IDEAS home Printed from https://ideas.repec.org/p/auc/wpaper/196.html
   My bibliography  Save this paper

New Unit Root Asymptotics in the Presence of Deterministic Trends

Author

Listed:
  • Phillips, Peter

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 -+ rn as the sample size n + w. 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.

Suggested Citation

  • Phillips, Peter, 1998. "New Unit Root Asymptotics in the Presence of Deterministic Trends," Working Papers 196, Department of Economics, The University of Auckland.
  • Handle: RePEc:auc:wpaper:196
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/2292/196
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Peter C. B. Phillips, 1998. "New Tools for Understanding Spurious Regressions," Econometrica, Econometric Society, vol. 66(6), pages 1299-1326, November.
    2. Durlauf, Steven N & Phillips, Peter C B, 1988. "Trends versus Random Walks in Time Series Analysis," Econometrica, Econometric Society, vol. 56(6), pages 1333-1354, November.
    3. Peter C.B. Phillips & Victor Solo, 1989. "Asymptotics for Linear Processes," Cowles Foundation Discussion Papers 932, Cowles Foundation for Research in Economics, Yale University.
    4. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    5. Keuzenkamp, H.A. & McAleer, M., 1994. "Simplicity, scientific inference and econometric modelling," Other publications TiSEM dabcc476-15d7-4177-a2f5-b, Tilburg University, School of Economics and Management.
    6. Werner Ploberger & Peter C. B. Phillips, 2003. "Empirical Limits for Time Series Econometric Models," Econometrica, Econometric Society, vol. 71(2), pages 627-673, March.
    7. Phillips, P.C.B., 1986. "Understanding spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 33(3), pages 311-340, December.
    8. Phillips, Peter C B, 1996. "Econometric Model Determination," Econometrica, Econometric Society, vol. 64(4), pages 763-812, July.
    9. Peter C. B. Phillips & Hyungsik R. Moon, 1999. "Linear Regression Limit Theory for Nonstationary Panel Data," Econometrica, Econometric Society, vol. 67(5), pages 1057-1112, September.
    10. 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.
    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. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Phillips, Peter C.B., 2014. "Optimal estimation of cointegrated systems with irrelevant instruments," Journal of Econometrics, Elsevier, vol. 178(P2), pages 210-224.
    2. Phillips, Peter C.B., 2005. "Challenges of trending time series econometrics," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 68(5), pages 401-416.
    3. 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.
    4. 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.
    5. 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.
    6. Peter C. B. Phillips & Xiaohu Wang & Yonghui Zhang, 2019. "HAR Testing for Spurious Regression in Trend," Econometrics, MDPI, Open Access Journal, vol. 7(4), pages 1-28, December.
    7. Tilak Abeysinghe & Gulasekaran Rajaguru, 2009. "A Gaussian Test for Cointegration," Microeconomics Working Papers 22013, East Asian Bureau of Economic Research.
    8. Peter C. B. Phillips, 2003. "Laws and Limits of Econometrics," Economic Journal, Royal Economic Society, vol. 113(486), pages 26-52, March.
    9. Shahidur Rahman, 2005. "An Alternative Estimation to Spurious Regression Model," Economic Growth Centre Working Paper Series 0507, Nanyang Technological University, School of Social Sciences, Economic Growth Centre.
    10. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Peter C. B. Phillips, 2003. "Laws and Limits of Econometrics," Economic Journal, Royal Economic Society, vol. 113(486), pages 26-52, March.
    2. Peter C.B. Phillips, 2001. "Bootstrapping Spurious Regression," Cowles Foundation Discussion Papers 1330, Cowles Foundation for Research in Economics, Yale University.
    3. Peter C. B. Phillips & Zhijie Xiao, 1998. "A Primer on Unit Root Testing," Journal of Economic Surveys, Wiley Blackwell, vol. 12(5), pages 423-470, December.
    4. Cheng, Xu & Phillips, Peter C.B., 2012. "Cointegrating rank selection in models with time-varying variance," Journal of Econometrics, Elsevier, vol. 169(2), pages 155-165.
    5. Peter C. B. Phillips & Xiaohu Wang & Yonghui Zhang, 2019. "HAR Testing for Spurious Regression in Trend," Econometrics, MDPI, Open Access Journal, vol. 7(4), pages 1-28, December.
    6. Aaron Schiff & Peter Phillips, 2000. "Forecasting New Zealand's real GDP," New Zealand Economic Papers, Taylor & Francis Journals, vol. 34(2), pages 159-181.
    7. Werner Ploberger & Peter C.B. Phillips, 1998. "Rissanen's Theorem and Econometric Time Series," Cowles Foundation Discussion Papers 1197, Cowles Foundation for Research in Economics, Yale University.
    8. Phillips, Peter C.B., 2005. "Challenges of trending time series econometrics," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 68(5), pages 401-416.
    9. Jürgen Wolters & Uwe Hassler, 2006. "Unit Root Testing," Springer Books, in: Olaf Hübler & Jachim Frohn (ed.), Modern Econometric Analysis, chapter 4, pages 41-56, Springer.
    10. Park, Joon Y & Phillips, Peter C B, 2001. "Nonlinear Regressions with Integrated Time Series," Econometrica, Econometric Society, vol. 69(1), pages 117-161, January.
    11. Patrick Marsh, "undated". "A Measure of Distance for the Unit Root Hypothesis," Discussion Papers 05/02, Department of Economics, University of York.
    12. 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.
    13. Joakim Westerlund, 2005. "New Simple Tests for Panel Cointegration," Econometric Reviews, Taylor & Francis Journals, vol. 24(3), pages 297-316.
    14. D. Ventosa-Santaulària, 2009. "Spurious Regression," Journal of Probability and Statistics, Hindawi, vol. 2009, pages 1-27, August.
    15. Athanasopoulos, George & de Carvalho Guillén, Osmani Teixeira & Issler, João Victor & Vahid, Farshid, 2011. "Model selection, estimation and forecasting in VAR models with short-run and long-run restrictions," Journal of Econometrics, Elsevier, vol. 164(1), pages 116-129, September.
    16. Entorf, Horst, 1997. "Random walks with drifts: Nonsense regression and spurious fixed-effect estimation," Journal of Econometrics, Elsevier, vol. 80(2), pages 287-296, October.
    17. Fan, Yanqin & Gençay, Ramazan, 2010. "Unit Root Tests With Wavelets," Econometric Theory, Cambridge University Press, vol. 26(5), pages 1305-1331, October.
    18. Joakim Westerlund, 2007. "Testing for Error Correction in Panel Data," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 69(6), pages 709-748, December.
    19. Neil R. Ericsson, 2021. "Dynamic Econometrics in Action: A Biography of David F. Hendry," International Finance Discussion Papers 1311, Board of Governors of the Federal Reserve System (U.S.).
    20. 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.

    More about this item

    Keywords

    Deterministic trends; Economics;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:auc:wpaper:196. 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: . General contact details of provider: https://edirc.repec.org/data/deaucnz.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Library Digital Development (email available below). General contact details of provider: https://edirc.repec.org/data/deaucnz.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.