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Critical Values And P Values Of Bessel Process Distributions: Computation And Application To Structural Break Tests

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  • Estrella, Arturo

Abstract

The p values of structural break tests, when the break date or dates are unknown, must be calculated in terms of the probability distributions of functions of Bessel processes. The literature so far has maintained that direct computation of these p values and of the corresponding critical values is too difficult and has relied on approximations based on simulations, asymptotic expansions, or curve fitting. This paper presents a fast simple method of calculating exact p values and critical values and uses the method to evaluate the accuracy of the various approximations.The author is grateful for comments and suggestions from Don Andrews, Clint Cummins, Jeff Fuhrer, Ken Garbade, Jim Mahoney, Tony Rodrigues, Josh Rosenberg, Sebastian Schich, participants in a workshop at the Federal Reserve Bank of New York, and the referees. The views expressed in this paper are those of the author and do not necessarily represent those of the Federal Reserve Bank of New York or the Federal Reserve System.

Suggested Citation

  • Estrella, Arturo, 2003. "Critical Values And P Values Of Bessel Process Distributions: Computation And Application To Structural Break Tests," Econometric Theory, Cambridge University Press, vol. 19(6), pages 1128-1143, December.
    • Handle: RePEc:cup:etheor:v:19:y:2003:i:06:p:1128-1143_19
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    Cited by:

    1. Hidalgo, Javier & Schafgans, Marcia, 2017. "Inference and testing breaks in large dynamic panels with strong cross sectional dependence," Journal of Econometrics, Elsevier, vol. 196(2), pages 259-274.
    2. Javier Hidalgo & Marcia M Schafgans, 2015. "Inference and Testing Breaks in Large Dynamic Panels with Strong Cross Sectional Dependence," STICERD - Econometrics Paper Series /2015/583, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    3. Paruolo, Paolo, 2006. "Common trends and cycles in I(2) VAR systems," Journal of Econometrics, Elsevier, vol. 132(1), pages 143-168, May.
    4. A. Batsidis & N. Martín & L. Pardo & K. Zografos, 2016. "ϕ-Divergence Based Procedure for Parametric Change-Point Problems," Methodology and Computing in Applied Probability, Springer, vol. 18(1), pages 21-35, March.
    5. Kim, Dukpa & Perron, Pierre, 2009. "Assessing the relative power of structural break tests using a framework based on the approximate Bahadur slope," Journal of Econometrics, Elsevier, vol. 149(1), pages 26-51, April.
    6. Jesús Gonzalo & Jean-Yves Pitarakis, 2011. "Regime-Specific Predictability in Predictive Regressions," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(2), pages 229-241, June.
    7. Christis Katsouris, 2023. "Predictability Tests Robust against Parameter Instability," Papers 2307.15151, arXiv.org.
    8. Arturo Estrella & Anthony P. Rodrigues, 2005. "One-sided test for an unknown breakpoint: theory, computation, and application to monetary theory," Staff Reports 232, Federal Reserve Bank of New York.
    9. Rosa, Carlo, 2011. "Words that shake traders," Journal of Empirical Finance, Elsevier, vol. 18(5), pages 915-934.
    10. Piterbarg, Vladimir I. & Rodionov, Igor V., 2020. "High excursions of Bessel and related random processes," Stochastic Processes and their Applications, Elsevier, vol. 130(8), pages 4859-4872.
    11. Heikki Kauppi, 2008. "Yield-Curve Based Probit Models for Forecasting U.S. Recessions: Stability and Dynamics," Discussion Papers 31, Aboa Centre for Economics.
    12. Castro, Carlos & Ferrari, Stijn, 2014. "Measuring and testing for the systemically important financial institutions," Journal of Empirical Finance, Elsevier, vol. 25(C), pages 1-14.
    13. Omtzigt, Pieter & Paruolo, Paolo, 2005. "Impact factors," Journal of Econometrics, Elsevier, vol. 128(1), pages 31-68, September.
    14. K. B. S. Huth & L. J. Waldorp & J. Luigjes & A. E. Goudriaan & R. J. Holst & M. Marsman, 2022. "A Note on the Structural Change Test in Highly Parameterized Psychometric Models," Psychometrika, Springer;The Psychometric Society, vol. 87(3), pages 1064-1080, September.
    15. Christiansen, Charlotte & Eriksen, Jonas Nygaard & Møller, Stig Vinther, 2014. "Forecasting US recessions: The role of sentiment," Journal of Banking & Finance, Elsevier, vol. 49(C), pages 459-468.
    16. Chen, Sanpan & Cui, Guowei & Zhang, Jianhua, 2017. "On testing for structural break of coefficients in factor-augmented regression models," Economics Letters, Elsevier, vol. 161(C), pages 141-145.
    17. Tom Campbell & Nathaniel T. Wilcox, 2020. "Younger Federal District Court Judges Favor Presidential Power," Journal of Law and Economics, University of Chicago Press, vol. 63(1), pages 181-202.
    18. Charles-Elie Rabier & Jean-Marc Azaïs & Jean-Michel Elsen & Céline Delmas, 2019. "Chi-square processes for gene mapping in a population with family structure," Statistical Papers, Springer, vol. 60(1), pages 239-271, February.
    19. Ng, Eric C.Y., 2012. "Forecasting US recessions with various risk factors and dynamic probit models," Journal of Macroeconomics, Elsevier, vol. 34(1), pages 112-125.
    20. Sandip Sinharay, 2016. "Person Fit Analysis in Computerized Adaptive Testing Using Tests for a Change Point," Journal of Educational and Behavioral Statistics, , vol. 41(5), pages 521-549, October.
    21. Matthew Davis & Fernando V. Ferreira, 2017. "Housing Disease and Public School Finances," NBER Working Papers 24140, National Bureau of Economic Research, Inc.
    22. Hidalgo, Javier & Schafgans, Marcia, 2017. "Inference and testing breaks in large dynamic panels with strong cross sectional dependence," LSE Research Online Documents on Economics 68839, London School of Economics and Political Science, LSE Library.
    23. Li, Kunpeng, 2018. "Spatial panel data models with structural change," MPRA Paper 85388, University Library of Munich, Germany.
    24. Gonzalo, Jesus & Pitarakis, Jean-Yves, 2010. "Regime specific predictability in predictive regressions," Discussion Paper Series In Economics And Econometrics 0916, Economics Division, School of Social Sciences, University of Southampton.
    25. Davis, Matthew & Ferreira, Fernando, 2022. "Housing disease and public school finances," Economics of Education Review, Elsevier, vol. 88(C).

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