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Multivariate high-frequency financial data via semi-Markov processes

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  • Guglielmo D'Amico
  • Filippo Petroni

Abstract

In this paper we propose a bivariate generalization of a weighted indexed semi-Markov chains to study the high frequency price dynamics of traded stocks. We assume that financial returns are described by a weighted indexed semi-Markov chain model. We show, through Monte Carlo simulations, that the model is able to reproduce important stylized facts of financial time series like the persistence of volatility and at the same time it can reproduce the correlation between stocks. The model is applied to data from Italian stock market from 1 January 2007 until the end of December 2010.

Suggested Citation

  • Guglielmo D'Amico & Filippo Petroni, 2013. "Multivariate high-frequency financial data via semi-Markov processes," Papers 1305.0436, arXiv.org.
  • Handle: RePEc:arx:papers:1305.0436
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    File URL: http://arxiv.org/pdf/1305.0436
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    References listed on IDEAS

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    1. Guglielmo D'Amico & Filippo Petroni & Flavio Prattico, 2013. "Wind speed modeled as an indexed semi‐Markov process," Environmetrics, John Wiley & Sons, Ltd., vol. 24(6), pages 367-376, September.
    2. D’Amico, Guglielmo & Petroni, Filippo, 2012. "A semi-Markov model for price returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(20), pages 4867-4876.
    3. Guglielmo D'Amico & Filippo Petroni, 2012. "Weighted-indexed semi-Markov models for modeling financial returns," Papers 1205.2551, arXiv.org, revised Jun 2012.
    4. F. Petroni & M. Serva, 2003. "Spot foreign exchange market and time series," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 34(4), pages 495-500, August.
    5. Mainardi, Francesco & Raberto, Marco & Gorenflo, Rudolf & Scalas, Enrico, 2000. "Fractional calculus and continuous-time finance II: the waiting-time distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(3), pages 468-481.
    6. Raberto, Marco & Scalas, Enrico & Mainardi, Francesco, 2002. "Waiting-times and returns in high-frequency financial data: an empirical study," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 314(1), pages 749-755.
    7. Scalas, Enrico & Gorenflo, Rudolf & Mainardi, Francesco, 2000. "Fractional calculus and continuous-time finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 284(1), pages 376-384.
    8. Guglielmo D'Amico & Filippo Petroni, 2011. "A semi-Markov model with memory for price changes," Papers 1109.4259, arXiv.org, revised Dec 2011.
    9. Ingve Simonsen & Mogens H. Jensen & Anders Johansen, 2002. "Optimal Investment Horizons," Papers cond-mat/0202352, arXiv.org.
    10. Jensen, M.H & Johansen, A & Petroni, F & Simonsen, I, 2004. "Inverse statistics in the foreign exchange market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 340(4), pages 678-684.
    11. D’Amico, Guglielmo & Petroni, Filippo & Prattico, Flavio, 2013. "First and second order semi-Markov chains for wind speed modeling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(5), pages 1194-1201.
    12. Richard B. Olsen & Ulrich A. Müller & Michel M. Dacorogna & Olivier V. Pictet & Rakhal R. Davé & Dominique M. Guillaume, 1997. "From the bird's eye to the microscope: A survey of new stylized facts of the intra-daily foreign exchange markets (*)," Finance and Stochastics, Springer, vol. 1(2), pages 95-129.
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    Cited by:

    1. Guglielmo D'Amico & Filippo Petroni, 2017. "A new approach to the modeling of financial volumes," Papers 1709.05823, arXiv.org.

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