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A Process-Reconstruction Analysis Of Market Fluctuations

Author

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  • R. VILELA MENDES

    (Laboratório de Mecatrónica, DEEC, Instituto Superior Técnico, Av. Rovisco Pais, 1096 Lisboa Codex, Portugal;
    Zentrum für interdisziplinäre Forschung, Universität Bielefeld, Wellenberg 1, 33615 Bielefeld, Germany)

  • R. LIMA

    (Zentrum für interdisziplinäre Forschung, Universität Bielefeld, Wellenberg 1, 33615 Bielefeld, Germany;
    Centre de Physique Théorique CNRS, Luminy, Case 907, F13288 Marseille Cedex 9, France)

  • T. ARAÚJO

    (Zentrum für interdisziplinäre Forschung, Universität Bielefeld, Wellenberg 1, 33615 Bielefeld, Germany;
    Dept. Economia, ISEG, R. Miguel Lupi 20, 1200 Lisboa, Portugal)

Abstract

The statistical properties of a stochastic process may be described (1) by the expectation values of the observables, (2) by the probability distribution functions or (3) by probability measures on path space. Here an analysis of level (3) is carried out for market fluctuation processes. Gibbs measures and chains with complete connections are considered. Some other topics are also discussed, in particular the asymptotic stationarity of the processes and the behavior of statistical indicators of level (1) and (2). We end up with some remarks concerning the nature and origin of the market fluctuation process and its relation to the efficient market hypothesis.

Suggested Citation

  • R. Vilela Mendes & R. Lima & T. Araújo, 2002. "A Process-Reconstruction Analysis Of Market Fluctuations," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 5(08), pages 797-821.
    • Handle: RePEc:wsi:ijtafx:v:05:y:2002:i:08:n:s0219024902001730
    DOI: 10.1142/S0219024902001730
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    Citations

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    Cited by:

    1. Hugo C. Mendes & Alberto Murta & R. Vilela Mendes, 2015. "Long Range Dependence And The Dynamics Of Exploited Fish Populations," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 18(07n08), pages 1-14, November.
    2. Vilela Mendes, R. & Araújo, Tanya & Louçã, Francisco, 2003. "Reconstructing an economic space from a market metric," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 323(C), pages 635-650.
    3. R. Vilela Mendes & M. J. Oliveira & A. M. Rodrigues, 2012. "The fractional volatility model: No-arbitrage, leverage and completeness," Papers 1205.2866, arXiv.org.
    4. Rui Vilela Mendes & M. J. Oliveira, 2006. "A data-reconstructed fractional volatility model," Papers math/0602013, arXiv.org, revised Jun 2007.
    5. Mansur Filho, J.C. & Silva, A.G. & Carvalho, A.T.G. & Martins, M.L., 2005. "Electrocrystallization under magnetic fields: experiment and model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 350(2), pages 393-406.
    6. Vilela Mendes, R. & Oliveira, M.J. & Rodrigues, A.M., 2015. "No-arbitrage, leverage and completeness in a fractional volatility model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 419(C), pages 470-478.
    7. Tanya Ara'ujo & Paulo Barbosa, 2023. "Reconstructing cryptocurrency processes via Markov chains," Papers 2308.07626, arXiv.org.

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