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In this paper I identify a condition on the finite dimensional copulas of a univariate time series that ensures the series is weakly dependent in the sense of Doukhan and Louhichi (1999). This condition relates to the Kolmogorov-Smirnov distance between the joint copula of a group of variables in the past and a group of variables in the future, and the(More)
We state a multidimensional Functional Central Limit Theorem for weakly dependent random vectors. We apply this result to copulas. We get the weak convergence of the empirical copula process and of its smoothed version. The finite dimensional convergence of smoothed copula densities is also proved. A new definition and the theoretical analysis of(More)
We give an introduction to a notion of weak dependence which is more general than mixing and allows to treat for example processes driven by discrete innovations as they appear with time series bootstrap. As a typical example, we analyze autoregressive processes and their bootstrap analogues in detail and show how weak dependence can be easily derived from(More)
Doukhan and Louhichi (1999) introduced a new concept of weak dependence which is more general than mixing. Such conditions are particularly well suited for deriving estimates for the cumulants of sums of random variables. We employ such cumulant estimates to derive inequalities of Bernstein and Rosenthal type which both improve on previous results.(More)
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(More)
– We discuss the asymptotic behavior of weighted empirical processes of stationary linear random fields in Z with long-range dependence. It is shown that an appropriately standardized empirical process converges weakly in the uniform-topology to a degenerated process of the form fZ, where Z is a standard normal random variable and f is the marginal(More)
We give rates of convergence in the strong invariance principle for stationary sequences satisfying some projective criteria. The conditions are expressed in terms of conditional expectations of partial sums of the initial sequence. Our results apply to a large variety of examples. We present some applications to a reversible Markov chain, to symmetric(More)
The purpose of this chapter is to propose a unified framework for the study of ARCH(∞) processes that are commonly used in the financial econometrics literature. We extend the study, based on Volterra expansions, of univariate ARCH(∞) processes by Giraitis et al. [GKL00] and Giraitis and Surgailis [GS02] to the multi-dimensional case. Let {ξt}t∈Z be a(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)
A nite range interacting particle system on a transitive graph is considered. Assuming that the dynamics and the initial measure are invariant, the normalized empirical distribution process converges in distribution to a centered di usion process. As an application, a central limit theorem for certain hitting times, interpreted as failure times of a(More)