We prove uniform convergence results for the integrated periodogram of a weakly dependent time series, namely a strong law of large numbers and a central limit theorem. These results are applied to Whittle's parametric estimation. Under general weak-dependence assumptions, the strong consistency...

We use a new weak dependence condition from Doukhan and Louhichi (Stoch. Process. Appl. 1999, 84, 313-342) to provide a central limit theorem for triangular arrays; this result applies for linear arrays (as in Peligrad and Utev, Ann. Probab. 1997, 25(1), 443-456) and standard kernel density...

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...