Kalman filter demystified: from intuition to probabilistic graphical model to real case in financial markets
Benhamou, Eric (2018), Kalman filter demystified: from intuition to probabilistic graphical model to real case in financial markets. https://basepub.dauphine.fr/handle/123456789/18923
TypeDocument de travail / Working paper
External document linkhttps://hal.archives-ouvertes.fr/hal-02012471
Series titlePreprint Lamsade
MetadataShow full item record
Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Abstract (EN)In this paper, we revisit the Kalman filter theory. After giving the intuition on a simplified financial markets example, we revisit the maths underlying it. We then show that Kalman filter can be presented in a very different fashion using graphical models. This enables us to establish the connection between Kalman filter and Hidden Markov Models. We then look at their application in financial markets and provide various intuitions in terms of their applicability for complex systems such as financial markets. Although this paper has been written more like a self contained work connecting Kalman filter to Hidden Markov Models and hence revisiting well known and establish results, it contains new results and brings additional contributions to the field. First, leveraging on the link between Kalman filter and HMM, it gives new algorithms for inference for extended Kalman filters. Second, it presents an alternative to the traditional estimation of parameters using EM algorithm thanks to the usage of CMA-ES optimization. Third, it examines the application of Kalman filter and its Hidden Markov models version to financial markets, providing various dynamics assumptions and tests. We conclude by connecting Kalman filter approach to trend following technical analysis system and showing their superior performances for trend following detection.
Subjects / Keywordskalman filter; hidden markov models; graphical model; CMA ES; trend detection; systematic trading
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