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On Robust Trend Function Hypothesis Testing

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  • David Harvey, Stephen Leybourne and A M Robert Taylor

Abstract

In this paper we build upon the robust procedures proposed in Vogelsang (1998) for testing hypotheses concerning the deterministric trend function of a univariate time series. Vogelsang proposes statistics formed from taking the product of a (normalised) Wald statistic for the trend function hypothesis under test with a specific function of a separate variable addition Wald statistic. The function of the second statistic is explicitly chosen such that the resultant product statistic has pivotal limiting null distributions, coincident at a chosen level, under I(0) or I(1) errors. The variable addition statistic in question has also been suggested as a unit root statistic, and we propose corresponding tests based on other well-known unit root statistics. We find that, in the case of the linear trend model, a test formed using the familiar augmented Dickey-Fuller [ADF] statistic provides a useful complement to Vogelsang's original tests, demonstrating generally superior power when the errors display strong serial correlation with this pattern tending to reverse as the degree of serial correlation in the errors lessens. Importantly for practical considerations, the ADF-based tests also display significantly less finite sample over-size in the presence of weakly dependent errors than the original tests.

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Bibliographic Info

Paper provided by Department of Economics, University of Birmingham in its series Discussion Papers with number 05-07.

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Length: 16 pages
Date of creation: Feb 2005
Date of revision:
Handle: RePEc:bir:birmec:05-07

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Postal: Edgbaston, Birmingham, B15 2TT
Web page: http://www.economics.bham.ac.uk
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Related research

Keywords: Wald tests; trend function hypotheses; unit root statistics;

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Cited by:
  1. David I. Harvey & Stephen J. Leybourne & Lisa Xiao, 2009. "Testing for nonlinear trends when the order of integration is unknown," Discussion Papers 09/04, University of Nottingham, Granger Centre for Time Series Econometrics.

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