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Bayesian analysis of chaos: The joint return-volatility dynamical system

Author

Listed:
  • Tsionas, Mike G.
  • Michaelides, Panayotis G.

Abstract

We use a novel Bayesian inference procedure for the Lyapunov exponent in the dynamical system of returns and their unobserved volatility. In the dynamical system, computation of largest Lyapunov exponent by tradi- tional methods is impossible as the stochastic nature has to be taken explicitly into account due to unobserved volatility. We apply the new techniques to daily stock return data for a group of six world countries, namely USA, UK, Switzerland, Netherlands, Germany and France, from 2003 to 2014 by means of Sequential Monte Carlo for Bayesian inference. The evidence points to the direction that there is indeed noisy chaos both before and after the recent financial crisis. However, when a much simpler model is examined where the interaction between returns and volatility is not taken into consideration jointly, the hypothesis of chaotic dynamics does not receive much support by the data (“neglected chaos”).

Suggested Citation

  • Tsionas, Mike G. & Michaelides, Panayotis G., 2017. "Bayesian analysis of chaos: The joint return-volatility dynamical system," MPRA Paper 80632, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:80632
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    File URL: https://mpra.ub.uni-muenchen.de/80632/1/MPRA_paper_80632.pdf
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    References listed on IDEAS

    as
    1. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    2. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 2002. "Bayesian Analysis of Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 69-87, January.
    3. Lahmiri, Salim, 2017. "A study on chaos in crude oil markets before and after 2008 international financial crisis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 466(C), pages 389-395.
    4. Mishra, Ritesh Kumar & Sehgal, Sanjay & Bhanumurthy, N.R., 2011. "A search for long-range dependence and chaotic structure in Indian stock market," Review of Financial Economics, Elsevier, vol. 20(2), pages 96-104, May.
    5. Roberto Casarin & Jean-Michel Marin, 2007. "Online data processing: comparison of Bayesian regularized particle filters," Working Papers 0703, University of Brescia, Department of Economics.
    6. Christophe Andrieu & Arnaud Doucet & Roman Holenstein, 2010. "Particle Markov chain Monte Carlo methods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(3), pages 269-342.
    7. Hall, Jamie & Pitt, Michael K. & Kohn, Robert, 2014. "Bayesian inference for nonlinear structural time series models," Journal of Econometrics, Elsevier, vol. 179(2), pages 99-111.
    8. Morales, Raffaello & Di Matteo, T. & Gramatica, Ruggero & Aste, Tomaso, 2012. "Dynamical generalized Hurst exponent as a tool to monitor unstable periods in financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(11), pages 3180-3189.
    9. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 1994. "Bayesian Analysis of Stochastic Volatility Models: Comments: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(4), pages 413-417, October.
    10. repec:bla:restud:v:65:y:1998:i:3:p:361-93 is not listed on IDEAS
    11. Michaelides, Panayotis G. & Tsionas, Efthymios G. & Vouldis, Angelos T. & Konstantakis, Konstantinos N., 2015. "Global approximation to arbitrary cost functions: A Bayesian approach with application to US banking," European Journal of Operational Research, Elsevier, vol. 241(1), pages 148-160.
    12. Flury, Thomas & Shephard, Neil, 2011. "Bayesian Inference Based Only On Simulated Likelihood: Particle Filter Analysis Of Dynamic Economic Models," Econometric Theory, Cambridge University Press, vol. 27(05), pages 933-956, October.
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    More about this item

    Keywords

    Noisy Chaos; Lyapunov exponent; Neural networks; Bayesian analysis; Sequential Monte Carlo; World Economy.;

    JEL classification:

    • C0 - Mathematical and Quantitative Methods - - General
    • G1 - Financial Economics - - General Financial Markets

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