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Pré-Publication, Document De Travail Année : 2018

Adaptive nonparametric drift estimation of an integrated jump diffusion process

Benedikt Funke
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Émeline Schmisser
  • Fonction : Auteur
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Résumé

In the present article, we investigate nonparametric estimation of the unknown drift function b in an integrated Lévy driven jump diffusion model. Our aim will be to estimate the unknown drift function on a compact set based on a high-frequency data sample. Instead of observing the jump-diffusion process V itself, we observe a discrete and high-frequent sample of the integrated process Xt := t 0 Vsds. Based on the available observations of (Xt), we will construct an adaptive penalized least-squares estimate in order to compute an adaptive estimator of the corresponding drift function b. Under appropriate assumptions, we will bound the L 2-risk of our proposed estimator. Moreover , we study the behavior of the proposed estimator in various Monte Carlo simulation setups.
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Dates et versions

hal-01528644 , version 1 (29-05-2017)
hal-01528644 , version 2 (08-01-2018)

Identifiants

  • HAL Id : hal-01528644 , version 2

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Benedikt Funke, Émeline Schmisser. Adaptive nonparametric drift estimation of an integrated jump diffusion process. 2018. ⟨hal-01528644v2⟩
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