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A Note on Asymptotic Power Calculations in Nearly Nonstationary Time Series

Published online by Cambridge University Press:  11 February 2009

Anders Rygh Swensen
Anders Rygh Swensen
Affiliation:
Central Bureau of Statistics of Norway
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Abstract

In the AR(2) model, with a double root at unity, we consider the asymptotic distribution of the likelihood ratio with respect to a nearly nonstationary alternative. It is shown how the distribution can be represented as a Radon-Nikodym derivative of an Ito process with respect to Brownian motion. Using this result, we point out how standard contiguity arguments can be applied to obtain a representation of the asymptotic power function in nearly nonstationary alternatives.

Type
Articles
Information
Econometric Theory , Volume 9 , Issue 4 , August 1993 , pp. 659 - 667
Copyright
Copyright © Cambridge University Press 1993

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