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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

    (Crest)

  • Paul Doukhan

    (Crest)

  • 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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    1. Giraitis, Liudas & Surgailis, Donatas, 0. "ARCH-type bilinear models with double long memory," Stochastic Processes and their Applications, Elsevier, vol. 100(1-2), pages 275-300, July.
    2. Robinson, P. M., 1991. "Testing for strong serial correlation and dynamic conditional heteroskedasticity in multiple regression," Journal of Econometrics, Elsevier, vol. 47(1), pages 67-84, January.
    3. Paul Doukhan & Gabriel Lang, 2002. "Rates in the Empirical Central Limit Theorem for Stationary Weakly Dependent Random Fields," Statistical Inference for Stochastic Processes, Springer, vol. 5(2), pages 199-228, May.
    4. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    5. Doukhan, Paul & Louhichi, Sana, 1999. "A new weak dependence condition and applications to moment inequalities," Stochastic Processes and their Applications, Elsevier, vol. 84(2), pages 313-342, December.
    6. Giraitis, Liudas & Robinson, Peter M., 2001. "Whittle Estimation Of Arch Models," Econometric Theory, Cambridge University Press, vol. 17(3), pages 608-631, June.
    7. Nze, Patrick Ango & Doukhan, Paul, 2004. "Weak Dependence: Models And Applications To Econometrics," Econometric Theory, Cambridge University Press, vol. 20(6), pages 995-1045, December.
    8. Giraitis, Liudas & Robinson, Peter M., 2001. "Whittle estimation of ARCH models," LSE Research Online Documents on Economics 316, London School of Economics and Political Science, LSE Library.
    9. Dedecker, Jérôme & Doukhan, Paul, 2003. "A new covariance inequality and applications," Stochastic Processes and their Applications, Elsevier, vol. 106(1), pages 63-80, July.
    10. Paul Doukhan & Olivier Wintenberger, 2005. "An Invariance Principle for New Weakly Dependent Stationary Models using Sharp Moment Assumptions," Working Papers 2005-51, Center for Research in Economics and Statistics.
    11. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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