This paper is concerned with the discrete time stochastic volatility model Yi=exp(Xi/2)[eta]i, Xi+1=b(Xi)+[sigma](Xi)[xi]i+1, where only (Yi) is observed. The model is rewritten as a particular hidden model: Zi=Xi+[epsilon]i, Xi+1=b(Xi)+[sigma](Xi)[xi]i+1, where ([xi]i) and ([epsilon]i) are...

We provide in this paper asymptotic theory for the multivariate GARCH(p,q) process. Strong consistency of the quasi-maximum likelihood estimator (MLE) is established by appealing to conditions given by Jeantheau (Econometric Theory 14 (1998), 70) in conjunction with a result given by Boussama...

In this paper, we study new definitions of noncausality, set in a continuous time framework, illustrated by the intuitive example of stochastic volatility models. Then, we define CIMA processes (i.e., processes admitting a continuous time invertible moving average representation), for which...

In this paper, we consider a stochastic volatility model ("Y"_"t", "V"_"t"), where the volatility (V_"t") is a positive stationary Markov process. We assume that ("ln""V"_"t") admits a stationary density "f" that we want to estimate. Only the price process "Y"_"t" is observed at "n" discrete times...

In this paper, we study nonparametric estimation of the Lévy density for pure jump Lévy processes. We consider n discrete time observations with step [Delta]. The asymptotic framework is: n tends to infinity, [Delta]=[Delta]n tends to zero while n[Delta]n tends to infinity. First, we use a...

In this paper, we study the problem of nonparametric estimation of the mean and variance functions b and [sigma]2 in a model: Xi+1=b(Xi)+[sigma](Xi)[var epsilon]i+1. For this purpose, we consider a collection of finite dimensional linear spaces. We estimate b using a mean squares estimator built...