet, J., Doukhan, P. & León, J.R. A functional limit theorem for η-weakly dependent processes and its applications. Stat Infer Stoch Process 11, 265–280 (2008).

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  • Central limit theorem
  • Weakly dependent processes
  • Sample moments and cumulants

Mathematics Subject Classification

  • 60F05
  • 62F12
  • 62M10