Strong consistency and asymptotic normality of the Quasi-Maximum Likelihood Estimator (QMLE) are given for a general class of multidimensional causal processes. For particular cases already studied in the literature (for instance univariate or multivariate GARCH, ARCH, ARMA-GARCH processes) the assumptions required for establishing these results are often weaker than existing conditions. The QMLE asymptotic behavior is also given for numerous new examples of univariate or multivariate processes (for instance TARCH or NLARCH processes).corresponds to the BEKK representation of multivariate GARCH(q, q ′ ) defined by Engle and Kroner [13], see also Bollerslev [4]. Their natural generalization,defines the multivariate ARCH(∞) processes. If M θ ≡ I d , a process X satisfying relation (1.1) is a multivariate Non Linear AR(∞) process.Various methods can be employed to estimate the unknown parameter θ 0 . Maximum Likelihood Estimation (MLE) is a common one. Several authors studied the asymptotic behavior of MLE for particular cases of multivariate processes satisfying (1.1), see for instance Bollerslev and Wooldridge [5], Jeantheau [19] for multivariate GARCH(q, q ′ ) processes and Dunsmuir and Hannan [11], Mauricio [22] for multivariate ARMA processes. A proof of the efficiency of those estimators was obtained in Berkes and Horváth [1], in the case of one-dimensional GARCH(q, q ′ ). Even if the convergence rate

The prognosis for patients with propionic acidaemia appeared to be satisfactory in terms of survival and outcome characteristics such as neurological and mental development. Despite these results the authors feel that the prognosis and quality of life of these patients might be improved with liver transplantation or possibly somatic gene therapy in the future.

A method for testing for the presence of self-similarity of a Gaussian time series with stationary increments is presented. The test is based on estimation of the distance between the time series and a set of time series containing all the fractional Brownian motions. This distance is constructed from two estimations of multiscale generalized quadratic variations expectations. The second one requires regression estimates of the self-similarity index H. Two estimations of H are then introduced. They present good robustness and computing time properties compared with the Whittle approach, with nearly similar convergence rate. The test is applied on simulated and real data. The self-similarity assumption is notably accepted for the famous Nile River data.

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Abstract.In this paper, a very useful lemma (in two versions) is proved: it simplifies notably the essential step to establish a Lindeberg central limit theorem for dependent processes. Then, applying this lemma to weakly dependent processes introduced in Doukhan and Louhichi (1999), a new central limit theorem is obtained for sample mean or kernel density estimator. Moreover, by using the subsampling, extensions under weaker assumptions of these central limit theorems are provided. All the usual causal or non causal time series: Gaussian, associated, linear, ARCH(∞), bilinear, Volterra processes, . . ., enter this frame.Mathematics Subject Classification. 60F05, 62G07, 62M10, 62G09.