Kalman Filters, Hidden Markov Models, and Financial Trend Detection

Summary

This paper explains Kalman filtering through a simplified financial example, its mathematical formulation, and a probabilistic graphical-model representation. The graphical view connects Kalman filters with Hidden Markov Models and is used to motivate inference methods for extended Kalman filters. The discussion also considers how these models might represent changing dynamics in financial markets.

For parameter estimation, the authors present CMA-ES optimization as an alternative to the traditional expectation-maximization approach. They examine different assumptions about market dynamics and report tests of Kalman-filter and Hidden Markov Model applications. The paper further relates Kalman-based methods to trend-following technical systems and reports stronger performance for trend detection. The provided description gives no datasets, test design, benchmark details, or performance measures, so it does not establish how robust the reported advantage is across markets or conditions.

Key ideas

• A Kalman filter can be described both through its update equations and as a probabilistic graphical model.
• The graphical-model formulation links Kalman filtering to Hidden Markov Models.
• The paper develops inference procedures for extended Kalman filters using this connection.
• CMA-ES is presented as an alternative to expectation-maximization for parameter estimation.
• The authors test these approaches in financial markets and report an application to trend detection.

Tags

# Kalman filter demystified: from intuition to probabilistic graphical model to real case in financial markets


# Kalman filter demystified: from intuition to probabilistic graphical model to real case in financial markets









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.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.