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

  • PERRON, Pierre
  • MALLET, Sylvie

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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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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  1. Perron, Pierre & Ng, Serena, 1996. "Useful Modifications to Some Unit Root Tests with Dependent Errors and Their Local Asymptotic Properties," Review of Economic Studies, Wiley Blackwell, vol. 63(3), pages 435-63, July.
  2. 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.
  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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