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

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  • Jean-Marc Bardet

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  • Paul Doukhan

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  • José Rafael Leon_

    (Crest)

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.

Suggested Citation

  • Jean-Marc Bardet & Paul Doukhan & José Rafael Leon_, 2005. "Uniform Limit Theorems for the Integrated Periodogram of Weakly Dependent Time Series and their Applications to Whittle's Estimate," Working Papers 2005-46, Center for Research in Economics and Statistics.
    • Handle: RePEc:crs:wpaper:2005-46
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    References listed on IDEAS

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