IDEAS home Printed from https://ideas.repec.org/a/plo/pone00/0259994.html
   My bibliography  Save this article

The probabilities of type I and II error of null of cointegration tests: A Monte Carlo comparison

Author

Listed:
  • Ahmet Faruk Aysan
  • Ibrahim Guney
  • Nicoleta Isac
  • Asad ul Islam Khan

Abstract

This paper evaluates the performance of eight tests with null hypothesis of cointegration on basis of probabilities of type I and II errors using Monte Carlo simulations. This study uses a variety of 132 different data generations covering three cases of deterministic part and four sample sizes. The three cases of deterministic part considered are: absence of both intercept and linear time trend, presence of only the intercept and presence of both the intercept and linear time trend. It is found that all of tests have either larger or smaller probabilities of type I error and concluded that tests face either problems of over rejection or under rejection, when asymptotic critical values are used. It is also concluded that use of simulated critical values leads to controlled probability of type I error. So, the use of asymptotic critical values may be avoided, and the use of simulated critical values is highly recommended. It is found and concluded that the simple LM test based on KPSS statistic performs better than rest for all specifications of deterministic part and sample sizes.

Suggested Citation

  • Ahmet Faruk Aysan & Ibrahim Guney & Nicoleta Isac & Asad ul Islam Khan, 2022. "The probabilities of type I and II error of null of cointegration tests: A Monte Carlo comparison," PLOS ONE, Public Library of Science, vol. 17(1), pages 1-15, January.
    • Handle: RePEc:plo:pone00:0259994
    DOI: 10.1371/journal.pone.0259994
    as

    Download full text from publisher

    File URL: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0259994
    Download Restriction: no
    File URL: https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0259994&type=printable
    Download Restriction: no
    File URL: https://libkey.io/10.1371/journal.pone.0259994?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. Johansen, Soren & Juselius, Katarina, 1990. "Maximum Likelihood Estimation and Inference on Cointegration--With Applications to the Demand for Money," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 52(2), pages 169-210, May.
    3. Haug, Alfred A., 1996. "Tests for cointegration a Monte Carlo comparison," Journal of Econometrics, Elsevier, vol. 71(1-2), pages 89-115.
    4. M. Hashem Pesaran & Yongcheol Shin & Richard J. Smith, 2001. "Bounds testing approaches to the analysis of level relationships," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 16(3), pages 289-326.
    5. Banerjee, Anindya, et al, 1986. "Exploring Equilibrium Relationships in Econometrics through Static Models: Some Monte Carlo Evidence," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 48(3), pages 253-277, August.
    6. Pesavento, Elena, 2004. "Analytical evaluation of the power of tests for the absence of cointegration," Journal of Econometrics, Elsevier, vol. 122(2), pages 349-384, October.
    7. 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.
    8. Engle, Robert & Granger, Clive, 2015. "Co-integration and error correction: Representation, estimation, and testing," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 39(3), pages 106-135.
    9. Vasco Gabriel, 2003. "Tests for the Null Hypothesis of Cointegration: A Monte Carlo Comparison," Econometric Reviews, Taylor & Francis Journals, vol. 22(4), pages 411-435.
    10. Peter C. B. Phillips & Bruce E. Hansen, 1990. "Statistical Inference in Instrumental Variables Regression with I(1) Processes," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 57(1), pages 99-125.
    11. Jansson, Michael, 2005. "Point optimal tests of the null hypothesis of cointegration," Journal of Econometrics, Elsevier, vol. 124(1), pages 187-201, January.
    12. Hansen, Bruce E, 2002. "Tests for Parameter Instability in Regressions with I(1) Processes," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 45-59, January.
    13. Novella Maugeri, 2014. "Some Pitfalls in Smooth Transition Models Estimation: A Monte Carlo Study," Computational Economics, Springer;Society for Computational Economics, vol. 44(3), pages 339-378, October.
    14. Shin, Yongcheol, 1994. "A Residual-Based Test of the Null of Cointegration Against the Alternative of No Cointegration," Econometric Theory, Cambridge University Press, vol. 10(1), pages 91-115, March.
    15. Gonzalo, Jesus & Lee, Tae-Hwy, 1998. "Pitfalls in testing for long run relationships," Journal of Econometrics, Elsevier, vol. 86(1), pages 129-154, June.
    16. A. Talha Yalta, 2016. "Bootstrap Inference of Level Relationships in the Presence of Serially Correlated Errors: A Large Scale Simulation Study and an Application in Energy Demand," Computational Economics, Springer;Society for Computational Economics, vol. 48(2), pages 339-366, August.
    17. Phillips, Peter C B & Ouliaris, S, 1990. "Asymptotic Properties of Residual Based Tests for Cointegration," Econometrica, Econometric Society, vol. 58(1), pages 165-193, January.
    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. Khan, Asad Ul Islam & Shahbaz, Muhammad & Napari, Ayuba, 2023. "Subsample stability, change detection and dynamics of oil and metal markets: A recursive approach," Resources Policy, Elsevier, vol. 83(C).

    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. Nicoleta ISAC & Cosmin DOBRIN & Mehmood HUSSAN & Asad ul Islam KHAN & Alina- Andreea MARIN, 2020. "On The Ranks Of Tests Having Null Of Cointegration: A Monte Carlo Comparison," Management Research and Practice, Research Centre in Public Administration and Public Services, Bucharest, Romania, vol. 12(2), pages 58-69, June.
    2. Javier Fernandez-Macho, 2013. "A Test for the Null of Multiple Cointegrating Vectors," Economics Series Working Papers 657, University of Oxford, Department of Economics.
    3. Österholm, Pär, 2003. "Testing for Cointegration in Misspecified Systems –A Monte Carlo Study of Size Distortions," Working Paper Series 2003:21, Uppsala University, Department of Economics.
    4. Matteo Mogliani, 2010. "Residual-based tests for cointegration and multiple deterministic structural breaks: A Monte Carlo study," Working Papers halshs-00564897, HAL.
    5. Ansgar Belke & Robert Czudaj, 2010. "Is Euro Area Money Demand (Still) Stable? Cointegrated VAR Versus Single Equation Techniques," Applied Economics Quarterly (formerly: Konjunkturpolitik), Duncker & Humblot, Berlin, vol. 56(4), pages 285-315.
    6. Norah Al-Ballaa, 2005. "Test for cointegration based on two-stage least squares," Journal of Applied Statistics, Taylor & Francis Journals, vol. 32(7), pages 707-713.
    7. repec:zbw:rwirep:0171 is not listed on IDEAS
    8. Tang, Chor Foon, 2008. "A re-examination of the relationship between electricity consumption and economic growth in Malaysia," Energy Policy, Elsevier, vol. 36(8), pages 3067-3075, August.
    9. Bibhuti Ranjan Mishra & Asit Mohanty, 2017. "An Empirical Analysis of Aggregate Import Demand Function for India," Global Economy Journal (GEJ), World Scientific Publishing Co. Pte. Ltd., vol. 17(4), pages 1-12, December.
    10. Philipp Lieberknecht & Philip Vermeulen, 2022. "Wealth and income inequality in the long run," Working Papers 2022-02, Auckland University of Technology, Department of Economics.
    11. Tang, Chor-Foon & Lau, Evan, 2011. "The Behaviour of Disaggregated Public Expenditures and Income in Malaysia," Review of Applied Economics, Lincoln University, Department of Financial and Business Systems, vol. 7(01-2), pages 1-13, March.
    12. Kirstin Hubrich & Helmut Lutkepohl & Pentti Saikkonen, 2001. "A Review Of Systems Cointegration Tests," Econometric Reviews, Taylor & Francis Journals, vol. 20(3), pages 247-318.
    13. Vasco Gabriel, 2003. "Tests for the Null Hypothesis of Cointegration: A Monte Carlo Comparison," Econometric Reviews, Taylor & Francis Journals, vol. 22(4), pages 411-435.
    14. Haug, Alfred A., 1996. "Tests for cointegration a Monte Carlo comparison," Journal of Econometrics, Elsevier, vol. 71(1-2), pages 89-115.
    15. Wang, Yi-Hsien & Lee, Jun-De, 2012. "Estimating the import demand function for China," Economic Modelling, Elsevier, vol. 29(6), pages 2591-2596.
    16. Samih Antoine Azar & Angelic Salha, 2017. "The Bias in the Long Run Relation between the Prices of BRENT and West Texas Intermediate Crude Oils," International Journal of Energy Economics and Policy, Econjournals, vol. 7(1), pages 44-54.
    17. Melo, Patricia C. & Sobreira, Nuno & Goulart, Pedro, 2019. "Estimating the long-run metro demand elasticities for Lisbon: A time-varying approach," Transportation Research Part A: Policy and Practice, Elsevier, vol. 126(C), pages 360-376.
    18. Ansgar Belke & Robert Czudaj, 2010. "Is Euro Area Money Demand (Still) Stable? – Cointegrated VAR versus Single Equation Techniques," Ruhr Economic Papers 0171, Rheinisch-Westfälisches Institut für Wirtschaftsforschung, Ruhr-Universität Bochum, Universität Dortmund, Universität Duisburg-Essen.
    19. Balsalobre-Lorente, Daniel & Bekun, Festus Victor & Etokakpan, Mfonobong Udom & Driha, Oana M., 2019. "A road to enhancements in natural gas use in Iran: A multivariate modelling approach," Resources Policy, Elsevier, vol. 64(C).
    20. Lise Pichette, 2000. "Les effets réels du cours des actions sur la consommation," Staff Working Papers 00-21, Bank of Canada.
    21. Caner Demir, 2019. "Macroeconomic Determinants of Stock Market Fluctuations: The Case of BIST-100," Economies, MDPI, vol. 7(1), pages 1-14, February.

    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:plo:pone00:0259994. 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: plosone (email available below). General contact details of provider: https://journals.plos.org/plosone/ .

    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.