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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.

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File URL: http://hdl.handle.net/1866/466
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Bibliographic Info

Paper provided by Universite de Montreal, Departement de sciences economiques in its series Cahiers de recherche with number 9817.

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Length: 14 pages
Date of creation: 1998
Date of revision:
Handle: RePEc:mtl:montde:9817

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Keywords: Wiener ocess; Brownian bridge; distribution function; serial correlation; asymotic aroximation;

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  1. Perron, P., 1994. "The Adequacy of Asymptotic Approximations in the Near-Integrated Autoregressive Model with Dependent Errors," Cahiers de recherche 9424, Universite de Montreal, Departement de sciences economiques.
  2. Perron, P. & Ng, S., 1994. "Useful Modifications to Some Unit Root Tests with Dependent Errors and Their Local Asymptotic Properties," Cahiers de recherche 9427, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  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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