Testing for Unit Roots in the Presence of a Possible Break in Trend and Non-Stationary Volatility

CREATES Research Paper No. 2008-62

44 Pages Posted: 2 Dec 2008

See all articles by Giuseppe Cavaliere

Giuseppe Cavaliere

University of Bologna - Department of Economics

David I. Harvey

University of Nottingham - School of Economics

Stephen J. Leybourne

University of Nottingham

A. M. Robert Taylor

University of Nottingham - School of Economics

Date Written: December 2, 2008

Abstract

In this paper we analyse the impact of non-stationary volatility on the recently developed unit root tests which allow for a possible break in trend occurring at an unknown point in the sample, considered in Harris, Harvey, Leybourne and Taylor (2008) [HHLT]. HHLT's analysis hinges on a new break fraction estimator which, when a break in trend occurs, is consistent for the true break fraction at rate Op(T=1). Unlike other available estimators, however, when there is no trend break HHLT's estimator converges to zero at rate Op(T1=2). In their analysis HHLT assume the shocks to follow a linear process driven by IID innovations. Our first contribution is to show that HHLT's break fraction estimator retains the same consistency properties as demonstrated by HHLT for the IID case when the innovations display non-stationary behaviour of a quite general form, including, for example, the case of a single break in the volatility of the innovations which may or may not occur at the same time as a break in trend. However, as we subsequently demonstrate, the limiting null distribution of unit root statistics based around this estimator are not pivotal in the presence of non-stationary volatility. Associated Monte Carlo evidence is presented to quantify the impact of various models of non-stationary volatility on both the asymptotic and finite sample behaviour of such tests. A solution to the identified inference problem is then provided by considering wild bootstrap-based implementations of the HHLT tests, using the trend break estimator from the original sample data. The proposed bootstrap method does not require the practitioner to specify a parametric model for volatility, and is shown to perform very well in practice across a range of models.

Keywords: Unit root tests, quasi difference de-trending, trend break, non-stationary volatility, wild bootstrap

JEL Classification: C22

Suggested Citation

Cavaliere, Giuseppe and Harvey, David I. and Leybourne, Stephen J. and Taylor, A. M. Robert, Testing for Unit Roots in the Presence of a Possible Break in Trend and Non-Stationary Volatility (December 2, 2008). CREATES Research Paper No. 2008-62, Available at SSRN: https://ssrn.com/abstract=1310189 or http://dx.doi.org/10.2139/ssrn.1310189

Giuseppe Cavaliere (Contact Author)

University of Bologna - Department of Economics ( email )

Bologna
Italy
+390512098489 (Phone)

David I. Harvey

University of Nottingham - School of Economics ( email )

University Park
Nottingham, NG7 2RD
United Kingdom

Stephen J. Leybourne

University of Nottingham ( email )

University Park
School of Economics
Nottingham NG7 2RD
United Kingdom
+44 (0)115 9515478 (Phone)
+44 (0)115 951 4159 (Fax)

A. M. Robert Taylor

University of Nottingham - School of Economics ( email )

University Park
Nottingham, NG7 2RD
United Kingdom

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