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Testing for Unit Roots and the Impact of Quadratic Trends, with an Application to Relative Primary Commodity Prices

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Author Info

  • David Harvey
  • Stephen Leybourne
  • A.M. Robert Taylor

Abstract

In practice a degree of uncertainty will always exist concerning what specification to adopt for the deterministic trend function when running unit root tests. While most macroeconomic time series appear to display an underlying trend, it is often far from clear whether this component is best modeled as a simple linear trend (so that long-run growth rates are constant) or by a more complicated nonlinear trend function which may, for instance, allow the deterministic trend component to evolve gradually over time. In this article, we consider the effects on unit root testing of allowing for a local quadratic trend, a simple yet very flexible example of the latter. Where a local quadratic trend is present but not modeled, we show that the quasi-differenced detrended Dickey-Fuller-type test of Elliott et al. (1996) has both size and power which tend to zero asymptotically. An extension of the Elliott et al. (1996) approach to allow for a quadratic trend resolves this problem but is shown to result in large power losses relative to the standard detrended test when no quadratic trend is present. We consequently propose a simple and practical approach to dealing with this form of uncertainty based on a union of rejections-based decision rule whereby the unit root is rejected whenever either of the detrended or quadratic detrended unit root tests rejects. A modification of this basic strategy is also suggested which further improves on the properties of the procedure. An application to relative primary commodity price data highlights the empirical relevance of the methods outlined in this article. A by-product of our analysis is the development of a test for the presence of a quadratic trend which is robust to whether the data admit a unit root.

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Bibliographic Info

Article provided by Taylor & Francis Journals in its journal Econometric Reviews.

Volume (Year): 30 (2011)
Issue (Month): 5 ()
Pages: 514-547

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Handle: RePEc:taf:emetrv:v:30:y:2011:i:5:p:514-547

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Related research

Keywords: Asymptotic power; Quadratic trends; Trend uncertainty; Union of rejections decision rule; Unit root test;

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References

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  1. Peter C.B. Phillips & Sam Ouliaris & Joon Y. Park, 1988. "Testing for a Unit Root in the Presence of a Maintained Trend," Cowles Foundation Discussion Papers 880, Cowles Foundation for Research in Economics, Yale University.
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  8. Kellard, Neil & Wohar, Mark E., 2006. "On the prevalence of trends in primary commodity prices," Journal of Development Economics, Elsevier, vol. 79(1), pages 146-167, February.
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  10. Peter C. B. Phillips, 1998. "New Tools for Understanding Spurious Regressions," Econometrica, Econometric Society, vol. 66(6), pages 1299-1326, November.
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  12. Ayat, Leila & Burridge, Peter, 2000. "Unit root tests in the presence of uncertainty about the non-stochastic trend," Journal of Econometrics, Elsevier, vol. 95(1), pages 71-96, March.
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  14. Stock, James H. & Watson, Mark W., 1999. "Business cycle fluctuations in us macroeconomic time series," Handbook of Macroeconomics, in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 1, pages 3-64 Elsevier.
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Citations

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Cited by:
  1. Presno, María José & Landajo, Manuel & Fernández, Paula, 2014. "Non-renewable resource prices: A robust evaluation from the stationarity perspective," Resource and Energy Economics, Elsevier, vol. 36(2), pages 394-416.
  2. Xuguang Sheng & Lan Cheng, 2012. "Combination of "Combinations of P-values," Working Papers 2012-11, American University, Department of Economics.
  3. Westerlund, Joakim, 2013. "Simple unit root testing in generally trending data with an application to precious metal prices in Asia," Journal of Asian Economics, Elsevier, vol. 28(C), pages 12-27.
  4. Presno, María José & Landajo, Manuel & Fernández, Paula, 2012. "Non-renewable resource prices. A robust evaluation from the stationarity perspective," MPRA Paper 42523, University Library of Munich, Germany.
  5. Yamada, Hiroshi & Yoon, Gawon, 2014. "When Grilli and Yang meet Prebisch and Singer: Piecewise linear trends in primary commodity prices," Journal of International Money and Finance, Elsevier, vol. 42(C), pages 193-207.

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