Kalman Filter Demystified: From Intuition to Probabilistic Graphical Model to Real Case in Financial Markets

44 Pages Posted: 3 Dec 2018 Last revised: 15 Dec 2018

See all articles by Eric Benhamou

Eric Benhamou

A.I. Square Connect; LAMSADE- Paris Dauphine University

Date Written: November 29, 2018

Abstract

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.

Keywords: kalman filter, hidden markov models, graphical model, CMA ES, trend detection, systematic trading

JEL Classification: G11, G12, G13

Suggested Citation

Benhamou, Eric, Kalman Filter Demystified: From Intuition to Probabilistic Graphical Model to Real Case in Financial Markets (November 29, 2018). Available at SSRN: https://ssrn.com/abstract=3292762 or http://dx.doi.org/10.2139/ssrn.3292762

Eric Benhamou (Contact Author)

A.I. Square Connect ( email )

35 Boulevard d'Inkermann
Neuilly sur Seine, 92200
France

LAMSADE- Paris Dauphine University ( email )

Place du Marechal de Lattre de Tassigny
Pais, 75016
France

HOME PAGE: http://https://www.lamsade.dauphine.fr/

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