IDEAS home Printed from https://ideas.repec.org/p/ehl/lserod/114620.html
   My bibliography  Save this paper

Testing for unit roots based on sample autocovariances

Author

Listed:
  • Chang, Jinyuan
  • Cheng, Guanghui
  • Yao, Qiwei

Abstract

We propose a new unit-root test for a stationary null hypothesis H0 against a unit-root alternative H1⁠. Our approach is nonparametric as H0 assumes only that the process concerned is I(0)⁠, without specifying any parametric forms. The new test is based on the fact that the sample autocovariance function converges to the finite population autocovariance function for an I(0) process, but diverges to infinity for a process with unit roots. Therefore, the new test rejects H0 for large values of the sample autocovariance function. To address the technical question of how large is large, we split the sample and establish an appropriate normal approximation for the null distribution of the test statistic. The substantial discriminative power of the new test statistic is due to the fact that it takes finite values under H0 and diverges to infinity under H1⁠. This property allows one to truncate the critical values of the test so that it has asymptotic power 1; it also alleviates the loss of power due to the sample-splitting. The test is implemented in R⁠.

Suggested Citation

  • Chang, Jinyuan & Cheng, Guanghui & Yao, Qiwei, 2022. "Testing for unit roots based on sample autocovariances," LSE Research Online Documents on Economics 114620, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:114620
    as

    Download full text from publisher

    File URL: http://eprints.lse.ac.uk/114620/
    File Function: Open access version.
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. Peter C.B. Phillips, 1987. "Multiple Regression with Integrated Time Series," Cowles Foundation Discussion Papers 852, Cowles Foundation for Research in Economics, Yale University.
    3. Cavaliere, Giuseppe & Taylor, A.M. Robert, 2007. "Testing for unit roots in time series models with non-stationary volatility," Journal of Econometrics, Elsevier, vol. 140(2), pages 919-947, October.
    4. Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, vol. 49(4), pages 1057-1072, June.
    5. M. Hashem Pesaran, 2007. "A simple panel unit root test in the presence of cross-section dependence," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 22(2), pages 265-312.
    6. Hylleberg, S. & Engle, R. F. & Granger, C. W. J. & Yoo, B. S., 1990. "Seasonal integration and cointegration," Journal of Econometrics, Elsevier, vol. 44(1-2), pages 215-238.
    7. Zivot, Eric & Andrews, Donald W K, 2002. "Further Evidence on the Great Crash, the Oil-Price Shock, and the Unit-Root Hypothesis," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 25-44, January.
    8. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    9. Pesaran, M. Hashem & Vanessa Smith, L. & Yamagata, Takashi, 2013. "Panel unit root tests in the presence of a multifactor error structure," Journal of Econometrics, Elsevier, vol. 175(2), pages 94-115.
    10. Paparoditis, Efstathios & Politis, Dimitris N., 2005. "Bootstrapping Unit Root Tests for Autoregressive Time Series," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 545-553, June.
    11. Rho, Yeonwoo & Shao, Xiaofeng, 2019. "Bootstrap-Assisted Unit Root Testing With Piecewise Locally Stationary Errors," Econometric Theory, Cambridge University Press, vol. 35(1), pages 142-166, February.
    12. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    13. Jinyuan Chang & Chao Zheng & Wen‐Xin Zhou & Wen Zhou, 2017. "Simulation‐based hypothesis testing of high dimensional means under covariance heterogeneity," Biometrics, The International Biometric Society, vol. 73(4), pages 1300-1310, December.
    14. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    15. 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.
    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. Christis Katsouris, 2023. "Statistical Estimation for Covariance Structures with Tail Estimates using Nodewise Quantile Predictive Regression Models," Papers 2305.11282, arXiv.org, revised Jul 2023.

    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. Jinyuan Chang & Guanghui Cheng & Qiwei Yao, 2022. "Testing for unit roots based on sample autocovariances [Heteroskedasticity and autocorrelation consistent covariance matrix estimation]," Biometrika, Biometrika Trust, vol. 109(2), pages 543-550.
    2. Niels Haldrup & Robinson Kruse & Timo Teräsvirta & Rasmus T. Varneskov, 2013. "Unit roots, non-linearities and structural breaks," Chapters, in: Nigar Hashimzade & Michael A. Thornton (ed.), Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 4, pages 61-94, Edward Elgar Publishing.
    3. 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.
    4. 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.
    5. Charles Nelson & Jeremy Piger & Eric Zivot, 1999. "Unit Root Tests in the Presence of Markov Regime-Switching," Discussion Papers in Economics at the University of Washington 0040, Department of Economics at the University of Washington.
    6. Franses,Philip Hans & Dijk,Dick van & Opschoor,Anne, 2014. "Time Series Models for Business and Economic Forecasting," Cambridge Books, Cambridge University Press, number 9780521520911.
    7. 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.
    8. Mitch Kunce, 2023. "Unemployment and Suicide in the United States: The Import of Addressing Cross-Sectional Dependence," Bulletin of Applied Economics, Risk Market Journals, vol. 10(1), pages 1-19.
    9. Laura Mayoral, 2006. "Further Evidence on the Statistical Properties of Real GNP," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 68(s1), pages 901-920, December.
    10. Serletis, Apostolos & Shahmoradi, Asghar, 2007. "Chaos, self-organized criticality, and SETAR nonlinearity: An analysis of purchasing power parity between Canada and the United States," Chaos, Solitons & Fractals, Elsevier, vol. 33(5), pages 1437-1444.
    11. Norman J. Morin & John M. Roberts, 1999. "Is hysteresis important for U.S. unemployment?," Finance and Economics Discussion Series 1999-56, Board of Governors of the Federal Reserve System (U.S.).
    12. Raghbendra Jha & Anurag Sharma, 2004. "Structural Breaks, Unit Roots, and Cointegration: A Further Test of the Sustainability of the Indian Fiscal Deficit," Public Finance Review, , vol. 32(2), pages 196-219, March.
    13. Ilias Lekkos, 2003. "Cross‐sectional Restrictions on the Spot and Forward Term Structures of Interest Rates and Panel Unit Root Tests," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 30(5‐6), pages 799-828, June.
    14. Bardsen, G. & Klovland, J.T., 1990. "Finding The Rigth Nominal Anchor: The Cointegration Of Money, Credit And Nominal Income In Norway," The Warwick Economics Research Paper Series (TWERPS) 350, University of Warwick, Department of Economics.
    15. Mitch Kunce, 2022. "The Tenuous Ecological Divorce and Unemployment Link with Suicide: A U.S. Panel Analysis 1968-2020," Journal of Statistical and Econometric Methods, SCIENPRESS Ltd, vol. 11(3), pages 1-2.
    16. 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.
    17. 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.
    18. Murray, Christian J. & Nelson, Charles R., 2000. "The uncertain trend in U.S. GDP," Journal of Monetary Economics, Elsevier, vol. 46(1), pages 79-95, August.
    19. Hayashi, Naotsugu, 2005. "Structural changes and unit roots in Japan's macroeconomic time series: is real business cycle theory supported?," Japan and the World Economy, Elsevier, vol. 17(2), pages 239-259, April.
    20. Angeliki N. Menegaki, 2021. "Towards a Global Energy-Sustainable Economy Nexus; Summing up Evidence from Recent Empirical Work," Energies, MDPI, vol. 14(16), pages 1-16, August.

    More about this item

    Keywords

    autocovariance; integrated processes; normal approximation; power-one test; sample-splitting; EP/V007556/1;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:ehl:lserod:114620. 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: LSERO Manager (email available below). General contact details of provider: https://edirc.repec.org/data/lsepsuk.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.