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Unit‐root testing: on the asymptotic equivalence of Dickey–Fuller with the log–log slope of a fitted autoregressive spectrum

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  • Evangelos E. Ioannidis

Abstract

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.

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  • Evangelos E. Ioannidis, 2010. "Unit‐root testing: on the asymptotic equivalence of Dickey–Fuller with the log–log slope of a fitted autoregressive spectrum," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(3), pages 153-166, May.
    • Handle: RePEc:bla:jtsera:v:31:y:2010:i:3:p:153-166
    DOI: 10.1111/j.1467-9892.2010.00652.x
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    4. Robinson, Peter M. & Velasco, Carlos, 2000. "Whittle pseudo-maximum likelihood estimation for nonstationary time series," LSE Research Online Documents on Economics 2273, London School of Economics and Political Science, LSE Library.
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