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Determining p-values for systems cointegration tests with a prior adjustment for deterministic terms

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  • Carsten Trenkler

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Abstract

In this paper I present a procedure to approximate the asymptotic distributions of systems cointegration tests with a prior adjustment for deterministic terms suggested by Lütkepohl, Saikkonen & Trenkler (2004), Saikkonen & Lütkepohl (2000a, 2000b, 2000c), and Saikkonen & Luukkonen (1997). The asymptotic distributions are approximated by the Gamma distribution and the parameters necessary to fit the Gamma distributions are obtained from response surfaces which I describe in this paper. The approximation can be easily used to derive arbitrary p-values or percentiles.
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Suggested Citation

  • 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.
  • Handle: RePEc:spr:compst:v:23:y:2008:i:1:p:19-39
    DOI: 10.1007/s00180-007-0066-8
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    References listed on IDEAS

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    1. MacKinnon, James G & Haug, Alfred A & Michelis, Leo, 1999. "Numerical Distribution Functions of Likelihood Ratio Tests for Cointegration," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(5), pages 563-577, Sept.-Oct.
    2. Saikkonen, Pentti & L tkepohl, Helmut, 2000. "Testing For The Cointegrating Rank Of A Var Process With An Intercept," Econometric Theory, Cambridge University Press, vol. 16(03), pages 373-406, June.
    3. Doornik, Jurgen A, 1998. " Approximations to the Asymptotic Distributions of Cointegration Tests," Journal of Economic Surveys, Wiley Blackwell, vol. 12(5), pages 573-593, December.
    4. van Giersbergen, Noud P A, 1996. "Bootstrapping the Trace Statistic in VAR Models: Monte Carlo Results and Applications," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 58(2), pages 391-408, May.
    5. Trenkler, Carsten, 2009. "Bootstrapping Systems Cointegration Tests With A Prior Adjustment For Deterministic Terms," Econometric Theory, Cambridge University Press, vol. 25(01), pages 243-269, February.
    6. Saikkonen, Pentti & Luukkonen, Ritva, 1997. "Testing cointegration in infinite order vector autoregressive processes," Journal of Econometrics, Elsevier, vol. 81(1), pages 93-126, November.
    7. Carsten Trenkler, 2003. "A new set of critical values for systems cointegration tests with a prior adjustment for deterministic terms," Economics Bulletin, AccessEcon, vol. 3(11), pages 1-9.
    8. Helmut Lütkepohl & Pentti Saikkonen & Carsten Trenkler, 2001. "Maximum eigenvalue versus trace tests for the cointegrating rank of a VAR process," Econometrics Journal, Royal Economic Society, vol. 4(2), pages 1-8.
    9. 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.
    10. Kirstin Hubrich & Helmut Lutkepohl & Pentti Saikkonen, 2001. "A Review Of Systems Cointegration Tests," Econometric Reviews, Taylor & Francis Journals, vol. 20(3), pages 247-318.
    11. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501.
    12. repec:ebl:ecbull:v:3:y:2003:i:11:p:1-9 is not listed on IDEAS
    13. 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.
    14. Harris, R. I. D. & Judge, G., 1998. "Small sample testing for cointegration using the bootstrap approach," Economics Letters, Elsevier, vol. 58(1), pages 31-37, January.
    15. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
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    Cited by:

    1. Byrne, Joseph P. & Nagayasu, Jun, 2010. "Structural breaks in the real exchange rate and real interest rate relationship," Global Finance Journal, Elsevier, vol. 21(2), pages 138-151.
    2. Yahia Salhi & Stéphane Loisel, 2012. "Basis risk modelling: a co-integration based approach," Working Papers hal-00746859, HAL.
    3. Carsten Trenkler & Pentti Saikkonen & Helmut Lütkepohl, 2008. "Testing for the Cointegrating Rank of a VAR Process with Level Shift and Trend Break," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(2), pages 331-358, March.
    4. Jamal HUSEIN, 2008. "Traditional Export Demand Relation: A Cointegration and Parameter Constancy Analysis," International Journal of Applied Econometrics and Quantitative Studies, Euro-American Association of Economic Development, vol. 5(2).
    5. Karaman Örsal, Deniz Dilan & Droge, Bernd, 2014. "Panel cointegration testing in the presence of a time trend," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 377-390.
    6. Cristopher Spencer & Paul Temple, 2013. "Standards, Learning and Growth in Britain 1901-2009," School of Economics Discussion Papers 0613, School of Economics, University of Surrey.
    7. Peter Claeys, 2007. "Estimating the effects of fiscal policy under the budget constraint," IREA Working Papers 200715, University of Barcelona, Research Institute of Applied Economics, revised Jul 2007.
    8. Enzo Weber, 2012. "Regional and outward economic integration in South-East Asia," Applied Economics, Taylor & Francis Journals, vol. 44(10), pages 1271-1283, April.
    9. Trenkler, Carsten, 2009. "Bootstrapping Systems Cointegration Tests With A Prior Adjustment For Deterministic Terms," Econometric Theory, Cambridge University Press, vol. 25(01), pages 243-269, February.
    10. Karel Mertens, 2006. "How the Removal of Deposit Rate Ceilings Has Changed Monetary Transmission in the US: Theory and Evidence," Economics Working Papers ECO2006/34, European University Institute.
    11. María Lorena Marí Del Cristo & Marta Gómez-Puig, 2013. "Pass-through in dollarized countries: should Ecuador abandon the US dollar?," Applied Economics, Taylor & Francis Journals, vol. 45(31), pages 4395-4411, November.
    12. Giuseppe Cavaliere & A. M. Robert Taylor & Carsten Trenkler, 2013. "Bootstrap Cointegration Rank Testing: The Role of Deterministic Variables and Initial Values in the Bootstrap Recursion," Econometric Reviews, Taylor & Francis Journals, vol. 32(7), pages 814-847, October.
    13. Weber, Enzo, 2009. "Common and uncommon sources of growth in Asia Pacific," Journal of the Japanese and International Economies, Elsevier, vol. 23(1), pages 20-36, March.
    14. Antonia Arsova & Deniz Dilan Karaman Örsal, 2016. "An intersection test for the cointegrating rank in dependent panel data," Working Paper Series in Economics 357, University of Lüneburg, Institute of Economics.
    15. Keen Meng Choy, 2012. "Trade Cycles in a Re-export Economy: The Case of Singapore," International Economic Journal, Taylor & Francis Journals, vol. 26(2), pages 189-201, January.
    16. Koukouritakis, Minoas & Papadopoulos, Athanasios P. & Yannopoulos, Andreas, 2014. "Transmission effects in the presence of structural breaks: Evidence from South-Eastern European countries," Economic Modelling, Elsevier, vol. 41(C), pages 298-311.
    17. Enzo Weber, 2009. "Macroeconomic Integration in Asia-Pacific: Common Stochastic Trends and Business Cycle Coherence," The IUP Journal of Applied Economics, IUP Publications, vol. 0(3-4), pages 84-106, May-July.
    18. Giannellis, Nikolaos & Koukouritakis, Minoas, 2013. "Exchange rate misalignment and inflation rate persistence: Evidence from Latin American countries," International Review of Economics & Finance, Elsevier, vol. 25(C), pages 202-218.
    19. Karaman Örsal, Deniz Dilan & Arsova, Antonia, 2017. "Meta-analytic cointegrating rank tests for dependent panels," Econometrics and Statistics, Elsevier, vol. 2(C), pages 61-72.
    20. Christopher Spencer & Paul Temple, 2012. "Alternative Paths of Learning: Standardisation and Growth in Britain, 1901-2009," Discussion Paper Series 2012_10, Department of Economics, Loughborough University, revised Oct 2012.
    21. Nikolaos Giannellis & Minoas Koukouritakis, 2011. "Behavioural equilibrium exchange rate and total misalignment: evidence from the euro exchange rate," Empirica, Springer;Austrian Institute for Economic Research;Austrian Economic Association, vol. 38(4), pages 555-578, November.
    22. Deniz Dilan Karaman Örsal & Antonia Arsova, 2015. "Meta-analytic cointegrating rank tests for dependent panels," Working Paper Series in Economics 349, University of Lüneburg, Institute of Economics.
    23. Husein, J, 2010. "Export-Led Growth Hypothesis In The Mena Region: A Multivariate Cointegration, Causality And Stability Analysis," Applied Econometrics and International Development, Euro-American Association of Economic Development, vol. 10(2).
    24. Minoas Koukouritakis, 2010. "Structural breaks and the expectations hypothesis of the term structure: evidence from Central European countries," Review of World Economics (Weltwirtschaftliches Archiv), Springer;Institut für Weltwirtschaft (Kiel Institute for the World Economy), vol. 145(4), pages 757-774, January.
    25. Antonia Arsova & Deniz Dilan Karaman Oersal, 2013. "Likelihood-based panel cointegration test in the presence of a linear time trend and cross-sectional dependence," Working Paper Series in Economics 280, University of Lüneburg, Institute of Economics.

    More about this item

    Keywords

    Systems cointegration tests; Response surface; p-values;

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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