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Fitting the Cusp Catastrophe in R: A cusp Package Primer

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  • Grasman, Raoul
  • van der Maas, Han L.J.
  • Wagenmakers, Eric-Jan

Abstract

Of the seven elementary catastrophes in catastrophe theory, the "cusp" model is the most widely applied. Most applications are however qualitative. Quantitative techniques for catastrophe modeling have been developed, but so far the limited availability of flexible software has hindered quantitative assessment. We present a package that implements and extends the method of Cobb (Cobb and Watson'80; Cobb, Koppstein, and Chen'83), and makes it easy to quantitatively fit and compare different cusp catastrophe models in a statistically principled way. After a short introduction to the cusp catastrophe, we demonstrate the package with two instructive examples.

Suggested Citation

  • Grasman, Raoul & van der Maas, Han L.J. & Wagenmakers, Eric-Jan, 2009. "Fitting the Cusp Catastrophe in R: A cusp Package Primer," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 32(i08).
    • Handle: RePEc:jss:jstsof:v:032:i08
    DOI: http://hdl.handle.net/10.18637/jss.v032.i08
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    References listed on IDEAS

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    1. Cobb, Loren, 1980. "Estimation Theory for the Cusp Catastrophe Model," MPRA Paper 37548, University Library of Munich, Germany, revised 05 Jun 2010.
    2. Rosser Jr., J. Barkley, 2007. "The rise and fall of catastrophe theory applications in economics: Was the baby thrown out with the bathwater?," Journal of Economic Dynamics and Control, Elsevier, vol. 31(10), pages 3255-3280, October.
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    Cited by:

    1. Jozef Barunik & Jiri Kukacka, 2015. "Realizing stock market crashes: stochastic cusp catastrophe model of returns under time-varying volatility," Quantitative Finance, Taylor & Francis Journals, vol. 15(6), pages 959-973, June.
    2. Ding-Geng Chen & Xinguang Chen, 2017. "Cusp Catastrophe Regression and Its Application in Public Health and Behavioral Research," IJERPH, MDPI, vol. 14(10), pages 1-15, October.
    3. Ding-Geng Chen & Haipeng Gao & Chuanshu Ji, 2021. "Bayesian Inference for Stochastic Cusp Catastrophe Model with Partially Observed Data," Mathematics, MDPI, vol. 9(24), pages 1-9, December.
    4. Cobb, Loren, 1980. "Estimation Theory for the Cusp Catastrophe Model," MPRA Paper 37548, University Library of Munich, Germany, revised 05 Jun 2010.
    5. Angélique O J Cramer & Claudia D van Borkulo & Erik J Giltay & Han L J van der Maas & Kenneth S Kendler & Marten Scheffer & Denny Borsboom, 2016. "Major Depression as a Complex Dynamic System," PLOS ONE, Public Library of Science, vol. 11(12), pages 1-20, December.
    6. Tim Loossens & Merijn Mestdagh & Egon Dejonckheere & Peter Kuppens & Francis Tuerlinckx & Stijn Verdonck, 2020. "The Affective Ising Model: A computational account of human affect dynamics," PLOS Computational Biology, Public Library of Science, vol. 16(5), pages 1-27, May.
    7. Mohamed M. Mostafa, 2020. "Catastrophe Theory Predicts International Concern for Global Warming," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 18(3), pages 709-731, September.
    8. Jiri Kukacka & Ladislav Kristoufek, 2023. "Fundamental and speculative components of the cryptocurrency pricing dynamics," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 9(1), pages 1-23, December.
    9. Bełej Mirosław & Kulesza Sławomir, 2012. "Modeling the Real Estate Prices in Olsztyn under Instability Conditions," Folia Oeconomica Stetinensia, Sciendo, vol. 11(1), pages 61-72, January.
    10. Diks, Cees & Wang, Juanxi, 2016. "Can a stochastic cusp catastrophe model explain housing market crashes?," Journal of Economic Dynamics and Control, Elsevier, vol. 69(C), pages 68-88.
    11. Wang, J., 2015. "Can a stochastic cusp catastrophe model explain housing market crashes?," CeNDEF Working Papers 15-12, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    12. Sotolongo-Costa, O. & Gaggero-Sager, L.M. & Becker, J.T. & Maestu, F. & Sotolongo-Grau, O., 2017. "A physical model for dementia," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 472(C), pages 86-93.
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