Testing for unit roots and the impact of quadratic trends, with an application to relative primary commodity prices
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 modelled as a simple linear trend (so that long-run growth rates are constant) or by a more complicated non-linear trend function which may, for instance, allow the deterministic trend component to evolve gradually over time. In this paper 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 modelled 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 null 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 paper. A by-product of our analysis is the development of a test for the presence of a quadratic trend which is robust to whether or not the data admit a unit root.
|Date of creation:||Jun 2008|
|Contact details of provider:|| Postal: School of Economics University of Nottingham University Park Nottingham NG7 2RD|
Phone: (44) 0115 951 5620
Fax: (0115) 951 4159
Web page: http://www.nottingham.ac.uk/research/groups/grangercentre/index.aspx
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- PERRON, Pierre & RODRIGUEZ, Gabriel, 1998.
"GLS Detrending, Efficient Unit Root Tests and Structural Change,"
Cahiers de recherche
9809, Universite de Montreal, Departement de sciences economiques.
- Perron, Pierre & Rodriguez, Gabriel, 2003. "GLS detrending, efficient unit root tests and structural change," Journal of Econometrics, Elsevier, vol. 115(1), pages 1-27, July.
- Charles Nelson & Christian Murray, 1997.
"The Uncertain Trend in U.S. GDP,"
- Nelson, C-R & Murray, C-J, 1997. "The Uncertain Trend in U.S. GDP," Working Papers 97-05, University of Washington, Department of Economics.
- Chris Murray & Charles Nelson, 1998. "The Uncertain Trend in U.S. GDP," Discussion Papers in Economics at the University of Washington 0074, Department of Economics at the University of Washington.
- Nelson, C-R & Murray, C-J, 1997. "The Uncertain Trend in U.S. GDP," Discussion Papers in Economics at the University of Washington 97-05, Department of Economics at the University of Washington.
- Chris Murray & Charles Nelson, 1998. "The Uncertain Trend in U.S. GDP," Working Papers 0074, University of Washington, Department of Economics.
- Graham Elliott & Thomas J. Rothenberg & James H. Stock, 1992.
"Efficient Tests for an Autoregressive Unit Root,"
NBER Technical Working Papers
0130, National Bureau of Economic Research, Inc.
- Prebisch, Raúl, 1950. "The economic development of Latin America and its principal problems," Sede de la CEPAL en Santiago (Estudios e Investigaciones) 29973, Naciones Unidas Comisión Económica para América Latina y el Caribe (CEPAL).
- Ayat, L. & Burridge, P., 1996.
"Unit Root Tests in the presence of Uncertainty about the Non-Stochastic Trends,"
96-28, Department of Economics, University of Birmingham.
- 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.
- David I. Harvey & Stephen J. Leybourne & A. M. Robert Taylor, 2007.
"Unit root testing in practice: dealing with uncertainty over the trend and initial condition,"
07/03, University of Nottingham, Granger Centre for Time Series Econometrics.
- Harvey, David I. & Leybourne, Stephen J. & Taylor, A.M. Robert, 2009. "Unit Root Testing In Practice: Dealing With Uncertainty Over The Trend And Initial Condition," Econometric Theory, Cambridge University Press, vol. 25(03), pages 587-636, June.
- Harvey, David I. & Leybourne, Stephen J. & Taylor, A.M. Robert, 2007.
"A simple, robust and powerful test of the trend hypothesis,"
Journal of Econometrics,
Elsevier, vol. 141(2), pages 1302-1330, December.
- David I. Harvey, & Stephen J. Leybourne, & A. M. Robert Taylor, 2006. "A simple, robust and powerful test of the trend hypothesis," Discussion Papers 06/01, University of Nottingham, Granger Centre for Time Series Econometrics.
- James H. Stock & Mark W. Watson, 1998.
"Business Cycle Fluctuations in U.S. Macroeconomic Time Series,"
NBER Working Papers
6528, National Bureau of Economic Research, Inc.
- 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.
- Stephan Pfaffenzeller & Paul Newbold & Anthony Rayner, 2007. "A Short Note on Updating the Grilli and Yang Commodity Price Index," World Bank Economic Review, World Bank Group, vol. 21(1), pages 151-163.
- Leon, Javier & Soto, Raimundo, 1995.
"Structural breaks and long-run trends in commodity prices,"
Policy Research Working Paper Series
1406, The World Bank.
- Javier León & Raimundo Soto, 1997. "Structural Breaks And Long-Run Trends In Commodity Prices," Journal of International Development, John Wiley & Sons, Ltd., vol. 9(3), pages 347-366.
- Kwiatkowski, Denis & Phillips, Peter C. B. & Schmidt, Peter & Shin, Yongcheol, 1992.
"Testing the null hypothesis of stationarity against the alternative of a unit root : How sure are we that economic time series have a unit root?,"
Journal of Econometrics,
Elsevier, vol. 54(1-3), pages 159-178.
- Kwiatkowski, D. & Phillips, P.C.B. & Schmidt, P., 1990. "Testing the Null Hypothesis of Stationarity Against the Alternative of Unit Root : How Sure are we that Economic Time Series have a Unit Root?," Papers 8905, Michigan State - Econometrics and Economic Theory.
- Denis Kwiatkowski & Peter C.B. Phillips & Peter Schmidt, 1991. "Testing the Null Hypothesis of Stationarity Against the Alternative of a Unit Root: How Sure Are We That Economic Time Series Have a Unit Root?," Cowles Foundation Discussion Papers 979, Cowles Foundation for Research in Economics, Yale University.
- Yoosoon Chang & Joon Park, 2002. "On The Asymptotics Of Adf Tests For Unit Roots," Econometric Reviews, Taylor & Francis Journals, vol. 21(4), pages 431-447.
- Bierens, Herman J., 1997. "Testing the unit root with drift hypothesis against nonlinear trend stationarity, with an application to the US price level and interest rate," Journal of Econometrics, Elsevier, vol. 81(1), pages 29-64, November.
- Serena Ng & Pierre Perron, 1997.
"Lag Length Selection and the Construction of Unit Root Tests with Good Size and Power,"
Boston College Working Papers in Economics
369, Boston College Department of Economics, revised 01 Sep 2000.
- Serena Ng & Pierre Perron, 2001. "LAG Length Selection and the Construction of Unit Root Tests with Good Size and Power," Econometrica, Econometric Society, vol. 69(6), pages 1519-1554, November.
- Perron, Pierre, 1989.
"The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis,"
Econometric Society, vol. 57(6), pages 1361-1401, November.
- Perron, P, 1988. "The Great Crash, The Oil Price Shock And The Unit Root Hypothesis," Papers 338, Princeton, Department of Economics - Econometric Research Program.
- 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.
- Peter C. B. Phillips, 1998. "New Tools for Understanding Spurious Regressions," Econometrica, Econometric Society, vol. 66(6), pages 1299-1326, November.
- Ulrich K. M¸ller & Graham Elliott, 2003. "Tests for Unit Roots and the Initial Condition," Econometrica, Econometric Society, vol. 71(4), pages 1269-1286, 07.
- 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.
When requesting a correction, please mention this item's handle: RePEc:not:notgts:08/04. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: ()
If references are entirely missing, you can add them using this form.