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Uniform limit theorems for the integrated periodogram of weakly dependent time series and their applications to Whittle's estimate
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 -weak dependence property allows a new and unified
proof of those results for ARCH() and bilinear processes. Non causal
-weak dependence yields the same limit theorems for two-sided linear
(with dependent inputs) or Volterra processes