Université Paris 6
Pierre et Marie Curie
Université Paris 7
Denis Diderot

CNRS U.M.R. 7599
``Probabilités et Modèles Aléatoires''

Semiparametric estimation in the (auto)-regressive ß-mixing model with errors-in-variables


Code(s) de Classification MSC:

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