  We prove uniform convergence results for the integrated periodogram of a
weakly dependent time series, namely a law of large numbers and a central limit
theorem. These results are applied to Whittle's parametric estimation. Under
general weak-dependence assumptions we derive uniform limit theorems and
asymptotic normality of Whittle's estimate for a large class of models. For
instance the causal $\theta$-weak dependence property allows a new and unified
proof of those results for ARCH($\infty$) and bilinear processes. Non causal
$\eta$-weak dependence yields the same limit theorems for two-sided linear
(with dependent inputs) or Volterra processes.
