Uniform Limit Theorems for the Integrated Periodogram of Weakly Dependent Time Series and their Applications to Whittle's Estimate

Jean-Marc Bardet, Paul Doukhan and José Rafael Leon_
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Jean-Marc Bardet: Crest
Paul Doukhan: Crest
José Rafael Leon_: Crest

No 2005-46, Working Papers from Center for Research in Economics and Statistics

Abstract: We prove uniform convergence results such as a law of large numbers and a central limit theorem for the integrated periodogram of a weak dependent time series. Those probabilistic results are used for Whittle's parametric estimation. Using a general weakly dependent frame, we derive results for a large variety of models; with causal weak dependence, we consider examples as GARCH(p,q), ARCH(8) or, more generally, bilinear models. Non-causal weak dependence is also considered yielding for instance the new case of a non-causal linear or ARCH(8) model.

Pages: 28
Date: 2005
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