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:**

- 62G05 Estimation
- 62J02 General nonlinear regression

**Résumé:** In this paper we consider a semiparametric autoregressive model with
errors-in-variables and propose an estimator
of the parameters. We prove the consistency of our estimate
and give an upper bound of its rate of convergence for different laws of errors.
We show throughout several examples that our main theorem allows to
calculate a rate for
the estimator as soon as the regression function is specified. Moreover,
while the nonparametric rates can fall until order $(\log(n))^{-c}$, $c>0$,
we show that our semiparametric context can imply rates of order $n^{-c}$,with c between 0 and 1/2,
and can reach the parametric rate $n^{-1/2}$ in particular cases.
We illustrate that the discrete time stochastic volatility model is a particular case of our
general model.
Our results also
apply to a general regression model with errors-in-variables in a
context of mixing variables.

**Mots Clés:** *Errors-in-variables model ; Absolutely regular variables ; Autoregression ; Stochastic volatility model*

**Date:** 2000-07-17

**Prépublication numéro:** *PMA-606*