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New unit root asymptotics in the presence of deterministic trends

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  • Phillips, Peter C. B.

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

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 111 (2002)
Issue (Month): 2 (December)
Pages: 323-353

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Handle: RePEc:eee:econom:v:111:y:2002:i:2:p:323-353

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Web page: http://www.elsevier.com/locate/jeconom

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References

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  1. Peter C. B. Phillips, 1998. "New Tools for Understanding Spurious Regressions," Econometrica, Econometric Society, vol. 66(6), pages 1299-1326, November.
  2. 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.
  3. Peter C.B. Phillips & Werner Ploberger, 1999. "Empirical Limits for Time Series Econometric Models," Cowles Foundation Discussion Papers 1220, Cowles Foundation for Research in Economics, Yale University.
  4. Phillips, P.C.B., 1986. "Understanding spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 33(3), pages 311-340, December.
  5. Zhijie Xiao & Peter C.B. Phillips, 1997. "An ADF Coefficient Test for a Unit Root in ARMA Models of Unknown Order with Empirical Applications to the U.S. Economy," Cowles Foundation Discussion Papers 1161, Cowles Foundation for Research in Economics, Yale University.
  6. 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.
  7. 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.
  8. Keuzenkamp, H.A. & McAleer, M., 1994. "Simplicity, scientific inference and econometric modelling," Discussion Paper 1994-56, Tilburg University, Center for Economic Research.
  9. 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.
  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. Phillips, Peter C B, 1996. "Econometric Model Determination," Econometrica, Econometric Society, vol. 64(4), pages 763-812, July.
  12. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
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Cited by:
  1. 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.
  2. 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.
  3. Peter C.B. Phillips, 2000. "Trending Time Series and Macroeconomic Activity: Some Present and Future Challenges," Cowles Foundation Discussion Papers 1264, Cowles Foundation for Research in Economics, Yale University.
  4. Gulasekaran Rajaguru & Tilak Abeysinghe, 2009. "A Gaussian Test for Cointegration," SCAPE Policy Research Working Paper Series 0905, National University of Singapore, Department of Economics, SCAPE.
  5. 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.
  6. 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.
  7. Peter C.B. Phillips, 2004. "Challenges of Trending Time Series Econometrics," Cowles Foundation Discussion Papers 1472, Cowles Foundation for Research in Economics, Yale University.
  8. Moon, Hyungsik Roger & Perron, Benoit & Phillips, Peter C.B., 2007. "Incidental trends and the power of panel unit root tests," Journal of Econometrics, Elsevier, vol. 141(2), pages 416-459, December.
  9. Peter C. B. Phillips, 2003. "Laws and Limits of Econometrics," Economic Journal, Royal Economic Society, vol. 113(486), pages C26-C52, March.

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