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.