| Université Paris 6 Pierre et Marie Curie | Université Paris 7 Denis Diderot | |
| CNRS U.M.R. 7599 | ||
| ``Probabilités et Modèles Aléatoires'' | ||
Auteur(s):
Code(s) de Classification MSC:
Résumé: In this paper, we study the problem of non parametric estimation of a stochastic volatility model $h_t=\exp(X_t/2)\xi_t, \; X_t=m(X_{t-1}) +\eta_t$ and show that an adaptation of the Kernel estimator proposed by Fan and Truong (1993) estimates the function $m$ with the optimal rate depending on the law of the noise. As those rates vary from powers of $n$ to powers of $\ln(n)$ depending on the characteristic function of the noise, we study the laws for $\xi$ leading to each kind of rates.
Mots Clés: Kernel estimator ; Stochastic volatility model ; Errors-in-variables model
Date: 2000-01-21
Prépublication numéro: PMA-560
Revised version, 2001-01-15 : PMA-560bis.dvi