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TESTING FOR UNIT ROOTS IN THE PRESENCE OF A POSSIBLE BREAK IN TREND AND NONSTATIONARY VOLATILITY

Published online by Cambridge University Press:  25 March 2011

Giuseppe Cavaliere ,
David I. Harvey ,
Stephen J. Leybourne  and
A.M. Robert Taylor
Giuseppe Cavaliere
Affiliation:
University of Bologna
David I. Harvey*
Affiliation:
University of Nottingham
Stephen J. Leybourne
Affiliation:
University of Nottingham
A.M. Robert Taylor
Affiliation:
University of Nottingham
*
*Address correspondence to David Harvey, School of Economics, University of Nottingham, Nottingham, NG7 2RD, United Kingdom; e-mail: dave.harvey@nottingham.ac.uk.
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Abstract

We analyze the impact of nonstationary volatility on the break fraction estimator and associated trend break unit root tests of Harris, Harvey, Leybourne, and Taylor (2009) (HHLT). We show that although HHLT’s break fraction estimator retains the same large-sample properties as demonstrated by HHLT for homoskedastic shocks, the limiting null distributions of unit root statistics based around this estimator are not pivotal under nonstationary volatility. A solution to the identified inference problem, which does not require the practitioner to specify a parametric model for volatility, is provided using the wild bootstrap and is shown to perform well in practice.

Type
ARTICLES
Information
Econometric Theory , Volume 27 , Issue 5: SPECIAL ISSUE ON BOOTSTRAP AND NUMERICAL METHODS IN TIME SERIES , October 2011 , pp. 957 - 991
Copyright
Copyright © Cambridge University Press 2011

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References

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