Learning the Kalman Filter Parameters: an Expectation-Maximization Approach

Kriouar, Lotvi (2023) Learning the Kalman Filter Parameters: an Expectation-Maximization Approach. Master's Thesis / Essay, Applied Mathematics.

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Abstract

The Kalman filter has been proven to be an optimal hidden-state estimator of a (linear) state-space model with Gaussian noise terms. In this thesis, we consider the Kalman filter in mathematical depth and derive the forming equations. We derive backward corrections on the produced estimates, also known as Kalman smoothing. Fur- thermore, we review estimations of the parameters of the underlying state-space model through the expectation- maximization algorithm and consider asymptotic theory of the resulting maximum likelihood estimates. We apply the methodology to simulations and an example from literature, before moving on to forecasting of stock prices, which we model in a state-space sense. The main result of this thesis is the implementation of a more flexible EM algorithm for the Kalman filter, compared to existing libraries, in Python. We also observed that although the chaotic nature of stock prices, the Kalman filter provides accurate estimates of the underlying hidden state.

Item Type:	Thesis (Master's Thesis / Essay)
Supervisor name:	Grzegorczyk, M.A. and Krijnen, W.P.
Degree programme:	Applied Mathematics
Thesis type:	Master's Thesis / Essay
Language:	English
Date Deposited:	31 Jul 2023 09:17
Last Modified:	31 Jul 2023 09:17
URI:	https://fse.studenttheses.ub.rug.nl/id/eprint/30985

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