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Some recent results fornon-linear processes with long range dependence

François Roueff 1, 2 
1 S2A - Signal, Statistique et Apprentissage
LTCI - Laboratoire Traitement et Communication de l'Information
Abstract : Linear processes with long range dependence are obtained by linear filtering of white noise using a fractional integration operator. Integrated on large scales, such processes can be approximated by a fractional Brownian motion. In the non-linear case, with similar second-order properties, such an approximation no longer holds. We will recall different limit distributions that may appear in the large scale asymptotic, depending on the type of non-linearity. The goal of this talk is to present recent results applying to non-linear long range dependent processes that go beyond the large scale approximation. For instance, we will answer the following question: is the large scale approximation sufficient to determine the asymptotic behavior of standard estimators of the long memory parameter ?
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Submitted on : Friday, September 13, 2019 - 3:39:39 PM
Last modification on : Tuesday, October 19, 2021 - 11:16:12 AM


  • HAL Id : hal-02286371, version 1



François Roueff. Some recent results fornon-linear processes with long range dependence. IWAP 2012 (workshop), Aug 2012, Jerusalem, Israel. ⟨hal-02286371⟩



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