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Valid Locally Uniform Edgeworth Expansions Under Weak Dependence and Sequences of Smooth Transformations

Author

Listed:
  • Stelios Arvanitis
  • Antonis Demos

    (www.aueb.gr/users/demos)

Abstract

In this paper we are concerned with the issue of the existence of locally uniform Edgeworth expansions for the distributions of parameterized random vectors. Our motivation resides on the fact that this could enable subsequent polynomial asymptotic expansions of moments. These could be useful for the establishment of asymptotic properties for estimators based on these moments. We derive sufficient conditions either in the case of stochastic processes exhibiting weak dependence, or in the case of smooth transformations of such expansions.

Suggested Citation

  • Stelios Arvanitis & Antonis Demos, 2012. "Valid Locally Uniform Edgeworth Expansions Under Weak Dependence and Sequences of Smooth Transformations," DEOS Working Papers 1229, Athens University of Economics and Business, revised 24 Aug 2012.
    • Handle: RePEc:aue:wpaper:1229
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    File URL: http://wpa.deos.aueb.gr/docs/Unif-Edg-fin-wp.pdf
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    References listed on IDEAS

    as
    1. Gourieroux, C & Monfort, A & Renault, E, 1993. "Indirect Inference," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages 85-118, Suppl. De.
    2. repec:aue:wpaper:1214 is not listed on IDEAS
    3. Demos, Antonis & Arvanitis, Stelios, 2010. "Stochastic Expansions and Moment Approximations for Three Indirect Estimators," MPRA Paper 122369, University Library of Munich, Germany.
    4. Magdalinos, Michael A., 1992. "Stochastic Expansions and Asymptotic Approximations," Econometric Theory, Cambridge University Press, vol. 8(3), pages 343-367, September.
    5. Corradi, Valentina & Iglesias, Emma M., 2008. "Bootstrap refinements for QML estimators of the GARCH(1,1) parameters," Journal of Econometrics, Elsevier, vol. 144(2), pages 500-510, June.
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    Cited by:

    1. Antonis Demos & Stelios Arvanitis, 2012. "On the Validity of Edgeworth Expansions and Moment Approximations for Three Indirect Estimators (Extended Revised Appendix)," DEOS Working Papers 1230, Athens University of Economics and Business.
    2. Antonis Demos & Stelios Arvanitis, 2012. "Stochastic Expansions and Moment Approximations for Three Indirect Estimators Revised (Extended Appendix)," DEOS Working Papers 1215, Athens University of Economics and Business.
    3. Arvanitis Stelios & Demos Antonis, 2018. "On the Validity of Edgeworth Expansions and Moment Approximations for Three Indirect Inference Estimators," Journal of Econometric Methods, De Gruyter, vol. 7(1), pages 1-38, January.
    4. Arvanitis Stelios & Demos Antonis, 2014. "Valid Locally Uniform Edgeworth Expansions for a Class of Weakly Dependent Processes or Sequences of Smooth Transformations," Journal of Time Series Econometrics, De Gruyter, vol. 6(2), pages 183-235, July.

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    More about this item

    Keywords

    Locally uniform Edgeworth expansion; formal Edgeworth distribution; weak dependence; smooth transformations; moment approximations; GMM estimators; Indirect estimators; GARCH model;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

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