Unit-root testing: on the asymptotic equivalence of Dickey-Fuller with the log-log slope of a fitted autoregressive spectrum
In this article we consider the problem of testing for the presence of a unit root against autoregressive alternatives. In this context we prove the asymptotic equivalence of the well-known (augmented) Dickey-Fuller test with a test based on an appropriate parametric modification of the technique of log-periodogram regression. This modification consists of considering, close to the origin, the slope (in log-log coordinates) of an autoregressively fitted spectral density. This provides a new interpretation of the Dickey-Fuller test and closes the gap between it and log-periodogram regression. This equivalence is based on monotonicity arguments and holds on the null as well as on the alternative. Finally, a simulation study provides indications of the finite-sample behaviour of this asymptotic equivalence. Copyright Copyright 2010 Blackwell Publishing Ltd
Year of publication: |
2010
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Authors: | Ioannidis, Evangelos E. |
Published in: |
Journal of Time Series Analysis. - Wiley Blackwell, ISSN 0143-9782. - Vol. 31.2010, 3, p. 153-166
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Publisher: |
Wiley Blackwell |
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freely available
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