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...