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New Unit Root Asymptotics in the Presence of Deterministic Trends

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Abstract

Recent work by the author (1998) has shown that stochastic trends can be validly represented in empirical regressions in terms of deterministic functions of time. These representations offer an alternative mechanism for modelling stochastic trends. It is shown here that the alternate representations affect the asymptotics of all commonly used unit root tests in the presence of trends. In particular, the critical values of unit root tests diverge when the number of deterministic regressors K approaches infinity as the sample size n approaches infinity. In such circumstances, use of conventional critical values based on fixed K will lead to rejection of the null of a unit root in favour of trend stationarity with probability one when the null is true. The results can be interpreted as saying that serious attempts to model trends by deterministic functions will always be successful and that these functions can validly represent stochastically trending data even when lagged variables are present in the regressor set, thereby undermining conventional unit root tests.

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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1196.

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Length: 25 pages
Date of creation: Oct 1998
Date of revision:
Publication status: Published in Journal of Econometrics (2002), 111(2): 323-353
Handle: RePEc:cwl:cwldpp:1196

Note: CFP 1059.
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Keywords: Deterministic trends; divergent critical values; large K asymptotics; test failure; unit root distributions;

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References

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  1. Peter C.B. Phillips & Hyungsik R. Moon, 1999. "Linear Regression Limit Theory for Nonstationary Panel Data," Cowles Foundation Discussion Papers 1222, Cowles Foundation for Research in Economics, Yale University.
  2. Werner Ploberger & Peter C. B. Phillips, 2003. "Empirical Limits for Time Series Econometric Models," Econometrica, Econometric Society, vol. 71(2), pages 627-673, March.
  3. Steven N. Durlauf & Peter C.B. Phillips, 1986. "Trends Versus Random Walks in Time Series Analysis," Cowles Foundation Discussion Papers 788, Cowles Foundation for Research in Economics, Yale University.
  4. Peter C.B. Phillips, 1985. "Time Series Regression with a Unit Root," Cowles Foundation Discussion Papers 740R, Cowles Foundation for Research in Economics, Yale University, revised Feb 1986.
  5. Peter C. B. Phillips, 1998. "New Tools for Understanding Spurious Regressions," Econometrica, Econometric Society, vol. 66(6), pages 1299-1326, November.
  6. Phillips, Peter C B & Ploberger, Werner, 1996. "An Asymptotic Theory of Bayesian Inference for Time Series," Econometrica, Econometric Society, vol. 64(2), pages 381-412, March.
  7. Keuzenkamp, H.A. & McAleer, M., 1994. "Simplicity, scientific inference and econometric modelling," Discussion Paper 1994-56, Tilburg University, Center for Economic Research.
  8. Phillips, Peter C B, 1996. "Econometric Model Determination," Econometrica, Econometric Society, vol. 64(4), pages 763-812, July.
  9. Zhije Xiao & Peter C.B. Phillips, 1998. "An ADF coefficient test for a unit root in ARMA models of unknown order with empirical applications to the US economy," Econometrics Journal, Royal Economic Society, vol. 1(RegularPa), pages 27-43.
  10. Peter C.B. Phillips & Victor Solo, 1989. "Asymptotics for Linear Processes," Cowles Foundation Discussion Papers 932, Cowles Foundation for Research in Economics, Yale University.
  11. Nelson, Charles R. & Plosser, Charles I., 1982. "Trends and random walks in macroeconmic time series : Some evidence and implications," Journal of Monetary Economics, Elsevier, vol. 10(2), pages 139-162.
  12. Peter C.B. Phillips, 1985. "Understanding Spurious Regressions in Econometrics," Cowles Foundation Discussion Papers 757, Cowles Foundation for Research in Economics, Yale University.
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Citations

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Cited by:
  1. Peter C.B. Phillips & Hyungsik Roger Moon & Benoit Perron, 2004. "Incidental Trends and the Power of Panel Unit Root Tests," Yale School of Management Working Papers ysm414, Yale School of Management.
  2. Peter C.B. Phillips, 2003. "Laws and Limits of Econometrics," Cowles Foundation Discussion Papers 1397, Cowles Foundation for Research in Economics, Yale University.
  3. Tanaka, Katsuto, 2011. "Linear Nonstationary Models : A Review of the Work of Professor P.C.B. Phillips," Discussion Papers 2011-05, Graduate School of Economics, Hitotsubashi University.
  4. Tilak Abeysinghe & Gulasekaran Rajaguru, 2009. "A Gaussian Test for Cointegration," Microeconomics Working Papers 22013, East Asian Bureau of Economic Research.
  5. Peter C.B. Phillips, 2004. "Challenges of Trending Time Series Econometrics," Cowles Foundation Discussion Papers 1472, Cowles Foundation for Research in Economics, Yale University.
  6. Peter C. B. Phillips, 2006. "Optimal Estimation of Cointegrated Systems with Irrelevant Instruments," Cowles Foundation Discussion Papers 1547, Cowles Foundation for Research in Economics, Yale University.
  7. Shahidur Rahman, 2005. "An Alternative Estimation to Spurious Regression Model," Economic Growth centre Working Paper Series 0507, Nanyang Technolgical University, School of Humanities and Social Sciences, Economic Growth centre.
  8. Phillips, Peter C. B., 2001. "Trending time series and macroeconomic activity: Some present and future challenges," Journal of Econometrics, Elsevier, vol. 100(1), pages 21-27, January.
  9. Peter C.B. Phillips & Zhipeng Liao, 2012. "Series Estimation of Stochastic Processes: Recent Developments and Econometric Applications," Cowles Foundation Discussion Papers 1871, Cowles Foundation for Research in Economics, Yale University.

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