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The log-periodic-AR(1)-GARCH(1,1) model for financial crashes

Author

Listed:
  • L. Gazola
  • C. Fernandes
  • A. Pizzinga
  • R. Riera

Abstract

This paper intends to meet recent claims for the attainment of more rigorous statistical methodology within the econophysics literature. To this end, we consider an econometric approach to investigate the outcomes of the log-periodic model of price movements, which has been largely used to forecast financial crashes. In order to accomplish reliable statistical inference for unknown parameters, we incorporate an autoregressive dynamic and a conditional heteroskedasticity structure in the error term of the original model, yielding the log-periodic-AR(1)-GARCH(1,1) model. Both the original and the extended models are fitted to financial indices of U. S. market, namely S&P500 and NASDAQ. Our analysis reveal two main points: (i) the log-periodic-AR(1)-GARCH(1,1) model has residuals with better statistical properties and (ii) the estimation of the parameter concerning the time of the financial crash has been improved.

Suggested Citation

  • L. Gazola & C. Fernandes & A. Pizzinga & R. Riera, 2008. "The log-periodic-AR(1)-GARCH(1,1) model for financial crashes," Papers 0801.4341, arXiv.org.
    • Handle: RePEc:arx:papers:0801.4341
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    Cited by:

    1. Petr Geraskin & Dean Fantazzini, 2013. "Everything you always wanted to know about log-periodic power laws for bubble modeling but were afraid to ask," The European Journal of Finance, Taylor & Francis Journals, vol. 19(5), pages 366-391, May.
    2. Hong Qiu & Genhua Hu & Yuhong Yang & Jeffrey Zhang & Ting Zhang, 2020. "Modeling the Risk of Extreme Value Dependence in Chinese Regional Carbon Emission Markets," Sustainability, MDPI, vol. 12(19), pages 1-15, September.
    3. Sornette, Didier & Woodard, Ryan & Yan, Wanfeng & Zhou, Wei-Xing, 2013. "Clarifications to questions and criticisms on the Johansen–Ledoit–Sornette financial bubble model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(19), pages 4417-4428.
    4. Phong Nguyen & Wei-han Liu, 2017. "Time-Varying Linkage of Possible Safe Haven Assets: A Cross-Market and Cross-asset Analysis," International Review of Finance, International Review of Finance Ltd., vol. 17(1), pages 43-76, March.
    5. C. Vladimir Rodríguez-Caballero & Mauricio Villanueva-Domínguez, 2022. "Predicting cryptocurrency crash dates," Empirical Economics, Springer, vol. 63(6), pages 2855-2873, December.

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