We prove uniform convergence results like a law of large numbers and a central limit theoremfor the integrated periodogram of a weak dependent time series. Those probabilistic results areused for Whittle’s parametric estimation. Using a general weakly dependent frame, we derivenew results,...

We prove a general functional central limit theorem for weak dependent time series. Those probabilisticresults are for a large variety of models. For instance, ARCH(1) and bilinear processes, andtwo sided linear, bilinear and ARCH(1) processes.

This paper is aimed at sharpen a weak invariance principle for stationary sequencesin Doukhan & Louhichi (1999). Our assumption is both beyond mixing and the causal-weak dependence in Dedecker and Doukhan (2003); those authors obtained a sharpresult which improves on an optimal one in Doukhan et...

A set of binary random variables indexed by a lattice torus is considered. Undera mixing hypothesis, the probability of any proposition belonging to the rst orderlogic of colored graphs tends to 0 or 1, as the size of the lattice tends to innity.For the particular case of the Ising model with...

Weak dependence properties of ARCH-type bilinear models as introduced by Doukhanand Louhichi (1999) is investigated here. Those models are usually considered for their longrange dependence properties, see Giraitis and Surgailis (2002). Decay of the weak dependencecoefficient sequence are...