Communication Dans Un Congrès Année : 2013

Equivalence for nonparametric drift estimation of a diffusion process and its Euler scheme

Résumé

At first consider a stationary and ergodic stochastic process which fulfills a nonparametric diffusion model driven by a Brownian motion. Our aim is the estimation of the unknown drift and volatility functions using a discrete high-frequency sample. Motivated by Bandi and Phillips, [1], we use Nadaraya-Watson like estimators and extend their results to bandwidths which depend on the available sample. Using a specific bandwidth, we can reach a faster rate of convergence of the bias term of our estimators. Furthermore, we prove asymptotic properties like consistency and asymptotic normality. Afterwards we consider a more general model, which is driven by an α-stable Lévy motion. Again we make use of a Nadaraya-Watson like estimator for the unknown drift function. Under comparable assumptions we prove the corresponding asymptotic properties. A short simulation study illustrates our results.

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hal-02748689 , version 1 (03-06-2020)

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  • HAL Id : hal-02748689 , version 1
  • PRODINRA : 192355

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Catherine Laredo, Valentine Genon-Catalot. Equivalence for nonparametric drift estimation of a diffusion process and its Euler scheme. DYNSTOCH 2013, Apr 2013, Copenhagen, Denmark. pp.43. ⟨hal-02748689⟩
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