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Article Dans Une Revue Statistics & Risk Modeling with Applications in Finance and Insurance Année : 2021

Kernel estimation for Lévy driven stochastic convolutions

Fabienne Comte
Valentine Genon-Catalot
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Résumé

We consider a Lévy driven stochastic convolution, also called continuous time Lévydriven moving average model, X(t) = t 0 a(t − s)dZ(s) where Z is a Lévy martingale and the kernel a(.) a deterministic function square integrable on R +. Given N i.i.d. continuous time observations (Xi(t)) t∈[0,T ] on [0, T ], for i = 1,. .. , N distributed like (X(t)) t∈[0,T ] , we propose two types of nonparametric projection estimators of a 2 under dierent sets of assumptions. We bound the L 2-risk of the estimators and propose a data-driven procedure to select the dimension of the projection space, illustrated by a short simulation study.
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Dates et versions

hal-03140184 , version 1 (12-02-2021)
hal-03140184 , version 2 (04-03-2021)
hal-03140184 , version 3 (14-07-2021)

Identifiants

Citer

Fabienne Comte, Valentine Genon-Catalot. Kernel estimation for Lévy driven stochastic convolutions. Statistics & Risk Modeling with Applications in Finance and Insurance, 2021, 38 (1-2), pp.1-24. ⟨10.1515/strm-2021-0007⟩. ⟨hal-03140184v3⟩
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