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Indexed Markov Chains for financial data: testing for the number of states of the index process

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  • Guglielmo D'Amico
  • Ada Lika
  • Filippo Petroni

Abstract

A new branch based on Markov processes is developing in the recent literature of financial time series modeling. In this paper, an Indexed Markov Chain has been used to model high frequency price returns of quoted firms. The peculiarity of this type of model is that through the introduction of an Index process it is possible to consider the market volatility endogenously and two very important stylized facts of financial time series can be taken into account: long memory and volatility clustering. In this paper, first we propose a method for the optimal determination of the state space of the Index process which is based on a change-point approach for Markov chains. Furthermore we provide an explicit formula for the probability distribution function of the first change of state of the index process. Results are illustrated with an application to intra-day prices of a quoted Italian firm from January $1^{st}$, 2007 to December $31^{st}$ 2010.

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  • Guglielmo D'Amico & Ada Lika & Filippo Petroni, 2018. "Indexed Markov Chains for financial data: testing for the number of states of the index process," Papers 1802.01540, arXiv.org.
    • Handle: RePEc:arx:papers:1802.01540
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    References listed on IDEAS

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    1. Holzmann, Hajo & Schwaiger, Florian, 2016. "Testing for the number of states in hidden Markov models," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 318-330.
    2. Guglielmo D'Amico & Filippo Petroni, 2012. "Weighted-indexed semi-Markov models for modeling financial returns," Papers 1205.2551, arXiv.org, revised Jun 2012.
    3. 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.
    4. Bulla, Jan & Bulla, Ingo, 2006. "Stylized facts of financial time series and hidden semi-Markov models," Computational Statistics & Data Analysis, Elsevier, vol. 51(4), pages 2192-2209, December.
    5. Guglielmo D'Amico & Filippo Petroni, 2011. "A semi-Markov model with memory for price changes," Papers 1109.4259, arXiv.org, revised Dec 2011.
    6. Polansky, Alan M., 2007. "Detecting change-points in Markov chains," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6013-6026, August.
    7. Guglielmo D'Amico & Filippo Petroni, 2013. "Multivariate high-frequency financial data via semi-Markov processes," Papers 1305.0436, arXiv.org.
    8. Augustyniak, Maciej, 2014. "Maximum likelihood estimation of the Markov-switching GARCH model," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 61-75.
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