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NEARLY EFFICIENT LIKELIHOOD RATIO TESTS OF A UNIT ROOT IN AN AUTOREGRESSIVE MODEL OF ARBITRARY ORDER

Published online by Cambridge University Press:  20 December 2022

Samuel Brien Open the ORCID record for Samuel Brien [Opens in a new window] ,
Michael Jansson Open the ORCID record for Michael Jansson [Opens in a new window]  and
Morten Ørregaard Nielsen Open the ORCID record for Morten Ørregaard Nielsen [Opens in a new window]
Samuel Brien
Affiliation:
Queen’s University
Michael Jansson*
Affiliation:
UC Berkeley and creates
Morten Ørregaard Nielsen
Affiliation:
Aarhus University
*
Address correspondence to Michael Jansson, Department of Economics, University of California, Berkeley, 530 Evans Hall #3880, Berkeley, CA 94720, USA; e-mail: [email protected].
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Abstract

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We study large sample properties of likelihood ratio tests of the unit-root hypothesis in an autoregressive model of arbitrary order. Earlier research on this testing problem has developed likelihood ratio tests in the autoregressive model of order 1, but resorted to a plug-in approach when dealing with higher-order models. In contrast, we consider the full model and derive the relevant large sample properties of likelihood ratio tests under a local-to-unity asymptotic framework. As in the simpler model, we show that the full likelihood ratio tests are nearly efficient, in the sense that their asymptotic local power functions are virtually indistinguishable from the Gaussian power envelopes. Extensions to sieve-type approximations and different classes of alternatives are also considered.

Type
MISCELLANEA
Information
Econometric Theory , Volume 40 , Issue 5 , October 2024 , pp. 1159 - 1183
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2022. Published by Cambridge University Press

Footnotes

We are grateful to Peter Phillips, two anonymous referees, and seminar participants at Queen’s University for comments and discussion, and to the Danish National Research Foundation for financial support (DNRF Chair Grant No. DNRF154).

References

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