On Robust Trend Function Hypothesis Testing

David Harvey, Stephen Leybourne () and Robert Taylor

Discussion Papers from Department of Economics, University of Birmingham

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.

Keywords: Wald tests; trend function hypotheses; unit root statistics (search for similar items in EconPapers)
JEL-codes: C22 (search for similar items in EconPapers)
Pages: 16 pages
Date: 2005-02
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-fin
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Journal Article: On Robust Trend Function Hypothesis Testing (2006)
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Persistent link: https://EconPapers.repec.org/RePEc:bir:birmec:05-07

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