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Copula based multivariate semi-Markov models with applications in high-frequency finance

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  • D’Amico, Guglielmo
  • Petroni, Filippo

Abstract

We introduce a new multivariate model of multiple asset returns. Our model is based on weighted indexed semi-Markov chains to describe the single (marginals) asset returns, whereas the dependence structure among the considered assets is described by introducing copula functions. A real application of the proposed multivariate model is presented based on the evolution of 6 stocks from the Italian Stock Exchange. We provide empirical evidence that the model is able to correctly reproduce statistical regularities of multivariate real data such as the cross-correlation function, value-at-risk, marginal value-at-risk and conditional value-at-risk. The model is also used for volatility forecasting of each stock.

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  • D’Amico, Guglielmo & Petroni, Filippo, 2018. "Copula based multivariate semi-Markov models with applications in high-frequency finance," European Journal of Operational Research, Elsevier, vol. 267(2), pages 765-777.
    • Handle: RePEc:eee:ejores:v:267:y:2018:i:2:p:765-777
    DOI: 10.1016/j.ejor.2017.12.016
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    16. D’Amico, Guglielmo & Petroni, Filippo & Prattico, Flavio, 2014. "Wind speed and energy forecasting at different time scales: A nonparametric approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 406(C), pages 59-66.
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    Cited by:

    1. D’Amico, Guglielmo & Gismondi, Fulvio & Petroni, Filippo & Prattico, Flavio, 2019. "Stock market daily volatility and information measures of predictability," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 518(C), pages 22-29.
    2. Guglielmo D'Amico & Filippo Petroni & Philippe Regnault & Stefania Scocchera & Loriano Storchi, 2019. "A copula based Markov Reward approach to the credit spread in European Union," Papers 1902.00691, arXiv.org.
    3. D’Amico, Guglielmo & Petroni, Filippo, 2023. "ROCOF of higher order for semi-Markov processes," Applied Mathematics and Computation, Elsevier, vol. 441(C).
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    5. Guglielmo D’Amico & Fulvio Gismondi & Filippo Petroni, 2020. "Insurance Contracts for Hedging Wind Power Uncertainty," Mathematics, MDPI, vol. 8(8), pages 1-16, August.
    6. Guglielmo D’Amico & Giovanni Masala & Filippo Petroni & Robert Adam Sobolewski, 2020. "Managing Wind Power Generation via Indexed Semi-Markov Model and Copula," Energies, MDPI, vol. 13(16), pages 1-21, August.
    7. Mubenga-Tshitaka, Jean-Luc & Muteba Mwamba, John W. & Dikgang, Johane & Gelo, Dambala, 2021. "Risk spillover between climate variables and the agricultural commodity market in East Africa," EconStor Preprints 243160, ZBW - Leibniz Information Centre for Economics.
    8. Anatoliy Swishchuk, 2021. "Modelling of Limit Order Books by General Compound Hawkes Processes with Implementations," Methodology and Computing in Applied Probability, Springer, vol. 23(1), pages 399-428, March.
    9. Nelson Vadori & Anatoliy Swishchuk, 2019. "Inhomogeneous Random Evolutions: Limit Theorems and Financial Applications," Mathematics, MDPI, vol. 7(5), pages 1-62, May.
    10. Guglielmo D'Amico & Filippo Petroni, 2020. "A micro-to-macro approach to returns, volumes and waiting times," Papers 2007.06262, arXiv.org.
    11. Guglielmo D’Amico & Ada Lika & Filippo Petroni, 2019. "Change point dynamics for financial data: an indexed Markov chain approach," Annals of Finance, Springer, vol. 15(2), pages 247-266, June.
    12. Xiaohong Wang & Shixiang Li & Lizhi Wang & Yaning Sun & Zhongxing Wang, 2020. "Degradation and Dependence Analysis of a Lithium-Ion Battery Pack in the Unbalanced State," Energies, MDPI, vol. 13(22), pages 1-25, November.
    13. Manahov, Viktor & Urquhart, Andrew, 2021. "The efficiency of Bitcoin: A strongly typed genetic programming approach to smart electronic Bitcoin markets," International Review of Financial Analysis, Elsevier, vol. 73(C).

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