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Filters and smoothers for self-exciting Markov modulated counting processes

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  • Samuel N. Cohen
  • Robert J. Elliott

Abstract

We consider a self-exciting counting process, the parameters of which depend on a hidden finite-state Markov chain. We derive the optimal filter and smoother for the hidden chain based on observation of the jump process. This filter is in closed form and is finite dimensional. We demonstrate the performance of this filter both with simulated data, and by analysing the `flash crash' of 6th May 2010 in this framework.

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  • Samuel N. Cohen & Robert J. Elliott, 2013. "Filters and smoothers for self-exciting Markov modulated counting processes," Papers 1311.6257, arXiv.org.
    • Handle: RePEc:arx:papers:1311.6257
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    Cited by:

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    4. Maxime Morariu-Patrichi & Mikko S. Pakkanen, 2017. "Hybrid marked point processes: characterisation, existence and uniqueness," Papers 1707.06970, arXiv.org, revised Oct 2018.

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