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

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Author Info
Giuseppe Cavaliere
David I. Harvey
Stephen J. Leybourne
A.M. Robert Taylor () (School of Economics and Management, University of Aarhus, Denmark and CREATES)

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Abstract

In this paper we analyse the impact of non-stationary volatility on the recently devel- oped 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, in- cluding, 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 es- timator 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.

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Publisher Info
Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2008-62.

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Length: 42
Date of creation: 02 Dec 2008
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Handle: RePEc:aah:create:2008-62

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

Find related papers by JEL classification:
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions

This paper has been announced in the following NEP Reports:

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