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Estimation Theory for the Cusp Catastrophe Model

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  • Cobb, Loren

Abstract

The cusp model of catastrophe theory is very closely related to certain multiparameter exponential families of probability density functions. This relationship is exploited to create an estimation theory for the cusp model. An example is presented in which an independent variable has a bifurcation effect on the dependent variable.

Suggested Citation

  • Cobb, Loren, 1980. "Estimation Theory for the Cusp Catastrophe Model," MPRA Paper 37548, University Library of Munich, Germany, revised 05 Jun 2010.
    • Handle: RePEc:pra:mprapa:37548
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    File URL: https://mpra.ub.uni-muenchen.de/37548/1/MPRA_paper_37548.pdf
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    References listed on IDEAS

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    1. 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).
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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. Gerß, Wolfgang, 2008. "Das Ende der DDR als konsequente mathematische Katastrophe," Duisburger Beiträge zur soziologischen Forschung 1/2008, University of Duisburg-Essen, Institute of Sociology.
    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. 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).
    5. Kukacka, Jiri & Kristoufek, Ladislav, 2020. "Do ‘complex’ financial models really lead to complex dynamics? Agent-based models and multifractality," Journal of Economic Dynamics and Control, Elsevier, vol. 113(C).
    6. Yi-Wen Kuo & Cheng-Hsien Hsieh & Yu-Chen Hung, 2021. "Non-linear characteristics in switching intention to use a docked bike-sharing system," Transportation, Springer, vol. 48(3), pages 1459-1479, June.
    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. Lange, Rense & McDade, Sean & Oliva, Terence A., 2001. "Technological choice and network externalities: a catastrophe model analysis of firm software adoption for competing operating systems," Structural Change and Economic Dynamics, Elsevier, vol. 12(1), pages 29-57, March.
    9. Asti Meiza & Sutawanir Darwis & Agus Yodi Gunawan & Efi Fitriana, 2017. "Quantitative Analysis of the Relationship between Three Psychological Parameters Based on Swallowtail Catastrophe Model," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2017, pages 1-6, September.
    10. 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.
    11. Miloslav Vošvrda & Jozef Baruník, 2008. "Modelování krachů na kapitálových trzích: aplikace teorie stochastických katastrof [Stock market crashes modeling: stochastic cusp catastrophe application]," Politická ekonomie, Prague University of Economics and Business, vol. 2008(6), pages 759-771.
    12. Yi-Wen Kuo & Cheng-Hsien Hsieh & Yu-Chen Hung, 0. "Non-linear characteristics in switching intention to use a docked bike-sharing system," Transportation, Springer, vol. 0, pages 1-21.

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    More about this item

    Keywords

    cusp; catastrophe; exponential family;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

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