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Multivariate high-frequency financial data via semi-Markov processes

  • Guglielmo D'Amico
  • Filippo Petroni

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.

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Paper provided by in its series Papers with number 1305.0436.

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Date of creation: May 2013
Date of revision:
Handle: RePEc:arx:papers:1305.0436
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  1. Enrico Scalas & Rudolf Gorenflo & Francesco Mainardi, 2000. "Fractional calculus and continuous-time finance," Papers cond-mat/0001120,
  2. Francesco Mainardi & Marco Raberto & Rudolf Gorenflo & Enrico Scalas, 2000. "Fractional calculus and continuous-time finance II: the waiting-time distribution," Papers cond-mat/0006454,, revised Nov 2000.
  3. 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.
  4. Marco Raberto & Enrico Scalas & Francesco Mainardi, 2004. "Waiting-times and returns in high-frequency financial data: an empirical study," Finance 0411014, EconWPA.
  5. Ingve Simonsen & Mogens H. Jensen & Anders Johansen, 2002. "Optimal Investment Horizons," Papers cond-mat/0202352,
  6. M. H. Jensen & A. Johansen & F. Petroni & I. Simonsen, 2004. "Inverse Statistics in the Foreign Exchange Market," Papers cond-mat/0402591,, revised Mar 2004.
  7. Guglielmo D'Amico & Filippo Petroni, 2011. "A semi-Markov model for price returns," Papers 1103.6143,
  8. 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.
  9. F. Petroni & M. Serva, 2003. "Spot foreign exchange market and time series," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, vol. 34(4), pages 495-500, August.
  10. Guglielmo D'Amico & Filippo Petroni, 2012. "Weighted-indexed semi-Markov models for modeling financial returns," Papers 1205.2551,, revised Jun 2012.
  11. 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, 09.
  12. Guglielmo D'Amico & Filippo Petroni, 2011. "A semi-Markov model with memory for price changes," Papers 1109.4259,, revised Dec 2011.
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