Olivier Wintenberger

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The aim of this paper is to provide conditions which ensure that the affinely transformed partial sums of a strictly stationary process converge in distribution to an infinite variance stable distribution. Conditions for this convergence to hold are known in the literature. However, most of these results are qualitative in the sense that the parameters of(More)
Assuming that (Xn)n∈Z is a vector valued time series with a common marginal distribution admitting a density f , our aim is to provide a wide range of consistent estimators of f . We consider different methods of estimation as kernel, projection or wavelets ones. Various cases of weakly dependent series are investigated including the Doukhan & Louhichi’s(More)
We study a precise large deviation principle for a stationary regularly varying sequence of random variables. This principle extends the classical results of A.V. Nagaev [44] and S.V. Nagaev [45] for iid regularly varying sequences. The proof uses an idea of Jakubowski [28, 29] in the context of central limit theorems with infinite variance stable limits.(More)
This paper provides a probabilistic and statistical comparison of the log-GARCH and EGARCH models, which both rely on multiplicative volatility dynamics without positivity constraints. We compare the main probabilistic properties (strict stationarity, existence of moments, tails) of the EGARCH model, which are already known, with those of an asymmetric(More)
We introduce the notion of continuous invertibility on a compact set for volatility models driven by a Stochastic Recurrence Equation (SRE). We prove the strong consistency of the Quasi Maximum Likelihood Estimator (QMLE) when the optimization procedure is done on a continuously invertible domain. This approach gives for the first time the strong(More)
Abstract. The aim of this article is to refine a weak invariance principle for stationary sequences given by Doukhan & Louhichi (1999). Since our conditions are not causal our assumptions need to be stronger than the mixing and causal θ-weak dependence assumptions used in Dedecker & Doukhan (2003). Here, if moments of order > 2 exist, a weak invariance(More)
In this paper we propagate a large deviations approach for proving limit theory for (generally) multivariate time series with heavy tails. We make this notion precise by introducing regularly varying time series. We provide general large deviation results for functionals acting on a sample path and vanishing in some neighborhood of the origin. We study a(More)
We introduce the cluster index of a multivariate regularly varying stationary sequence and characterize the index in terms of the spectral tail process. This index plays a major role in limit theory for partial sums of regularly varying sequences. We illustrate the use of the cluster index by characterizing infinite variance stable limit distributions and(More)
We introduce the notion of continuous invertibility on a compact set for volatility models driven by a Stochastic Recurrence Equation (SRE). We prove in this context the strong consistency and the asymptotic normality of the M-estimator associated with the Quasi-Likelihood criteria. We recover known results on univariate and multivariate GARCH type models(More)