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A semi-Markov model for price returns


  • Guglielmo D'Amico
  • Filippo Petroni


We study the high frequency price dynamics of traded stocks by a model of returns using a semi-Markov approach. More precisely we assume that the intraday return are described by a discrete time homogeneous semi-Markov process and the overnight returns are modeled by a Markov chain. Based on this assumptions we derived the equations for the first passage time distribution and the volatility autocorreletion function. Theoretical results have been compared with empirical findings from real data. In particular we analyzed high frequency data from the Italian stock market from first of January 2007 until end of December 2010. The semi-Markov hypothesis is also tested through a nonparametric test of hypothesis.

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  • Guglielmo D'Amico & Filippo Petroni, 2011. "A semi-Markov model for price returns," Papers 1103.6143,
  • Handle: RePEc:arx:papers:1103.6143

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    References listed on IDEAS

    1. Ivan O. KITOV, 2008. "The Driving Force of Labor Force Participation in Developed Countries," Journal of Applied Economic Sciences, Spiru Haret University, Faculty of Financial Management and Accounting Craiova, vol. 3(3(5)_Fall), pages 203-222.
    2. Ivan O. KITOV & Oleg I. KITOV, 2010. "Dynamics Of Unemployment And Inflation In Western Europe: Solution By The 1- D Boundary Elements Method," Journal of Applied Economic Sciences, Spiru Haret University, Faculty of Financial Management and Accounting Craiova, vol. 5(2(12)/Sum), pages 94-113.
    3. Rudd, Jeremy & Whelan, Karl, 2005. "New tests of the new-Keynesian Phillips curve," Journal of Monetary Economics, Elsevier, vol. 52(6), pages 1167-1181, September.
    4. Benati, Luca, 2009. "Are 'intrinsic inflation persistence' models structural in the sense of Lucas (1976)?," Working Paper Series 1038, European Central Bank.
    5. Jeremy M. Piger & Robert H. Rasche, 2008. "Inflation: Do Expectations Trump the Gap?," International Journal of Central Banking, International Journal of Central Banking, vol. 4(4), pages 85-116, December.
    6. Doug Hostland, "undated". "CHANGES IN THE INFLATION PROCESS IN CANADA: Evidence and Implications," Staff Working Papers 95-5, Bank of Canada.
    7. Kitov, Ivan & Kitov, Oleg & Dolinskaya, Svetlana, 2007. "Inflation as a function of labor force change rate: cointegration test for the USA," MPRA Paper 2734, University Library of Munich, Germany.
    8. Carl Chiarella & Shenhuai Gao, 2002. "Type I Spurious Regression in Econometrics," Working Paper Series 114, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    9. Andrew Atkeson & Lee E. Ohanian, 2001. "Are Phillips curves useful for forecasting inflation?," Quarterly Review, Federal Reserve Bank of Minneapolis, issue Win, pages 2-11.
    10. James Rossiter, 2005. "Measurement Bias in the Canadian Consumer Price Index," Staff Working Papers 05-39, Bank of Canada.
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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,
    2. Guglielmo D'Amico & Filippo Petroni, 2012. "Weighted-indexed semi-Markov models for modeling financial returns," Papers 1205.2551,, revised Jun 2012.
    3. Filippo Petroni & Maurizio Serva, 2015. "Observability of Market Daily Volatility," Papers 1503.08032,
    4. 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,
    5. 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.
    6. repec:eee:reensy:v:144:y:2015:i:c:p:170-177 is not listed on IDEAS
    7. Guglielmo D'Amico & Filippo Petroni, 2013. "Multivariate high-frequency financial data via semi-Markov processes," Papers 1305.0436,
    8. Petroni, Filippo & Serva, Maurizio, 2016. "Observability of market daily volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 838-842.
    9. repec:eee:ejores:v:267:y:2018:i:2:p:765-777 is not listed on IDEAS
    10. G. D'Amico & F. Petroni & F. Prattico, 2013. "Semi-Markov Models in High Frequency Finance: A Review," Papers 1312.3894,

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