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Valid Locally Uniform Edgeworth Expansions for a Class of Weakly Dependent Processes or Sequences of Smooth Transformations

Author

Listed:
  • Arvanitis Stelios

    (Department of Economics, AUEB, Patision 76, Athens 10434, Greece)

  • Demos Antonis

    (Department of IEES, AUEB, Patision 76, Athens 10434, Greece)

Abstract

This article examines the existence of locally uniform Edgeworth expansions for the distributions of parameterized random vectors. This could be useful for the establishment of high-order asymptotic properties for estimators and test statistics that are potentially based on moments of those vectors. We derive sufficient conditions either in the case of stationary stochastic processes exhibiting weak dependence or in the case of smooth transformations of such expansions.

Suggested Citation

  • 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.
    • Handle: RePEc:bpj:jtsmet:v:6:y:2014:i:2:p:53:n:1
    DOI: 10.1515/jtse-2012-0003
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    References listed on IDEAS

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    1. 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.
    2. Phillips, Peter C.B. & Magdalinos, Tassos, 2007. "Limit theory for moderate deviations from a unit root," Journal of Econometrics, Elsevier, vol. 136(1), pages 115-130, January.
    3. Andrews, Donald W.K. & Lieberman, Offer, 2005. "Valid Edgeworth Expansions For The Whittle Maximum Likelihood Estimator For Stationary Long-Memory Gaussian Time Series," Econometric Theory, Cambridge University Press, vol. 21(4), pages 710-734, August.
    4. Iglesias, Emma M. & Linton, Oliver B., 2007. "Higher Order Asymptotic Theory When A Parameter Is On A Boundary With An Application To Garch Models," Econometric Theory, Cambridge University Press, vol. 23(6), pages 1136-1161, December.
    5. Andrews, Donald W.K., 2002. "EQUIVALENCE OF THE HIGHER ORDER ASYMPTOTIC EFFICIENCY OF k-STEP AND EXTREMUM STATISTICS," Econometric Theory, Cambridge University Press, vol. 18(5), pages 1040-1085, October.
    6. Phillips, Peter C B & Park, Joon Y, 1988. "On the Formulation of Wald Tests of Nonlinear Restrictions," Econometrica, Econometric Society, vol. 56(5), pages 1065-1083, September.
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    Cited by:

    1. Stelios Arvanitis & Antonis Demos, 2015. "A class of indirect inference estimators: higher‐order asymptotics and approximate bias correction," Econometrics Journal, Royal Economic Society, vol. 18(2), pages 200-241, June.

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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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