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Self-exciting jump processes with applications to energy markets


  • Heidar Eyjolfsson

    () (University of Iceland)

  • Dag Tjøstheim

    () (University of Bergen)


Abstract In this paper, we discuss a class of mean-reverting, and self-exciting continuous-time jump processes. We give a short overview, with references, of the development of such processes, discuss maximum likelihood estimation, and put them into context with processes that have been proposed recently. More specifically, we introduce a class of SDE-governed intensity processes with varying jump intensity. We study Markovian aspects of this process, and analyse its stability properties. Finally, we consider parameter estimation of our model class with daily quotes of UK electricity prices over a specific period.

Suggested Citation

  • Heidar Eyjolfsson & Dag Tjøstheim, 2018. "Self-exciting jump processes with applications to energy markets," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(2), pages 373-393, April.
  • Handle: RePEc:spr:aistmt:v:70:y:2018:i:2:d:10.1007_s10463-016-0591-8
    DOI: 10.1007/s10463-016-0591-8

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    References listed on IDEAS

    1. Fokianos, Konstantinos & Rahbek, Anders & Tjøstheim, Dag, 2009. "Poisson Autoregression," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1430-1439.
    2. Thibault Jaisson & Mathieu Rosenbaum, 2013. "Limit theorems for nearly unstable Hawkes processes," Papers 1310.2033,, revised Mar 2015.
    3. Bacry, E. & Delattre, S. & Hoffmann, M. & Muzy, J.F., 2013. "Some limit theorems for Hawkes processes and application to financial statistics," Stochastic Processes and their Applications, Elsevier, vol. 123(7), pages 2475-2499.
    4. repec:wsi:ijtafx:v:11:y:2008:i:05:n:s0219024908004907 is not listed on IDEAS
    5. Helyette Geman & A. Roncoroni, 2006. "Understanding the Fine Structure of Electricity Prices," Post-Print halshs-00144198, HAL.
    6. Jean-Luc Prigent, 2001. "Option Pricing with a General Marked Point Process," Mathematics of Operations Research, INFORMS, vol. 26(1), pages 50-66, February.
    7. Emmanuel Bacry & Jean-François Muzy, 2014. "Hawkes model for price and trades high-frequency dynamics," Quantitative Finance, Taylor & Francis Journals, vol. 14(7), pages 1147-1166, July.
    8. repec:dau:papers:123456789/1433 is not listed on IDEAS
    9. Hélyette Geman & Andrea Roncoroni, 2006. "Understanding the Fine Structure of Electricity Prices," The Journal of Business, University of Chicago Press, vol. 79(3), pages 1225-1262, May.
    10. Aït-Sahalia, Yacine & Cacho-Diaz, Julio & Laeven, Roger J.A., 2015. "Modeling financial contagion using mutually exciting jump processes," Journal of Financial Economics, Elsevier, vol. 117(3), pages 585-606.
    11. Konstantinos Fokianos & Dag Tjøstheim, 2012. "Nonlinear Poisson autoregression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(6), pages 1205-1225, December.
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