The FCLT with Dependent Errors: an Helicopter Tour of the Quality of the Approximation
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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- 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.
- 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.
- Perron, P., 1994. "The Adequacy of Asymptotic Approximations in the Near- Integrated Autoregressive Model with Dependent Errors," Cahiers de recherche 9424, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
- 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.
- Nabeya, S. & Perron, P., 1991.
"Local Asymtotic Distributions Related to the AR(1) MOdel with Dependent Errors,"
362, Princeton, Department of Economics - Econometric Research Program.
- 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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