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The FCLT with Dependent Errors: an Helicopter Tour of the Quality of the Approximation

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  • PERRON, Pierre
  • MALLET, Sylvie

Abstract

This note investigates the adequacy of the finite-sample approximation provided by the Functional Central Limit Theorem (FCLT) when the errors are allowed to be dependent. We compare the distribution of the scaled partial sums of some data with the distribution of the Wiener process to which it converges. Our setup is purposely very simple in that it considers data generated from an ARMA(1,1) process. Yet, this is sufficient to bring out interesting conclusions about the particular elements which cause the approximations to be inadequate in even quite large sample sizes.

Suggested Citation

  • PERRON, Pierre & MALLET, Sylvie, 1998. "The FCLT with Dependent Errors: an Helicopter Tour of the Quality of the Approximation," Cahiers de recherche 9817, Universite de Montreal, Departement de sciences economiques.
    • Handle: RePEc:mtl:montde:9817
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    File URL: http://hdl.handle.net/1866/466
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    References listed on IDEAS

    as
    1. Perron, Pierre, 1996. "The adequacy of asymptotic approximations in the near-integrated autoregressive model with dependent errors," Journal of Econometrics, Elsevier, vol. 70(2), pages 317-350, February.
    2. Pierre Perron & Serena Ng, 1996. "Useful Modifications to some Unit Root Tests with Dependent Errors and their Local Asymptotic Properties," Review of Economic Studies, Oxford University Press, vol. 63(3), pages 435-463.
    3. Nabeya, Seiji & Perron, Pierre, 1994. "Local asymptotic distribution related to the AR(1) model with dependent errors," Journal of Econometrics, Elsevier, vol. 62(2), pages 229-264, June.
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    More about this item

    Keywords

    Wiener ocess; Brownian bridge; distribution function; serial correlation; asymotic aroximation;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C20 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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