IDEAS home Printed from https://ideas.repec.org/p/cwl/cwldpp/740r.html
   My bibliography  Save this paper

Time Series Regression with a Unit Root

Author

Abstract

This paper studies the random walk in a general time series setting that allows for weakly dependent and heterogeneously distributed innovations. It is shown that simple least squares regression consistently estimates a unit root under very general conditions in spite of the presence of autocorrelated errors. The limiting distribution of the standardized estimator and the associated regression t-statistic are found using functional central limit theory. New tests of the random walk hypothesis are developed which permit a wide class of dependent and heterogeneous innovation sequences. A new limiting distribution theory is constructed based on the concept of continuous data recording. This theory, together with an asymptotic expansion that is developed in the paper for the unit root case, explain many of the interesting experimental results recently reported in Evans and Savin (1981, 1984).

Suggested Citation

  • 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.
  • Handle: RePEc:cwl:cwldpp:740r
    Note: CFP 674.
    as

    Download full text from publisher

    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d07/d0740-r.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Hall, Robert E, 1978. "Stochastic Implications of the Life Cycle-Permanent Income Hypothesis: Theory and Evidence," Journal of Political Economy, University of Chicago Press, vol. 86(6), pages 971-987, December.
    2. Robert B. Litterman, 1984. "Forecasting with Bayesian vector autoregressions four years of experience," Staff Report 95, Federal Reserve Bank of Minneapolis.
    3. Phillips, Peter C B, 1977. "Approximations to Some Finite Sample Distributions Associated with a First-Order Stochastic Difference Equation," Econometrica, Econometric Society, vol. 45(2), pages 463-485, March.
    4. Sargan, John Denis & Bhargava, Alok, 1983. "Testing Residuals from Least Squares Regression for Being Generated by the Gaussian Random Walk," Econometrica, Econometric Society, vol. 51(1), pages 153-174, January.
    5. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 33(1), pages 125-132.
    6. Thomas Doan & Robert B. Litterman & Christopher A. Sims, 1983. "Forecasting and Conditional Projection Using Realistic Prior Distributions," NBER Working Papers 1202, National Bureau of Economic Research, Inc.
    7. Granger, C. W. J. & Newbold, P., 1974. "Spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 2(2), pages 111-120, July.
    8. Nankervis, J. C. & Savin, N. E., 1985. "Testing the autoregressive parameter with the t statistic," Journal of Econometrics, Elsevier, vol. 27(2), pages 143-161, February.
    9. White, Halbert & Domowitz, Ian, 1984. "Nonlinear Regression with Dependent Observations," Econometrica, Econometric Society, vol. 52(1), pages 143-161, January.
    10. Alok Bhargava, 1986. "On the Theory of Testing for Unit Roots in Observed Time Series," Review of Economic Studies, Oxford University Press, vol. 53(3), pages 369-384.
    Full references (including those not matched with items on IDEAS)

    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. Phillips, P. C. B., 1987. "Asymptotic Expansions in Nonstationary Vector Autoregressions," Econometric Theory, Cambridge University Press, vol. 3(1), pages 45-68, February.
    2. PHILIP E.T. LEWIS & GARRY A. MacDONALD, 1993. "Testing for Equilibrium in the Australian Wage Equation," The Economic Record, The Economic Society of Australia, vol. 69(3), pages 295-304, September.
    3. Russell Davidson & Victoria Zinde‐Walsh, 2017. "Advances in specification testing," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 50(5), pages 1595-1631, December.
    4. David Greasley & Les Oxley, 2010. "Cliometrics And Time Series Econometrics: Some Theory And Applications," Journal of Economic Surveys, Wiley Blackwell, vol. 24(5), pages 970-1042, December.
    5. Erdogdu, Erkan, 2007. "Electricity demand analysis using cointegration and ARIMA modelling: A case study of Turkey," Energy Policy, Elsevier, vol. 35(2), pages 1129-1146, February.
    6. Giorgio Canarella & Rangan Gupta & Stephen M. Miller & Stephen K. Pollard, 2019. "Unemployment rate hysteresis and the great recession: exploring the metropolitan evidence," Empirical Economics, Springer, vol. 56(1), pages 61-79, January.
    7. P. C. B. Phillips & S. N. Durlauf, 1986. "Multiple Time Series Regression with Integrated Processes," Review of Economic Studies, Oxford University Press, vol. 53(4), pages 473-495.
    8. Charles G. Renfro, 2009. "The Practice of Econometric Theory," Advanced Studies in Theoretical and Applied Econometrics, Springer, number 978-3-540-75571-5, July-Dece.
    9. Franses,Philip Hans & Dijk,Dick van & Opschoor,Anne, 2014. "Time Series Models for Business and Economic Forecasting," Cambridge Books, Cambridge University Press, number 9780521520911, October.
    10. Ye Cai & Mototsugu Shintani, 2005. "On the Long-Run Variance Ratio Test for a Unit Root," Vanderbilt University Department of Economics Working Papers 0506, Vanderbilt University Department of Economics.
    11. David F. Hendry & Peter C.B. Phillips, 2017. "John Denis Sargan at the London School of Economics," Cowles Foundation Discussion Papers 2082, Cowles Foundation for Research in Economics, Yale University.
    12. Schlitzer, Giuseppe, 1995. "Testing the stationarity of economic time series: further Monte Carlo evidence," Ricerche Economiche, Elsevier, vol. 49(2), pages 125-144, June.
    13. Fan, Yanqin & Gençay, Ramazan, 2010. "Unit Root Tests With Wavelets," Econometric Theory, Cambridge University Press, vol. 26(5), pages 1305-1331, October.
    14. N. Vijayamohanan Pillai, 2010. "Electricity Demand Analysis and Forecasting- The Tradition is Questioned," Working Papers id:2966, eSocialSciences.
    15. John Y. Campbell & Pierre Perron, 1991. "Pitfalls and Opportunities: What Macroeconomists Should Know about Unit Roots," NBER Chapters, in: NBER Macroeconomics Annual 1991, Volume 6, pages 141-220, National Bureau of Economic Research, Inc.
    16. María del Mar Sánchez de la Vega & Arielle Beyaert, 1994. "Los contrastes de raiz unitaria: una panorámica," Estudios de Economia Aplicada, Estudios de Economia Aplicada, vol. 1, pages 109-154, Junio.
    17. Gabriel Rodriguez & Pierre Perron, 2013. "Single-equation tests for Cointegration with GLS Detrended Data," Boston University - Department of Economics - Working Papers Series 2013-016, Boston University - Department of Economics.
    18. Marco Morales, 2014. "Cointegration testing under structural change: reducing size distortions and improving power of residual based tests," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 23(2), pages 265-282, June.
    19. Lavan Mahadeva and Paul Robinson, 2004. "Unit Root Testing in a Central Bank," Handbooks, Centre for Central Banking Studies, Bank of England, number 22, April.
    20. Todd E. Clark & Michael W. McCracken, 2010. "Averaging forecasts from VARs with uncertain instabilities," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(1), pages 5-29, January.

    More about this item

    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:cwl:cwldpp:740r. See general information about how to correct material in RePEc.

    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: Brittany Ladd (email available below). General contact details of provider: https://edirc.repec.org/data/cowleus.html .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.