IDEAS home Printed from https://ideas.repec.org/p/tky/fseres/2023cf1216.html
   My bibliography  Save this paper

Johansen Test with Fourier-Type Smooth Nonlinear Trends in Cointegrating Relations

Author

Listed:
  • Takamitsu Kurita

    (Faculty of Economics, Kyoto Sangyo University)

  • Mototsugu Shintani

    (Faculty of Economics, The University of Tokyo)

Abstract

We develop methodology for testing cointegrating rank in vector autoregressive (VAR) models in the presence of Fourier-type smooth nonlinear deterministic trends in cointegrating relations. The limiting distribution of log-likelihood ratio test statistics is derived and approximated limit quantiles are tabulated. A sequential procedure to select cointegrating rank is evaluated by Monte Carlo simulations. Our empirical application to economic data also demonstrates the usefulness of the proposed methodology in a practical context.

Suggested Citation

  • Takamitsu Kurita & Mototsugu Shintani, 2023. "Johansen Test with Fourier-Type Smooth Nonlinear Trends in Cointegrating Relations," CIRJE F-Series CIRJE-F-1216, CIRJE, Faculty of Economics, University of Tokyo.
    • Handle: RePEc:tky:fseres:2023cf1216
    as

    Download full text from publisher

    File URL: http://www.cirje.e.u-tokyo.ac.jp/research/dp/2023/2023cf1216.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Zheng‐Feng Guo & Mototsugu Shintani, 2013. "Consistent co‐trending rank selection when both stochastic and non‐linear deterministic trends are present," Econometrics Journal, Royal Economic Society, vol. 16(3), pages 473-484, October.
    2. David I. Harvey & Stephen J. Leybourne & Lisa Xiao, 2010. "Testing for nonlinear deterministic components when the order of integration is unknown," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(5), pages 379-391, September.
    3. Søren Johansen & Rocco Mosconi & Bent Nielsen, 2000. "Cointegration analysis in the presence of structural breaks in the deterministic trend," Econometrics Journal, Royal Economic Society, vol. 3(2), pages 216-249.
    4. Håvard Hungnes, 2010. "Identifying Structural Breaks in Cointegrated Vector Autoregressive Models," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 72(4), pages 551-565, August.
    5. Saikkonen, Pentti, 2001. "Statistical Inference In Cointegrated Vector Autoregressive Models With Nonlinear Time Trends In Cointegrating Relations," Econometric Theory, Cambridge University Press, vol. 17(2), pages 327-356, April.
    6. Saikkonen, Pentti, 2001. "Consistent Estimation In Cointegrated Vector Autoregressive Models With Nonlinear Time Trends In Cointegrating Relations," Econometric Theory, Cambridge University Press, vol. 17(2), pages 296-326, April.
    7. Hendry, David F., 2006. "Robustifying forecasts from equilibrium-correction systems," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 399-426.
    8. Helmut Lütkepohl & Pentti Saikkonen & Carsten Trenkler, 2004. "Testing for the Cointegrating Rank of a VAR Process with Level Shift at Unknown Time," Econometrica, Econometric Society, vol. 72(2), pages 647-662, March.
    9. Razvan Pascalau, 2010. "Unit root tests with smooth breaks: an application to the Nelson-Plosser data set," Applied Economics Letters, Taylor & Francis Journals, vol. 17(6), pages 565-570.
    10. Søren Johansen & Rocco Mosconi & Bent Nielsen, 2000. "Cointegration analysis in the presence of structural breaks in the deterministic trend," Econometrics Journal, Royal Economic Society, vol. 3(2), pages 216-249.
    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. Takamitsu Kurita & B. Nielsen, 2018. "Partial cointegrated vector autoregressive models with structural breaks in deterministic terms," Economics Papers 2018-W03, Economics Group, Nuffield College, University of Oxford.
    2. Takamitsu Kurita & Bent Nielsen, 2019. "Partial Cointegrated Vector Autoregressive Models with Structural Breaks in Deterministic Terms," Econometrics, MDPI, vol. 7(4), pages 1-35, October.
    3. Razvan Pascalau & Junsoo Lee & Saban Nazlioglu & Yan (Olivia) Lu, 2022. "Johansen‐type cointegration tests with a Fourier function," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(5), pages 828-852, September.
    4. Kosei Fukuda, 2011. "Cointegration rank switching model: an application to forecasting interest rates," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 30(5), pages 509-522, August.
    5. Takamitsu Kurita & Patrick James, 2022. "The Canadian–US dollar exchange rate over the four decades of the post‐Bretton Woods float: An econometric study allowing for structural breaks," Metroeconomica, Wiley Blackwell, vol. 73(3), pages 856-883, July.
    6. Norman-Lόpez, Ana & Pascoe, Sean & Thébaud, Olivier & Van Putten, Ingrid & Innes, James & Jennings, Sarah & Hobday, Alistair & Green, Bridget & Plaganyi, Eva, 2014. "Price integration in the Australian rock lobster industry: implications for management and climate change adaptation," Australian Journal of Agricultural and Resource Economics, Australian Agricultural and Resource Economics Society, vol. 58(1), January.
    7. Khaled Chnaina & Farid Makhlouf, 2015. "Impact des Transferts de Fonds sur le Taux de Change Réel Effectif en Tunisie," African Development Review, African Development Bank, vol. 27(2), pages 145-160, June.
    8. Pierre Perron & Mototsugu Shintani & Tomoyoshi Yabu, 2017. "Testing for Flexible Nonlinear Trends with an Integrated or Stationary Noise Component," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 79(5), pages 822-850, October.
    9. Takamitsu Kurita, 2019. "A Recursive Monte Carlo Study of Structural-Break Sensitivity of Adjustment Coefficients in Cointegrated VAR Systems," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 17(2), pages 251-270, June.
    10. Harris, David & Leybourne, Stephen J. & Taylor, A.M. Robert, 2016. "Tests of the co-integration rank in VAR models in the presence of a possible break in trend at an unknown point," Journal of Econometrics, Elsevier, vol. 192(2), pages 451-467.
    11. Gormus, Alper & Nazlioglu, Saban & Soytas, Ugur, 2018. "High-yield bond and energy markets," Energy Economics, Elsevier, vol. 69(C), pages 101-110.
    12. Carlomagno, Guillermo & Espasa, Antoni, 2015. "Forecasting a large set of disaggregates with common trends and outliers," DES - Working Papers. Statistics and Econometrics. WS ws1518, Universidad Carlos III de Madrid. Departamento de Estadística.
    13. Banerjee, Piyali & Arčabić, Vladimir & Lee, Hyejin, 2017. "Fourier ADL cointegration test to approximate smooth breaks with new evidence from Crude Oil Market," Economic Modelling, Elsevier, vol. 67(C), pages 114-124.
    14. David H. Bernstein & Bent Nielsen, 2019. "Asymptotic Theory for Cointegration Analysis When the Cointegration Rank Is Deficient," Econometrics, MDPI, vol. 7(1), pages 1-24, January.
    15. Hannu KOSKINEN, 2010. "Modelling of Structural Changes in Demand for Money Cointegration Relations," EcoMod2004 330600082, EcoMod.
    16. Fatih Kaplan & Ayşe E. Ünal, 2020. "Industrial Production Index - Crude Oil Price Nexus: Russia, Kazakhstan And Azerbaijan," Economic Annals, Faculty of Economics and Business, University of Belgrade, vol. 65(227), pages 119-142, October –.
    17. Skrobotov, Anton, 2021. "Structural breaks in cointegration models: Multivariate case," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 64, pages 83-106.
    18. Carsten Trenkler*, 2005. "The Effects of Ignoring Level Shifts on Systems Cointegration Tests," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 89(3), pages 281-301, August.
    19. Carsten Trenkler, 2008. "Determining p-values for systems cointegration tests with a prior adjustment for deterministic terms," Computational Statistics, Springer, vol. 23(1), pages 19-39, January.
    20. Winkelried, Diego, 2018. "Unit roots, flexible trends, and the Prebisch-Singer hypothesis," Journal of Development Economics, Elsevier, vol. 132(C), pages 1-17.

    More about this item

    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:tky:fseres:2023cf1216. 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: CIRJE administrative office (email available below). General contact details of provider: https://edirc.repec.org/data/ritokjp.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.