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

Pierre Perron and Sylvie Mallet

Cahiers de recherche from Universite de Montreal, Departement de sciences economiques

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.

Keywords: Wiener ocess; Brownian bridge; distribution function; serial correlation; asymotic aroximation (search for similar items in EconPapers)
JEL-codes: C10 C20 C21 (search for similar items in EconPapers)
Pages: 14 pages
Date: 1998
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Persistent link: https://EconPapers.repec.org/RePEc:mtl:montde:9817

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